KILLED
proof of input_YdUnXYyqv1.trs
# AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished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), 0 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 1595 ms]
        (16) typed CpxTrs
    (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 ms]
    (18) TRS for Loop Detection
(19) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(20) CdtProblem
    (21) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CdtProblem
    (23) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxRelTRS
        (25) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTRS
        (27) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (28) CpxWeightedTrs
            (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (30) CpxTypedWeightedTrs
            (31) CompletionProof [UPPER BOUND(ID), 0 ms]
            (32) CpxTypedWeightedCompleteTrs
                (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (34) CpxRNTS
            (35) CompletionProof [UPPER BOUND(ID), 0 ms]
            (36) CpxTypedWeightedCompleteTrs
                (37) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (38) CpxTypedWeightedCompleteTrs
                (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (40) CpxRNTS
                (41) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms]
                (42) CpxRNTS
    (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
        (45) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (58) CdtProblem
        (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
        (86) CdtProblem
        (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
        (106) CdtProblem
        (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (114) CdtProblem
        (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms]
        (130) CdtProblem
        (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 265 ms]
        (146) CdtProblem
        (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 14 ms]
        (148) CdtProblem
        (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (154) CdtProblem
        (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
        (158) CdtProblem
        (159) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 256 ms]
        (160) CdtProblem
        (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 303 ms]
        (166) CdtProblem
        (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 274 ms]
        (170) CdtProblem
        (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 320 ms]
        (172) CdtProblem
(173) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(174) CpxWeightedTrs
    (175) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CpxTypedWeightedTrs
    (177) CompletionProof [UPPER BOUND(ID), 0 ms]
    (178) CpxTypedWeightedCompleteTrs
        (179) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CpxTypedWeightedCompleteTrs
        (181) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (182) CpxRNTS
        (183) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (184) CpxRNTS
    (185) CompletionProof [UPPER BOUND(ID), 0 ms]
    (186) CpxTypedWeightedCompleteTrs
        (187) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (188) CpxRNTS


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

(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:

   a__f(X) -> a__if(mark(X), c, f(true))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   mark(f(X)) -> a__f(mark(X))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
   a__f(X) -> f(X)
   a__if(X1, X2, X3) -> if(X1, X2, X3)

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:

   a__f(X) -> a__if(mark(X), c, f(true))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   mark(f(X)) -> a__f(mark(X))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
   a__f(X) -> f(X)
   a__if(X1, X2, X3) -> if(X1, X2, X3)

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:

   a__f(X) -> a__if(mark(X), c, f(true))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   mark(f(X)) -> a__f(mark(X))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
   a__f(X) -> f(X)
   a__if(X1, X2, X3) -> if(X1, X2, X3)

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:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11
S tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__F_1, A__IF_3, MARK_1

Compound Symbols:   c1_2, c2, c3_1, c4_1, c5, c6_2, c7_2, c8_2, c9, c10, c11


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

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

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


The TRS R consists of the following rules:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11

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

   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false

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

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

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


The TRS R consists of the following rules:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11

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

   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false

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

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

(12)
Obligation:
Innermost TRS:
Rules:
A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
A__F(z0) -> c2
A__IF(true, z0, z1) -> c3(MARK(z0))
A__IF(false, z0, z1) -> c4(MARK(z1))
A__IF(z0, z1, z2) -> c5
MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
MARK(c) -> c9
MARK(true) -> c10
MARK(false) -> c11
a__f(z0) -> a__if(mark(z0), c, f(true))
a__f(z0) -> f(z0)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
mark(f(z0)) -> a__f(mark(z0))
mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
mark(c) -> c
mark(true) -> true
mark(false) -> false

Types:
A__F :: c:true:f:false:if -> c1:c2
c1 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c1:c2
A__IF :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c3:c4:c5
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
MARK :: c:true:f:false:if -> c6:c7:c8:c9:c10:c11
c2 :: c1:c2
c3 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
false :: c:true:f:false:if
c4 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
c5 :: c3:c4:c5
c6 :: c1:c2 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
c7 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c8 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c9 :: c6:c7:c8:c9:c10:c11
c10 :: c6:c7:c8:c9:c10:c11
c11 :: c6:c7:c8:c9:c10:c11
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
hole_c1:c21_12 :: c1:c2
hole_c:true:f:false:if2_12 :: c:true:f:false:if
hole_c3:c4:c53_12 :: c3:c4:c5
hole_c6:c7:c8:c9:c10:c114_12 :: c6:c7:c8:c9:c10:c11
gen_c:true:f:false:if5_12 :: Nat -> c:true:f:false:if
gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__F, A__IF, mark, MARK, a__f, a__if

They will be analysed ascendingly in the following order:
A__F = A__IF
mark < A__F
A__F = MARK
A__IF = MARK
mark < MARK
mark = a__f
mark = a__if
a__f = a__if

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

(14)
Obligation:
Innermost TRS:
Rules:
A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
A__F(z0) -> c2
A__IF(true, z0, z1) -> c3(MARK(z0))
A__IF(false, z0, z1) -> c4(MARK(z1))
A__IF(z0, z1, z2) -> c5
MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
MARK(c) -> c9
MARK(true) -> c10
MARK(false) -> c11
a__f(z0) -> a__if(mark(z0), c, f(true))
a__f(z0) -> f(z0)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
mark(f(z0)) -> a__f(mark(z0))
mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
mark(c) -> c
mark(true) -> true
mark(false) -> false

Types:
A__F :: c:true:f:false:if -> c1:c2
c1 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c1:c2
A__IF :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c3:c4:c5
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
MARK :: c:true:f:false:if -> c6:c7:c8:c9:c10:c11
c2 :: c1:c2
c3 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
false :: c:true:f:false:if
c4 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
c5 :: c3:c4:c5
c6 :: c1:c2 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
c7 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c8 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c9 :: c6:c7:c8:c9:c10:c11
c10 :: c6:c7:c8:c9:c10:c11
c11 :: c6:c7:c8:c9:c10:c11
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
hole_c1:c21_12 :: c1:c2
hole_c:true:f:false:if2_12 :: c:true:f:false:if
hole_c3:c4:c53_12 :: c3:c4:c5
hole_c6:c7:c8:c9:c10:c114_12 :: c6:c7:c8:c9:c10:c11
gen_c:true:f:false:if5_12 :: Nat -> c:true:f:false:if
gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11


Generator Equations:
gen_c:true:f:false:if5_12(0) <=> c
gen_c:true:f:false:if5_12(+(x, 1)) <=> f(gen_c:true:f:false:if5_12(x))
gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9
gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c1(c3(c9), c9), gen_c6:c7:c8:c9:c10:c116_12(x))


The following defined symbols remain to be analysed:
a__f, A__F, A__IF, mark, MARK, a__if

They will be analysed ascendingly in the following order:
A__F = A__IF
mark < A__F
A__F = MARK
A__IF = MARK
mark < MARK
mark = a__f
mark = a__if
a__f = a__if

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_c:true:f:false:if5_12(+(1, n9997_12))) -> *7_12, rt in Omega(0)

Induction Base:
mark(gen_c:true:f:false:if5_12(+(1, 0)))

Induction Step:
mark(gen_c:true:f:false:if5_12(+(1, +(n9997_12, 1)))) ->_R^Omega(0)
a__f(mark(gen_c:true:f:false:if5_12(+(1, n9997_12)))) ->_IH
a__f(*7_12)

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

(16)
Obligation:
Innermost TRS:
Rules:
A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
A__F(z0) -> c2
A__IF(true, z0, z1) -> c3(MARK(z0))
A__IF(false, z0, z1) -> c4(MARK(z1))
A__IF(z0, z1, z2) -> c5
MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
MARK(c) -> c9
MARK(true) -> c10
MARK(false) -> c11
a__f(z0) -> a__if(mark(z0), c, f(true))
a__f(z0) -> f(z0)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
mark(f(z0)) -> a__f(mark(z0))
mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
mark(c) -> c
mark(true) -> true
mark(false) -> false

Types:
A__F :: c:true:f:false:if -> c1:c2
c1 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c1:c2
A__IF :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c3:c4:c5
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
MARK :: c:true:f:false:if -> c6:c7:c8:c9:c10:c11
c2 :: c1:c2
c3 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
false :: c:true:f:false:if
c4 :: c6:c7:c8:c9:c10:c11 -> c3:c4:c5
c5 :: c3:c4:c5
c6 :: c1:c2 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
c7 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c8 :: c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11
c9 :: c6:c7:c8:c9:c10:c11
c10 :: c6:c7:c8:c9:c10:c11
c11 :: c6:c7:c8:c9:c10:c11
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
hole_c1:c21_12 :: c1:c2
hole_c:true:f:false:if2_12 :: c:true:f:false:if
hole_c3:c4:c53_12 :: c3:c4:c5
hole_c6:c7:c8:c9:c10:c114_12 :: c6:c7:c8:c9:c10:c11
gen_c:true:f:false:if5_12 :: Nat -> c:true:f:false:if
gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11


Lemmas:
mark(gen_c:true:f:false:if5_12(+(1, n9997_12))) -> *7_12, rt in Omega(0)


Generator Equations:
gen_c:true:f:false:if5_12(0) <=> c
gen_c:true:f:false:if5_12(+(x, 1)) <=> f(gen_c:true:f:false:if5_12(x))
gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9
gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c1(c3(c9), c9), gen_c6:c7:c8:c9:c10:c116_12(x))


The following defined symbols remain to be analysed:
a__f, A__F, A__IF, MARK, a__if

They will be analysed ascendingly in the following order:
A__F = A__IF
mark < A__F
A__F = MARK
A__IF = MARK
mark < MARK
mark = a__f
mark = a__if
a__f = a__if

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

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

(18)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11

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

   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false

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

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

(20)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11
S tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__F(z0) -> c2
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__IF(z0, z1, z2) -> c5
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   MARK(c) -> c9
   MARK(true) -> c10
   MARK(false) -> c11
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__F_1, A__IF_3, MARK_1

Compound Symbols:   c1_2, c2, c3_1, c4_1, c5, c6_2, c7_2, c8_2, c9, c10, c11


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

(21) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   MARK(c) -> c9
   MARK(false) -> c11
   A__IF(z0, z1, z2) -> c5
   A__F(z0) -> c2
   MARK(true) -> c10

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

(22)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
S tuples:
   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__F_1, A__IF_3, MARK_1

Compound Symbols:   c1_2, c3_1, c4_1, c6_2, c7_2, c8_2


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

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

(24)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))

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

   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false

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

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

(26)
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:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0))
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false

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

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

(28)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0)) [1]
   A__IF(true, z0, z1) -> c3(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c4(MARK(z1)) [1]
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) [1]
   a__f(z0) -> a__if(mark(z0), c, f(true)) [0]
   a__f(z0) -> f(z0) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   mark(f(z0)) -> a__f(mark(z0)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2) [0]
   mark(c) -> c [0]
   mark(true) -> true [0]
   mark(false) -> false [0]

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

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

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

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0)) [1]
   A__IF(true, z0, z1) -> c3(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c4(MARK(z1)) [1]
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) [1]
   a__f(z0) -> a__if(mark(z0), c, f(true)) [0]
   a__f(z0) -> f(z0) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   mark(f(z0)) -> a__f(mark(z0)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2) [0]
   mark(c) -> c [0]
   mark(true) -> true [0]
   mark(false) -> false [0]

The TRS has the following type information:
A__F :: c:true:f:false:if -> c1
c1 :: c3:c4 -> c6:c7:c8 -> c1
A__IF :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c3:c4
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
MARK :: c:true:f:false:if -> c6:c7:c8
c3 :: c6:c7:c8 -> c3:c4
false :: c:true:f:false:if
c4 :: c6:c7:c8 -> c3:c4
c6 :: c1 -> c6:c7:c8 -> c6:c7:c8
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
c7 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
c8 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if

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

(31) 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:

   a__f(v0) -> null_a__f [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   mark(v0) -> null_mark [0]
   A__IF(v0, v1, v2) -> null_A__IF [0]
   MARK(v0) -> null_MARK [0]

And the following fresh constants:    null_a__f, null_a__if, null_mark, null_A__IF, null_MARK, const

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

(32)
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:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0)) [1]
   A__IF(true, z0, z1) -> c3(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c4(MARK(z1)) [1]
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) [1]
   a__f(z0) -> a__if(mark(z0), c, f(true)) [0]
   a__f(z0) -> f(z0) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   mark(f(z0)) -> a__f(mark(z0)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2) [0]
   mark(c) -> c [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__f(v0) -> null_a__f [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   mark(v0) -> null_mark [0]
   A__IF(v0, v1, v2) -> null_A__IF [0]
   MARK(v0) -> null_MARK [0]

The TRS has the following type information:
A__F :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c1
c1 :: c3:c4:null_A__IF -> c6:c7:c8:null_MARK -> c1
A__IF :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c3:c4:null_A__IF
mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c :: c:true:f:false:if:null_a__f:null_a__if:null_mark
f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
true :: c:true:f:false:if:null_a__f:null_a__if:null_mark
MARK :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c6:c7:c8:null_MARK
c3 :: c6:c7:c8:null_MARK -> c3:c4:null_A__IF
false :: c:true:f:false:if:null_a__f:null_a__if:null_mark
c4 :: c6:c7:c8:null_MARK -> c3:c4:null_A__IF
c6 :: c1 -> c6:c7:c8:null_MARK -> c6:c7:c8:null_MARK
if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c7 :: c3:c4:null_A__IF -> c6:c7:c8:null_MARK -> c6:c7:c8:null_MARK
c8 :: c3:c4:null_A__IF -> c6:c7:c8:null_MARK -> c6:c7:c8:null_MARK
a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_A__IF :: c3:c4:null_A__IF
null_MARK :: c6:c7:c8:null_MARK
const :: c1

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

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

   c => 0
   true => 2
   false => 1
   null_a__f => 0
   null_a__if => 0
   null_mark => 0
   null_A__IF => 0
   null_MARK => 0
   const => 0

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

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

   A__F(z) -{ 1 }-> 1 + A__IF(mark(z0), 0, 1 + 2) + MARK(z0) :|: z = z0, z0 >= 0
   A__IF(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   a__f(z) -{ 0 }-> a__if(mark(z0), 0, 1 + 2) :|: z = z0, z0 >= 0
   a__f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__f(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(mark(z0), mark(z1), z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__f(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

Only complete derivations are relevant for the runtime complexity.

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

(35) 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:

   A__F_1
   A__IF_3
   MARK_1

(c) The following functions are completely defined:

   a__f_1
   a__if_3
   mark_1

Due to the following rules being added:

   a__f(v0) -> null_a__f [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__f, null_a__if, null_mark, const, const1, const2

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

(36)
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:

   A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0)) [1]
   A__IF(true, z0, z1) -> c3(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c4(MARK(z1)) [1]
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) [1]
   a__f(z0) -> a__if(mark(z0), c, f(true)) [0]
   a__f(z0) -> f(z0) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   mark(f(z0)) -> a__f(mark(z0)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2) [0]
   mark(c) -> c [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__f(v0) -> null_a__f [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__F :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c1
c1 :: c3:c4 -> c6:c7:c8 -> c1
A__IF :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c3:c4
mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c :: c:true:f:false:if:null_a__f:null_a__if:null_mark
f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
true :: c:true:f:false:if:null_a__f:null_a__if:null_mark
MARK :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c6:c7:c8
c3 :: c6:c7:c8 -> c3:c4
false :: c:true:f:false:if:null_a__f:null_a__if:null_mark
c4 :: c6:c7:c8 -> c3:c4
c6 :: c1 -> c6:c7:c8 -> c6:c7:c8
if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c7 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
c8 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark
const :: c1
const1 :: c3:c4
const2 :: c6:c7:c8

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

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

(38)
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:

   A__F(f(z0')) -> c1(A__IF(a__f(mark(z0')), c, f(true)), MARK(f(z0'))) [1]
   A__F(if(z0'', z1', z2')) -> c1(A__IF(a__if(mark(z0''), mark(z1'), z2'), c, f(true)), MARK(if(z0'', z1', z2'))) [1]
   A__F(c) -> c1(A__IF(c, c, f(true)), MARK(c)) [1]
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true)) [1]
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false)) [1]
   A__F(z0) -> c1(A__IF(null_mark, c, f(true)), MARK(z0)) [1]
   A__IF(true, z0, z1) -> c3(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c4(MARK(z1)) [1]
   MARK(f(f(z01))) -> c6(A__F(a__f(mark(z01))), MARK(f(z01))) [1]
   MARK(f(if(z02, z1'', z2''))) -> c6(A__F(a__if(mark(z02), mark(z1''), z2'')), MARK(if(z02, z1'', z2''))) [1]
   MARK(f(c)) -> c6(A__F(c), MARK(c)) [1]
   MARK(f(true)) -> c6(A__F(true), MARK(true)) [1]
   MARK(f(false)) -> c6(A__F(false), MARK(false)) [1]
   MARK(f(z0)) -> c6(A__F(null_mark), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) [1]
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) [1]
   a__f(f(z031)) -> a__if(a__f(mark(z031)), c, f(true)) [0]
   a__f(if(z032, z115, z215)) -> a__if(a__if(mark(z032), mark(z115), z215), c, f(true)) [0]
   a__f(c) -> a__if(c, c, f(true)) [0]
   a__f(true) -> a__if(true, c, f(true)) [0]
   a__f(false) -> a__if(false, c, f(true)) [0]
   a__f(z0) -> a__if(null_mark, c, f(true)) [0]
   a__f(z0) -> f(z0) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   mark(f(f(z033))) -> a__f(a__f(mark(z033))) [0]
   mark(f(if(z034, z116, z216))) -> a__f(a__if(mark(z034), mark(z116), z216)) [0]
   mark(f(c)) -> a__f(c) [0]
   mark(f(true)) -> a__f(true) [0]
   mark(f(false)) -> a__f(false) [0]
   mark(f(z0)) -> a__f(null_mark) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2) [0]
   mark(c) -> c [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__f(v0) -> null_a__f [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__F :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c1
c1 :: c3:c4 -> c6:c7:c8 -> c1
A__IF :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c3:c4
mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c :: c:true:f:false:if:null_a__f:null_a__if:null_mark
f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
true :: c:true:f:false:if:null_a__f:null_a__if:null_mark
MARK :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c6:c7:c8
c3 :: c6:c7:c8 -> c3:c4
false :: c:true:f:false:if:null_a__f:null_a__if:null_mark
c4 :: c6:c7:c8 -> c3:c4
c6 :: c1 -> c6:c7:c8 -> c6:c7:c8
if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
c7 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
c8 :: c3:c4 -> c6:c7:c8 -> c6:c7:c8
a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark -> c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__f :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_a__if :: c:true:f:false:if:null_a__f:null_a__if:null_mark
null_mark :: c:true:f:false:if:null_a__f:null_a__if:null_mark
const :: c1
const1 :: c3:c4
const2 :: c6:c7:c8

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

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

   c => 0
   true => 2
   false => 1
   null_a__f => 0
   null_a__if => 0
   null_mark => 0
   const => 0
   const1 => 0
   const2 => 0

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

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

   A__F(z) -{ 1 }-> 1 + A__IF(a__if(mark(z0''), mark(z1'), z2'), 0, 1 + 2) + MARK(1 + z0'' + z1' + z2') :|: z = 1 + z0'' + z1' + z2', z1' >= 0, z2' >= 0, z0'' >= 0
   A__F(z) -{ 1 }-> 1 + A__IF(a__f(mark(z0')), 0, 1 + 2) + MARK(1 + z0') :|: z0' >= 0, z = 1 + z0'
   A__F(z) -{ 1 }-> 1 + A__IF(2, 0, 1 + 2) + MARK(2) :|: z = 2
   A__F(z) -{ 1 }-> 1 + A__IF(1, 0, 1 + 2) + MARK(1) :|: z = 1
   A__F(z) -{ 1 }-> 1 + A__IF(0, 0, 1 + 2) + MARK(z0) :|: z = z0, z0 >= 0
   A__F(z) -{ 1 }-> 1 + A__IF(0, 0, 1 + 2) + MARK(0) :|: z = 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(a__if(mark(z02), mark(z1''), z2'')) + MARK(1 + z02 + z1'' + z2'') :|: z = 1 + (1 + z02 + z1'' + z2''), z02 >= 0, z2'' >= 0, z1'' >= 0
   MARK(z) -{ 1 }-> 1 + A__F(a__f(mark(z01))) + MARK(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(2) + MARK(2) :|: z = 1 + 2
   MARK(z) -{ 1 }-> 1 + A__F(1) + MARK(1) :|: z = 1 + 1
   MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(0) :|: z = 1 + 0
   a__f(z) -{ 0 }-> a__if(a__if(mark(z032), mark(z115), z215), 0, 1 + 2) :|: z = 1 + z032 + z115 + z215, z032 >= 0, z115 >= 0, z215 >= 0
   a__f(z) -{ 0 }-> a__if(a__f(mark(z031)), 0, 1 + 2) :|: z031 >= 0, z = 1 + z031
   a__f(z) -{ 0 }-> a__if(2, 0, 1 + 2) :|: z = 2
   a__f(z) -{ 0 }-> a__if(1, 0, 1 + 2) :|: z = 1
   a__f(z) -{ 0 }-> a__if(0, 0, 1 + 2) :|: z = 0
   a__f(z) -{ 0 }-> a__if(0, 0, 1 + 2) :|: z = z0, z0 >= 0
   a__f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__f(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(mark(z0), mark(z1), z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__f(a__if(mark(z034), mark(z116), z216)) :|: z = 1 + (1 + z034 + z116 + z216), z216 >= 0, z034 >= 0, z116 >= 0
   mark(z) -{ 0 }-> a__f(a__f(mark(z033))) :|: z033 >= 0, z = 1 + (1 + z033)
   mark(z) -{ 0 }-> a__f(2) :|: z = 1 + 2
   mark(z) -{ 0 }-> a__f(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__f(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__f(0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

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

   A__F(z) -{ 1 }-> 1 + A__IF(a__if(mark(z0''), mark(z1'), z2'), 0, 1 + 2) + MARK(1 + z0'' + z1' + z2') :|: z = 1 + z0'' + z1' + z2', z1' >= 0, z2' >= 0, z0'' >= 0
   A__F(z) -{ 1 }-> 1 + A__IF(a__f(mark(z - 1)), 0, 1 + 2) + MARK(1 + (z - 1)) :|: z - 1 >= 0
   A__F(z) -{ 1 }-> 1 + A__IF(2, 0, 1 + 2) + MARK(2) :|: z = 2
   A__F(z) -{ 1 }-> 1 + A__IF(1, 0, 1 + 2) + MARK(1) :|: z = 1
   A__F(z) -{ 1 }-> 1 + A__IF(0, 0, 1 + 2) + MARK(z) :|: z >= 0
   A__F(z) -{ 1 }-> 1 + A__IF(0, 0, 1 + 2) + MARK(0) :|: z = 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z') :|: z = 2, z'' >= 0, z' >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), mark(z1), z2) + MARK(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(a__if(mark(z02), mark(z1''), z2'')) + MARK(1 + z02 + z1'' + z2'') :|: z = 1 + (1 + z02 + z1'' + z2''), z02 >= 0, z2'' >= 0, z1'' >= 0
   MARK(z) -{ 1 }-> 1 + A__F(a__f(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0
   MARK(z) -{ 1 }-> 1 + A__F(2) + MARK(2) :|: z = 1 + 2
   MARK(z) -{ 1 }-> 1 + A__F(1) + MARK(1) :|: z = 1 + 1
   MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(0) :|: z = 1 + 0
   MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(z - 1) :|: z - 1 >= 0
   a__f(z) -{ 0 }-> a__if(a__if(mark(z032), mark(z115), z215), 0, 1 + 2) :|: z = 1 + z032 + z115 + z215, z032 >= 0, z115 >= 0, z215 >= 0
   a__f(z) -{ 0 }-> a__if(a__f(mark(z - 1)), 0, 1 + 2) :|: z - 1 >= 0
   a__f(z) -{ 0 }-> a__if(2, 0, 1 + 2) :|: z = 2
   a__f(z) -{ 0 }-> a__if(1, 0, 1 + 2) :|: z = 1
   a__f(z) -{ 0 }-> a__if(0, 0, 1 + 2) :|: z = 0
   a__f(z) -{ 0 }-> a__if(0, 0, 1 + 2) :|: z >= 0
   a__f(z) -{ 0 }-> 0 :|: z >= 0
   a__f(z) -{ 0 }-> 1 + z :|: z >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0
   a__if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   mark(z) -{ 0 }-> a__if(mark(z0), mark(z1), z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__f(a__if(mark(z034), mark(z116), z216)) :|: z = 1 + (1 + z034 + z116 + z216), z216 >= 0, z034 >= 0, z116 >= 0
   mark(z) -{ 0 }-> a__f(a__f(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__f(2) :|: z = 1 + 2
   mark(z) -{ 0 }-> a__f(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__f(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__f(0) :|: z - 1 >= 0
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: z >= 0


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

(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__F(z0) -> c1(A__IF(mark(z0), c, f(true)), MARK(z0)) by 
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(c) -> c1(A__IF(c, c, f(true)), MARK(c))
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true))
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(c) -> c1(A__IF(c, c, f(true)), MARK(c))
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true))
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(c) -> c1(A__IF(c, c, f(true)), MARK(c))
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true))
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c8_2, c1_2


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

(45) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__F(c) -> c1(A__IF(c, c, f(true)), MARK(c))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true))
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)), MARK(true))
   A__F(false) -> c1(A__IF(false, c, f(true)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c8_2, c1_2


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

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c6_2, c7_2, c8_2, c1_2, c1_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(f(z0)) -> c6(A__F(mark(z0)), MARK(z0)) by 
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(c)) -> c6(A__F(c), MARK(c))
   MARK(f(true)) -> c6(A__F(true), MARK(true))
   MARK(f(false)) -> c6(A__F(false), MARK(false))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(c)) -> c6(A__F(c), MARK(c))
   MARK(f(true)) -> c6(A__F(true), MARK(true))
   MARK(f(false)) -> c6(A__F(false), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(c)) -> c6(A__F(c), MARK(c))
   MARK(f(true)) -> c6(A__F(true), MARK(true))
   MARK(f(false)) -> c6(A__F(false), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c7_2, c8_2, c1_2, c1_1, c6_2


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

(51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(f(c)) -> c6(A__F(c), MARK(c))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true), MARK(true))
   MARK(f(false)) -> c6(A__F(false), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true), MARK(true))
   MARK(f(false)) -> c6(A__F(false), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c7_2, c8_2, c1_2, c1_1, c6_2


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

(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c7_2, c8_2, c1_2, c1_1, c6_2, c6_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(z0, z1, z2)) -> c7(A__IF(mark(z0), mark(z1), z2), MARK(z0)) by 
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, x1, x2)) -> c7(A__IF(c, mark(x1), x2), MARK(c))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2), MARK(true))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2), MARK(false))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, x1, x2)) -> c7(A__IF(c, mark(x1), x2), MARK(c))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2), MARK(true))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, x1, x2)) -> c7(A__IF(c, mark(x1), x2), MARK(c))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2), MARK(true))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c8_2, c1_2, c1_1, c6_2, c6_1, c7_2


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, x1, x2)) -> c7(A__IF(c, mark(x1), x2), MARK(c))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2), MARK(true))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2), MARK(true))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c8_2, c1_2, c1_1, c6_2, c6_1, c7_2


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

(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, MARK_1, A__F_1

Compound Symbols:   c3_1, c4_1, c8_2, c1_2, c1_1, c6_2, c6_1, c7_2, c7_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(z0, z1, z2)) -> c8(A__IF(mark(z0), mark(z1), z2), MARK(z1)) by 
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2), MARK(c))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2), MARK(true))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2), MARK(false))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(A__IF(c, mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2), MARK(c))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2), MARK(true))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2), MARK(false))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(A__IF(c, mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2), MARK(c))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2), MARK(true))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2), MARK(false))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(A__IF(c, mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_2, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2


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

(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0)))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_2, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__F(f(z0)) -> c1(A__IF(a__f(mark(z0)), c, f(true)), MARK(f(z0))) by 
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(x0)) -> c1(A__IF(f(mark(x0)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)), MARK(f(c)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(x0)) -> c1(A__IF(f(mark(x0)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)), MARK(f(c)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(x0)) -> c1(A__IF(f(mark(x0)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)), MARK(f(c)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_2, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1


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

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2)))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_2, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__F(if(z0, z1, z2)) -> c1(A__IF(a__if(mark(z0), mark(z1), z2), c, f(true)), MARK(if(z0, z1, z2))) by 
   A__F(if(x0, x1, z2)) -> c1(A__IF(if(mark(x0), mark(x1), z2), c, f(true)), MARK(if(x0, x1, z2)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, x1, z2)) -> c1(A__IF(if(mark(x0), mark(x1), z2), c, f(true)), MARK(if(x0, x1, z2)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, x1, z2)) -> c1(A__IF(if(mark(x0), mark(x1), z2), c, f(true)), MARK(if(x0, x1, z2)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2


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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(f(f(z0))) -> c6(A__F(a__f(mark(z0))), MARK(f(z0))) by 
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)), MARK(f(c)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)), MARK(f(c)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)), MARK(f(c)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2


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

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(f(if(z0, z1, z2))) -> c6(A__F(a__if(mark(z0), mark(z1), z2)), MARK(if(z0, z1, z2))) by 
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, f(z0), x2)) -> c7(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(x0)) by 
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, f(x1), x2)) -> c7(A__IF(c, a__f(mark(x1)), x2), MARK(c))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2), MARK(true))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2), MARK(false))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, f(x1), x2)) -> c7(A__IF(c, a__f(mark(x1)), x2), MARK(c))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2), MARK(true))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(c, f(x1), x2)) -> c7(A__IF(c, a__f(mark(x1)), x2), MARK(c))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2), MARK(true))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, f(x1), x2)) -> c7(A__IF(c, a__f(mark(x1)), x2), MARK(c))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2), MARK(true))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2), MARK(true))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, if(z0, z1, z2), x2)) -> c7(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(x0)) by 
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c7(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(c))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(true))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(false))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c7(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(c))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(true))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c7(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(c))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(true))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, if(x1, x2, x3), x4)) -> c7(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(c))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(true))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(true))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, c, x2)) -> c7(A__IF(mark(x0), c, x2), MARK(x0)) by 
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, c, x1)) -> c7(A__IF(c, c, x1), MARK(c))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1), MARK(true))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1), MARK(false))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, c, x1)) -> c7(A__IF(c, c, x1), MARK(c))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1), MARK(true))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, c, x1)) -> c7(A__IF(c, c, x1), MARK(c))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1), MARK(true))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, c, x1)) -> c7(A__IF(c, c, x1), MARK(c))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1), MARK(true))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1), MARK(true))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, true, x2)) -> c7(A__IF(mark(x0), true, x2), MARK(x0)) by 
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, true, x1)) -> c7(A__IF(c, true, x1), MARK(c))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1), MARK(true))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1), MARK(false))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, true, x1)) -> c7(A__IF(c, true, x1), MARK(c))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1), MARK(true))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, true, x1)) -> c7(A__IF(c, true, x1), MARK(c))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1), MARK(true))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, true, x1)) -> c7(A__IF(c, true, x1), MARK(c))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1), MARK(true))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1), MARK(true))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, false, x2)) -> c7(A__IF(mark(x0), false, x2), MARK(x0)) by 
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, false, x1)) -> c7(A__IF(c, false, x1), MARK(c))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1), MARK(true))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1), MARK(false))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, false, x1)) -> c7(A__IF(c, false, x1), MARK(c))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1), MARK(true))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(c, false, x1)) -> c7(A__IF(c, false, x1), MARK(c))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1), MARK(true))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, false, x1)) -> c7(A__IF(c, false, x1), MARK(c))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1), MARK(true))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1), MARK(false))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1), MARK(true))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(f(z0), x1, x2)) -> c7(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(f(z0))) by 
   MARK(if(f(x0), f(z0), x2)) -> c7(A__IF(a__f(mark(x0)), a__f(mark(z0)), x2), MARK(f(x0)))
   MARK(if(f(x0), if(z0, z1, z2), x2)) -> c7(A__IF(a__f(mark(x0)), a__if(mark(z0), mark(z1), z2), x2), MARK(f(x0)))
   MARK(if(f(x0), c, x2)) -> c7(A__IF(a__f(mark(x0)), c, x2), MARK(f(x0)))
   MARK(if(f(x0), true, x2)) -> c7(A__IF(a__f(mark(x0)), true, x2), MARK(f(x0)))
   MARK(if(f(x0), false, x2)) -> c7(A__IF(a__f(mark(x0)), false, x2), MARK(f(x0)))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(f(mark(x0)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2), MARK(f(c)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(f(mark(x0)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2), MARK(f(c)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(f(mark(x0)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2), MARK(f(c)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_2, c7_1, c8_2, c8_1, c1_2, c6_2


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(if(z0, z1, z2), x1, x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(if(z0, z1, z2))) by 
   MARK(if(if(x0, x1, x2), f(z0), x4)) -> c7(A__IF(a__if(mark(x0), mark(x1), x2), a__f(mark(z0)), x4), MARK(if(x0, x1, x2)))
   MARK(if(if(x0, x1, x2), if(z0, z1, z2), x4)) -> c7(A__IF(a__if(mark(x0), mark(x1), x2), a__if(mark(z0), mark(z1), z2), x4), MARK(if(x0, x1, x2)))
   MARK(if(if(x0, x1, x2), c, x4)) -> c7(A__IF(a__if(mark(x0), mark(x1), x2), c, x4), MARK(if(x0, x1, x2)))
   MARK(if(if(x0, x1, x2), true, x4)) -> c7(A__IF(a__if(mark(x0), mark(x1), x2), true, x4), MARK(if(x0, x1, x2)))
   MARK(if(if(x0, x1, x2), false, x4)) -> c7(A__IF(a__if(mark(x0), mark(x1), x2), false, x4), MARK(if(x0, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(if(x0, x1, z2)))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(if(x0, x1, z2)))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(if(x0, x1, z2)))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, f(z0), x2)) -> c8(A__IF(mark(x0), a__f(mark(z0)), x2), MARK(f(z0))) by 
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2), MARK(f(c)))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(c, f(x1), x2)) -> c8(A__IF(c, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2), MARK(f(c)))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(c, f(x1), x2)) -> c8(A__IF(c, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2), MARK(f(c)))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(c, f(x1), x2)) -> c8(A__IF(c, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, if(z0, z1, z2), x2)) -> c8(A__IF(mark(x0), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2))) by 
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(A__IF(c, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(f(z0), x1, x2)) -> c8(A__IF(a__f(mark(z0)), mark(x1), x2), MARK(x1)) by 
   MARK(if(f(x0), f(z0), x2)) -> c8(A__IF(a__f(mark(x0)), a__f(mark(z0)), x2), MARK(f(z0)))
   MARK(if(f(x0), if(z0, z1, z2), x2)) -> c8(A__IF(a__f(mark(x0)), a__if(mark(z0), mark(z1), z2), x2), MARK(if(z0, z1, z2)))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2), MARK(c))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2), MARK(true))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2), MARK(false))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(f(mark(x0)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2), MARK(c))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2), MARK(true))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2), MARK(false))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(f(mark(x0)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2), MARK(c))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2), MARK(true))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2), MARK(false))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(f(mark(x0)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(if(z0, z1, z2), x1, x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), mark(x1), x2), MARK(x1)) by 
   MARK(if(if(x0, x1, x2), f(z0), x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), a__f(mark(z0)), x4), MARK(f(z0)))
   MARK(if(if(x0, x1, x2), if(z0, z1, z2), x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), a__if(mark(z0), mark(z1), z2), x4), MARK(if(z0, z1, z2)))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4), MARK(c))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4), MARK(true))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4), MARK(false))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4), MARK(c))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4), MARK(true))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4), MARK(false))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4), MARK(c))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4), MARK(true))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4), MARK(false))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(A__IF(if(mark(x0), mark(x1), z2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, c, x2)) -> c8(A__IF(mark(x0), c, x2)) by 
   MARK(if(f(z0), c, x1)) -> c8(A__IF(a__f(mark(z0)), c, x1))
   MARK(if(if(z0, z1, z2), c, x1)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), c, x1))
   MARK(if(c, c, x1)) -> c8(A__IF(c, c, x1))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(c, c, x1)) -> c8(A__IF(c, c, x1))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(c, c, x1)) -> c8(A__IF(c, c, x1))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, c, x1)) -> c8(A__IF(c, c, x1))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
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   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, true, x2)) -> c8(A__IF(mark(x0), true, x2)) by 
   MARK(if(f(z0), true, x1)) -> c8(A__IF(a__f(mark(z0)), true, x1))
   MARK(if(if(z0, z1, z2), true, x1)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), true, x1))
   MARK(if(c, true, x1)) -> c8(A__IF(c, true, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(c, true, x1)) -> c8(A__IF(c, true, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(c, true, x1)) -> c8(A__IF(c, true, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, true, x1)) -> c8(A__IF(c, true, x1))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(x0, false, x2)) -> c8(A__IF(mark(x0), false, x2)) by 
   MARK(if(f(z0), false, x1)) -> c8(A__IF(a__f(mark(z0)), false, x1))
   MARK(if(if(z0, z1, z2), false, x1)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), false, x1))
   MARK(if(c, false, x1)) -> c8(A__IF(c, false, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(c, false, x1)) -> c8(A__IF(c, false, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(c, false, x1)) -> c8(A__IF(c, false, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(c, false, x1)) -> c8(A__IF(c, false, x1))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
S tuples:
   A__IF(true, z0, z1) -> c3(MARK(z0))
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c3_1, c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2


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

(145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace A__IF(true, z0, z1) -> c3(MARK(z0)) by 
   A__IF(true, f(true), z1) -> c3(MARK(f(true)))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(true), z1) -> c3(MARK(f(true)))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
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   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(true), z1) -> c3(MARK(f(true)))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing nodes:
   A__IF(true, f(true), z1) -> c3(MARK(f(true)))
   MARK(f(true)) -> c6(A__F(true))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   A__F(true) -> c1(A__IF(true, c, f(true)))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
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   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
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   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
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   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
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   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
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   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
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   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
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   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
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   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
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   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
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   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
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   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
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   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
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   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
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   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
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   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
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   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
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   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
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   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
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   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)), MARK(f(true)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(true))) -> c6(A__F(a__f(true)), MARK(f(true)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2), MARK(f(true)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2), MARK(f(true)))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
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   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
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   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
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   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
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   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
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   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
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   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
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   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(true, x1, x2)) -> c7(A__IF(true, mark(x1), x2)) by 
   MARK(if(true, f(z0), x1)) -> c7(A__IF(true, a__f(mark(z0)), x1))
   MARK(if(true, if(z0, z1, z2), x1)) -> c7(A__IF(true, a__if(mark(z0), mark(z1), z2), x1))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
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   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(if(true, c, x1)) -> c7(A__IF(true, c, x1))
   MARK(if(true, true, x1)) -> c7(A__IF(true, true, x1))
   MARK(if(true, false, x1)) -> c7(A__IF(true, false, x1))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
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   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(true, x1, x2)) -> c8(A__IF(true, mark(x1), x2), MARK(x1)) by 
   MARK(if(true, f(z0), x1)) -> c8(A__IF(true, a__f(mark(z0)), x1), MARK(f(z0)))
   MARK(if(true, if(z0, z1, z2), x1)) -> c8(A__IF(true, a__if(mark(z0), mark(z1), z2), x1), MARK(if(z0, z1, z2)))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1), MARK(c))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1), MARK(true))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1), MARK(false))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
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   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1), MARK(c))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1), MARK(true))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1), MARK(false))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1), MARK(c))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1), MARK(true))
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1), MARK(false))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   MARK(if(true, false, x1)) -> c8(A__IF(true, false, x1), MARK(false))
   A__IF(true, if(true, c, y0), z1) -> c3(MARK(if(true, c, y0)))
   MARK(if(true, true, x1)) -> c8(A__IF(true, true, x1), MARK(true))
   MARK(if(true, c, x1)) -> c8(A__IF(true, c, x1), MARK(c))
   A__IF(true, if(true, true, y0), z1) -> c3(MARK(if(true, true, y0)))
   A__IF(true, if(true, false, y0), z1) -> c3(MARK(if(true, false, y0)))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
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   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
S tuples:
   A__IF(false, z0, z1) -> c4(MARK(z1))
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__IF_3, A__F_1, MARK_1

Compound Symbols:   c4_1, c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1


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

(159) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace A__IF(false, z0, z1) -> c4(MARK(z1)) by 
   A__IF(false, z0, f(false)) -> c4(MARK(f(false)))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, f(false)) -> c4(MARK(f(false)))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
S tuples:
   A__F(false) -> c1(A__IF(false, c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, f(false)) -> c4(MARK(f(false)))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   A__F_1, MARK_1, A__IF_3

Compound Symbols:   c1_1, c6_1, c7_1, c8_2, c8_1, c1_2, c6_2, c7_2, c3_1, c4_1


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

(161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   A__IF(false, z0, f(false)) -> c4(MARK(f(false)))
   A__F(f(false)) -> c1(A__IF(a__f(false), c, f(true)), MARK(f(false)))
   A__F(f(true)) -> c1(A__IF(a__f(true), c, f(true)))
   MARK(f(false)) -> c6(A__F(false))
   A__IF(true, f(false), z1) -> c3(MARK(f(false)))
   A__F(f(c)) -> c1(A__IF(a__f(c), c, f(true)))
   A__F(false) -> c1(A__IF(false, c, f(true)))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(A__IF(a__if(mark(mark(x0)), c, f(true)), c, f(true)), MARK(f(x0)))
   A__F(f(f(z0))) -> c1(A__IF(a__f(a__f(mark(z0))), c, f(true)), MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), c, f(true)), MARK(f(if(z0, z1, z2))))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, f(z0), x2)) -> c1(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), c, f(true)), MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), c, f(true)), MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(A__IF(a__if(mark(x0), c, x2), c, f(true)), MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(A__IF(a__if(mark(x0), true, x2), c, f(true)), MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(A__IF(a__if(mark(x0), false, x2), c, f(true)), MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), c, f(true)), MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), c, f(true)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(A__IF(a__if(c, mark(x1), x2), c, f(true)), MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(A__IF(a__if(true, mark(x1), x2), c, f(true)), MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(A__IF(a__if(false, mark(x1), x2), c, f(true)), MARK(if(false, x1, x2)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(false))) -> c6(A__F(a__f(false)), MARK(f(false)))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2), MARK(f(false)))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2), MARK(f(false)))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c8_1, c1_2, c1_1, c6_2, c6_1, c7_2, c3_1, c4_1


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

(163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 16 trailing tuple parts
----------------------------------------

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(if(c, x1, x2)) -> c8(MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c8_1, c1_1, c6_2, c6_1, c7_2, c3_1, c4_1


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

(165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MARK(if(c, x1, x2)) -> c8(MARK(x1)) by 
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
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   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
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   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
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   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
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   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
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   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
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   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
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   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
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   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
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   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c1_1, c6_2, c6_1, c7_2, c8_1, c3_1, c4_1


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

(167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace A__F(f(x0)) -> c1(MARK(f(x0))) by 
   A__F(f(f(y0))) -> c1(MARK(f(f(y0))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, y1, y2))) -> c1(MARK(f(if(y0, y1, y2))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c1_1, c6_2, c6_1, c7_2, c8_1, c3_1, c4_1


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

(169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace A__F(if(x0, x1, z2)) -> c1(MARK(if(x0, x1, z2))) by 
   A__F(if(false, z1, z2)) -> c1(MARK(if(false, z1, z2)))
   A__F(if(z0, f(y1), z2)) -> c1(MARK(if(z0, f(y1), z2)))
   A__F(if(z0, f(f(y1)), z2)) -> c1(MARK(if(z0, f(f(y1)), z2)))
   A__F(if(z0, f(if(y1, y2, y3)), z2)) -> c1(MARK(if(z0, f(if(y1, y2, y3)), z2)))
   A__F(if(z0, f(c), z2)) -> c1(MARK(if(z0, f(c), z2)))
   A__F(if(z0, f(true), z2)) -> c1(MARK(if(z0, f(true), z2)))
   A__F(if(z0, f(false), z2)) -> c1(MARK(if(z0, f(false), z2)))
   A__F(if(f(y0), f(y1), z2)) -> c1(MARK(if(f(y0), f(y1), z2)))
   A__F(if(if(y0, y1, y2), f(y3), z2)) -> c1(MARK(if(if(y0, y1, y2), f(y3), z2)))
   A__F(if(true, f(y0), z2)) -> c1(MARK(if(true, f(y0), z2)))
   A__F(if(false, f(y0), z2)) -> c1(MARK(if(false, f(y0), z2)))
   A__F(if(z0, if(y1, y2, y3), z2)) -> c1(MARK(if(z0, if(y1, y2, y3), z2)))
   A__F(if(z0, if(y1, f(y2), y3), z2)) -> c1(MARK(if(z0, if(y1, f(y2), y3), z2)))
   A__F(if(z0, if(y1, if(y2, y3, y4), y5), z2)) -> c1(MARK(if(z0, if(y1, if(y2, y3, y4), y5), z2)))
   A__F(if(z0, if(y1, c, y2), z2)) -> c1(MARK(if(z0, if(y1, c, y2), z2)))
   A__F(if(z0, if(y1, true, y2), z2)) -> c1(MARK(if(z0, if(y1, true, y2), z2)))
   A__F(if(z0, if(y1, false, y2), z2)) -> c1(MARK(if(z0, if(y1, false, y2), z2)))
   A__F(if(z0, if(f(y1), y2, y3), z2)) -> c1(MARK(if(z0, if(f(y1), y2, y3), z2)))
   A__F(if(z0, if(if(y1, y2, y3), y4, y5), z2)) -> c1(MARK(if(z0, if(if(y1, y2, y3), y4, y5), z2)))
   A__F(if(z0, if(c, y1, y2), z2)) -> c1(MARK(if(z0, if(c, y1, y2), z2)))
   A__F(if(z0, if(true, y1, y2), z2)) -> c1(MARK(if(z0, if(true, y1, y2), z2)))
   A__F(if(z0, if(false, y1, y2), z2)) -> c1(MARK(if(z0, if(false, y1, y2), z2)))
   A__F(if(f(y0), if(y1, y2, y3), z2)) -> c1(MARK(if(f(y0), if(y1, y2, y3), z2)))
   A__F(if(if(y0, y1, y2), if(y3, y4, y5), z2)) -> c1(MARK(if(if(y0, y1, y2), if(y3, y4, y5), z2)))
   A__F(if(true, if(y0, y1, y2), z2)) -> c1(MARK(if(true, if(y0, y1, y2), z2)))
   A__F(if(false, if(y0, y1, y2), z2)) -> c1(MARK(if(false, if(y0, y1, y2), z2)))
   A__F(if(f(y0), c, z2)) -> c1(MARK(if(f(y0), c, z2)))
   A__F(if(if(y0, y1, y2), c, z2)) -> c1(MARK(if(if(y0, y1, y2), c, z2)))
   A__F(if(false, c, z2)) -> c1(MARK(if(false, c, z2)))
   A__F(if(f(y0), true, z2)) -> c1(MARK(if(f(y0), true, z2)))
   A__F(if(if(y0, y1, y2), true, z2)) -> c1(MARK(if(if(y0, y1, y2), true, z2)))
   A__F(if(false, true, z2)) -> c1(MARK(if(false, true, z2)))
   A__F(if(f(y0), false, z2)) -> c1(MARK(if(f(y0), false, z2)))
   A__F(if(if(y0, y1, y2), false, z2)) -> c1(MARK(if(if(y0, y1, y2), false, z2)))
   A__F(if(false, false, z2)) -> c1(MARK(if(false, false, z2)))
   A__F(if(f(y0), z1, z2)) -> c1(MARK(if(f(y0), z1, z2)))
   A__F(if(f(f(y0)), z1, z2)) -> c1(MARK(if(f(f(y0)), z1, z2)))
   A__F(if(f(if(y0, y1, y2)), z1, z2)) -> c1(MARK(if(f(if(y0, y1, y2)), z1, z2)))
   A__F(if(f(c), z1, z2)) -> c1(MARK(if(f(c), z1, z2)))
   A__F(if(if(y0, f(y1), y2), z1, z2)) -> c1(MARK(if(if(y0, f(y1), y2), z1, z2)))
   A__F(if(if(y0, if(y1, y2, y3), y4), z1, z2)) -> c1(MARK(if(if(y0, if(y1, y2, y3), y4), z1, z2)))
   A__F(if(if(y0, c, y1), z1, z2)) -> c1(MARK(if(if(y0, c, y1), z1, z2)))
   A__F(if(if(y0, true, y1), z1, z2)) -> c1(MARK(if(if(y0, true, y1), z1, z2)))
   A__F(if(if(y0, false, y1), z1, z2)) -> c1(MARK(if(if(y0, false, y1), z1, z2)))
   A__F(if(if(f(y0), y1, y2), z1, z2)) -> c1(MARK(if(if(f(y0), y1, y2), z1, z2)))
   A__F(if(if(if(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(if(if(if(y0, y1, y2), y3, y4), z1, z2)))
   A__F(if(if(c, y0, y1), z1, z2)) -> c1(MARK(if(if(c, y0, y1), z1, z2)))
   A__F(if(if(true, y0, y1), z1, z2)) -> c1(MARK(if(if(true, y0, y1), z1, z2)))
   A__F(if(if(false, y0, y1), z1, z2)) -> c1(MARK(if(if(false, y0, y1), z1, z2)))
   A__F(if(if(y0, y1, y2), z1, z2)) -> c1(MARK(if(if(y0, y1, y2), z1, z2)))
   A__F(if(c, f(y0), z2)) -> c1(MARK(if(c, f(y0), z2)))
   A__F(if(c, if(y0, y1, y2), z2)) -> c1(MARK(if(c, if(y0, y1, y2), z2)))
   A__F(if(f(true), z1, z2)) -> c1(MARK(if(f(true), z1, z2)))
   A__F(if(f(false), z1, z2)) -> c1(MARK(if(f(false), z1, z2)))
   A__F(if(c, if(false, y0, y1), z2)) -> c1(MARK(if(c, if(false, y0, y1), z2)))
   A__F(if(c, if(c, y0, y1), z2)) -> c1(MARK(if(c, if(c, y0, y1), z2)))
   A__F(if(c, f(f(y0)), z2)) -> c1(MARK(if(c, f(f(y0)), z2)))
   A__F(if(c, f(f(f(y0))), z2)) -> c1(MARK(if(c, f(f(f(y0))), z2)))
   A__F(if(c, f(f(if(y0, y1, y2))), z2)) -> c1(MARK(if(c, f(f(if(y0, y1, y2))), z2)))
   A__F(if(c, f(f(c)), z2)) -> c1(MARK(if(c, f(f(c)), z2)))
   A__F(if(c, f(if(y0, y1, y2)), z2)) -> c1(MARK(if(c, f(if(y0, y1, y2)), z2)))
   A__F(if(c, f(if(y0, f(y1), y2)), z2)) -> c1(MARK(if(c, f(if(y0, f(y1), y2)), z2)))
   A__F(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)) -> c1(MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)))
   A__F(if(c, f(if(y0, c, y1)), z2)) -> c1(MARK(if(c, f(if(y0, c, y1)), z2)))
   A__F(if(c, f(if(y0, true, y1)), z2)) -> c1(MARK(if(c, f(if(y0, true, y1)), z2)))
   A__F(if(c, f(if(y0, false, y1)), z2)) -> c1(MARK(if(c, f(if(y0, false, y1)), z2)))
   A__F(if(c, f(if(f(y0), y1, y2)), z2)) -> c1(MARK(if(c, f(if(f(y0), y1, y2)), z2)))
   A__F(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)) -> c1(MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)))
   A__F(if(c, f(if(c, y0, y1)), z2)) -> c1(MARK(if(c, f(if(c, y0, y1)), z2)))
   A__F(if(c, f(if(true, y0, y1)), z2)) -> c1(MARK(if(c, f(if(true, y0, y1)), z2)))
   A__F(if(c, f(if(false, y0, y1)), z2)) -> c1(MARK(if(c, f(if(false, y0, y1)), z2)))
   A__F(if(c, if(y0, f(y1), y2), z2)) -> c1(MARK(if(c, if(y0, f(y1), y2), z2)))
   A__F(if(c, if(y0, f(f(y1)), y2), z2)) -> c1(MARK(if(c, if(y0, f(f(y1)), y2), z2)))
   A__F(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)) -> c1(MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)))
   A__F(if(c, if(y0, f(c), y1), z2)) -> c1(MARK(if(c, if(y0, f(c), y1), z2)))
   A__F(if(c, if(y0, f(true), y1), z2)) -> c1(MARK(if(c, if(y0, f(true), y1), z2)))
   A__F(if(c, if(y0, f(false), y1), z2)) -> c1(MARK(if(c, if(y0, f(false), y1), z2)))
   A__F(if(c, if(f(y0), f(y1), y2), z2)) -> c1(MARK(if(c, if(f(y0), f(y1), y2), z2)))
   A__F(if(c, if(if(y0, y1, y2), f(y3), y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z2)))
   A__F(if(c, if(true, f(y0), y1), z2)) -> c1(MARK(if(c, if(true, f(y0), y1), z2)))
   A__F(if(c, if(false, f(y0), y1), z2)) -> c1(MARK(if(c, if(false, f(y0), y1), z2)))
   A__F(if(c, if(y0, if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, f(y2), y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)))
   A__F(if(c, if(y0, if(y1, c, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, c, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, true, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, true, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, false, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, false, y2), y3), z2)))
   A__F(if(c, if(y0, if(f(y1), y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)))
   A__F(if(c, if(y0, if(c, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(c, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(true, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(true, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(false, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(false, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)))
   A__F(if(c, if(true, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(true, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(false, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(false, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), c, y1), z2)) -> c1(MARK(if(c, if(f(y0), c, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), c, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), c, y3), z2)))
   A__F(if(c, if(false, c, y0), z2)) -> c1(MARK(if(c, if(false, c, y0), z2)))
   A__F(if(c, if(f(y0), true, y1), z2)) -> c1(MARK(if(c, if(f(y0), true, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), true, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), true, y3), z2)))
   A__F(if(c, if(false, true, y0), z2)) -> c1(MARK(if(c, if(false, true, y0), z2)))
   A__F(if(c, if(f(y0), false, y1), z2)) -> c1(MARK(if(c, if(f(y0), false, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), false, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), false, y3), z2)))
   A__F(if(c, if(false, false, y0), z2)) -> c1(MARK(if(c, if(false, false, y0), z2)))
   A__F(if(c, if(f(y0), y1, y2), z2)) -> c1(MARK(if(c, if(f(y0), y1, y2), z2)))
   A__F(if(c, if(f(f(y0)), y1, y2), z2)) -> c1(MARK(if(c, if(f(f(y0)), y1, y2), z2)))
   A__F(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)) -> c1(MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)))
   A__F(if(c, if(f(c), y0, y1), z2)) -> c1(MARK(if(c, if(f(c), y0, y1), z2)))
   A__F(if(c, if(if(y0, f(y1), y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z2)))
   A__F(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)))
   A__F(if(c, if(if(y0, c, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, c, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, true, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, true, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, false, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, false, y1), y2, y3), z2)))
   A__F(if(c, if(if(f(y0), y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z2)))
   A__F(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)))
   A__F(if(c, if(if(c, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(c, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(true, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(true, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(false, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(false, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), y3, y4), z2)))
   A__F(if(c, if(c, f(y0), y1), z2)) -> c1(MARK(if(c, if(c, f(y0), y1), z2)))
   A__F(if(c, if(c, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(c, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(true), y0, y1), z2)) -> c1(MARK(if(c, if(f(true), y0, y1), z2)))
   A__F(if(c, if(f(false), y0, y1), z2)) -> c1(MARK(if(c, if(f(false), y0, y1), z2)))
   A__F(if(c, f(f(true)), z2)) -> c1(MARK(if(c, f(f(true)), z2)))
   A__F(if(c, f(f(false)), z2)) -> c1(MARK(if(c, f(f(false)), z2)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
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   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
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   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
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   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
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   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
   A__F(if(z0, f(f(y1)), z2)) -> c1(MARK(if(z0, f(f(y1)), z2)))
   A__F(if(z0, f(if(y1, y2, y3)), z2)) -> c1(MARK(if(z0, f(if(y1, y2, y3)), z2)))
   A__F(if(z0, f(c), z2)) -> c1(MARK(if(z0, f(c), z2)))
   A__F(if(z0, f(true), z2)) -> c1(MARK(if(z0, f(true), z2)))
   A__F(if(z0, f(false), z2)) -> c1(MARK(if(z0, f(false), z2)))
   A__F(if(f(y0), f(y1), z2)) -> c1(MARK(if(f(y0), f(y1), z2)))
   A__F(if(if(y0, y1, y2), f(y3), z2)) -> c1(MARK(if(if(y0, y1, y2), f(y3), z2)))
   A__F(if(true, f(y0), z2)) -> c1(MARK(if(true, f(y0), z2)))
   A__F(if(false, f(y0), z2)) -> c1(MARK(if(false, f(y0), z2)))
   A__F(if(z0, if(y1, f(y2), y3), z2)) -> c1(MARK(if(z0, if(y1, f(y2), y3), z2)))
   A__F(if(z0, if(y1, if(y2, y3, y4), y5), z2)) -> c1(MARK(if(z0, if(y1, if(y2, y3, y4), y5), z2)))
   A__F(if(z0, if(y1, c, y2), z2)) -> c1(MARK(if(z0, if(y1, c, y2), z2)))
   A__F(if(z0, if(y1, true, y2), z2)) -> c1(MARK(if(z0, if(y1, true, y2), z2)))
   A__F(if(z0, if(y1, false, y2), z2)) -> c1(MARK(if(z0, if(y1, false, y2), z2)))
   A__F(if(z0, if(f(y1), y2, y3), z2)) -> c1(MARK(if(z0, if(f(y1), y2, y3), z2)))
   A__F(if(z0, if(if(y1, y2, y3), y4, y5), z2)) -> c1(MARK(if(z0, if(if(y1, y2, y3), y4, y5), z2)))
   A__F(if(z0, if(c, y1, y2), z2)) -> c1(MARK(if(z0, if(c, y1, y2), z2)))
   A__F(if(z0, if(true, y1, y2), z2)) -> c1(MARK(if(z0, if(true, y1, y2), z2)))
   A__F(if(z0, if(false, y1, y2), z2)) -> c1(MARK(if(z0, if(false, y1, y2), z2)))
   A__F(if(f(y0), if(y1, y2, y3), z2)) -> c1(MARK(if(f(y0), if(y1, y2, y3), z2)))
   A__F(if(if(y0, y1, y2), if(y3, y4, y5), z2)) -> c1(MARK(if(if(y0, y1, y2), if(y3, y4, y5), z2)))
   A__F(if(true, if(y0, y1, y2), z2)) -> c1(MARK(if(true, if(y0, y1, y2), z2)))
   A__F(if(false, if(y0, y1, y2), z2)) -> c1(MARK(if(false, if(y0, y1, y2), z2)))
   A__F(if(f(y0), c, z2)) -> c1(MARK(if(f(y0), c, z2)))
   A__F(if(if(y0, y1, y2), c, z2)) -> c1(MARK(if(if(y0, y1, y2), c, z2)))
   A__F(if(false, c, z2)) -> c1(MARK(if(false, c, z2)))
   A__F(if(f(y0), true, z2)) -> c1(MARK(if(f(y0), true, z2)))
   A__F(if(if(y0, y1, y2), true, z2)) -> c1(MARK(if(if(y0, y1, y2), true, z2)))
   A__F(if(false, true, z2)) -> c1(MARK(if(false, true, z2)))
   A__F(if(f(y0), false, z2)) -> c1(MARK(if(f(y0), false, z2)))
   A__F(if(if(y0, y1, y2), false, z2)) -> c1(MARK(if(if(y0, y1, y2), false, z2)))
   A__F(if(false, false, z2)) -> c1(MARK(if(false, false, z2)))
   A__F(if(f(f(y0)), z1, z2)) -> c1(MARK(if(f(f(y0)), z1, z2)))
   A__F(if(f(if(y0, y1, y2)), z1, z2)) -> c1(MARK(if(f(if(y0, y1, y2)), z1, z2)))
   A__F(if(f(c), z1, z2)) -> c1(MARK(if(f(c), z1, z2)))
   A__F(if(if(y0, f(y1), y2), z1, z2)) -> c1(MARK(if(if(y0, f(y1), y2), z1, z2)))
   A__F(if(if(y0, if(y1, y2, y3), y4), z1, z2)) -> c1(MARK(if(if(y0, if(y1, y2, y3), y4), z1, z2)))
   A__F(if(if(y0, c, y1), z1, z2)) -> c1(MARK(if(if(y0, c, y1), z1, z2)))
   A__F(if(if(y0, true, y1), z1, z2)) -> c1(MARK(if(if(y0, true, y1), z1, z2)))
   A__F(if(if(y0, false, y1), z1, z2)) -> c1(MARK(if(if(y0, false, y1), z1, z2)))
   A__F(if(if(f(y0), y1, y2), z1, z2)) -> c1(MARK(if(if(f(y0), y1, y2), z1, z2)))
   A__F(if(if(if(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(if(if(if(y0, y1, y2), y3, y4), z1, z2)))
   A__F(if(if(c, y0, y1), z1, z2)) -> c1(MARK(if(if(c, y0, y1), z1, z2)))
   A__F(if(if(true, y0, y1), z1, z2)) -> c1(MARK(if(if(true, y0, y1), z1, z2)))
   A__F(if(if(false, y0, y1), z1, z2)) -> c1(MARK(if(if(false, y0, y1), z1, z2)))
   A__F(if(c, f(y0), z2)) -> c1(MARK(if(c, f(y0), z2)))
   A__F(if(c, if(y0, y1, y2), z2)) -> c1(MARK(if(c, if(y0, y1, y2), z2)))
   A__F(if(f(true), z1, z2)) -> c1(MARK(if(f(true), z1, z2)))
   A__F(if(f(false), z1, z2)) -> c1(MARK(if(f(false), z1, z2)))
   A__F(if(c, if(false, y0, y1), z2)) -> c1(MARK(if(c, if(false, y0, y1), z2)))
   A__F(if(c, if(c, y0, y1), z2)) -> c1(MARK(if(c, if(c, y0, y1), z2)))
   A__F(if(c, f(f(y0)), z2)) -> c1(MARK(if(c, f(f(y0)), z2)))
   A__F(if(c, f(f(f(y0))), z2)) -> c1(MARK(if(c, f(f(f(y0))), z2)))
   A__F(if(c, f(f(if(y0, y1, y2))), z2)) -> c1(MARK(if(c, f(f(if(y0, y1, y2))), z2)))
   A__F(if(c, f(f(c)), z2)) -> c1(MARK(if(c, f(f(c)), z2)))
   A__F(if(c, f(if(y0, y1, y2)), z2)) -> c1(MARK(if(c, f(if(y0, y1, y2)), z2)))
   A__F(if(c, f(if(y0, f(y1), y2)), z2)) -> c1(MARK(if(c, f(if(y0, f(y1), y2)), z2)))
   A__F(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)) -> c1(MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)))
   A__F(if(c, f(if(y0, c, y1)), z2)) -> c1(MARK(if(c, f(if(y0, c, y1)), z2)))
   A__F(if(c, f(if(y0, true, y1)), z2)) -> c1(MARK(if(c, f(if(y0, true, y1)), z2)))
   A__F(if(c, f(if(y0, false, y1)), z2)) -> c1(MARK(if(c, f(if(y0, false, y1)), z2)))
   A__F(if(c, f(if(f(y0), y1, y2)), z2)) -> c1(MARK(if(c, f(if(f(y0), y1, y2)), z2)))
   A__F(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)) -> c1(MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)))
   A__F(if(c, f(if(c, y0, y1)), z2)) -> c1(MARK(if(c, f(if(c, y0, y1)), z2)))
   A__F(if(c, f(if(true, y0, y1)), z2)) -> c1(MARK(if(c, f(if(true, y0, y1)), z2)))
   A__F(if(c, f(if(false, y0, y1)), z2)) -> c1(MARK(if(c, f(if(false, y0, y1)), z2)))
   A__F(if(c, if(y0, f(y1), y2), z2)) -> c1(MARK(if(c, if(y0, f(y1), y2), z2)))
   A__F(if(c, if(y0, f(f(y1)), y2), z2)) -> c1(MARK(if(c, if(y0, f(f(y1)), y2), z2)))
   A__F(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)) -> c1(MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)))
   A__F(if(c, if(y0, f(c), y1), z2)) -> c1(MARK(if(c, if(y0, f(c), y1), z2)))
   A__F(if(c, if(y0, f(true), y1), z2)) -> c1(MARK(if(c, if(y0, f(true), y1), z2)))
   A__F(if(c, if(y0, f(false), y1), z2)) -> c1(MARK(if(c, if(y0, f(false), y1), z2)))
   A__F(if(c, if(f(y0), f(y1), y2), z2)) -> c1(MARK(if(c, if(f(y0), f(y1), y2), z2)))
   A__F(if(c, if(if(y0, y1, y2), f(y3), y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z2)))
   A__F(if(c, if(true, f(y0), y1), z2)) -> c1(MARK(if(c, if(true, f(y0), y1), z2)))
   A__F(if(c, if(false, f(y0), y1), z2)) -> c1(MARK(if(c, if(false, f(y0), y1), z2)))
   A__F(if(c, if(y0, if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, f(y2), y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)))
   A__F(if(c, if(y0, if(y1, c, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, c, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, true, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, true, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, false, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, false, y2), y3), z2)))
   A__F(if(c, if(y0, if(f(y1), y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)))
   A__F(if(c, if(y0, if(c, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(c, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(true, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(true, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(false, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(false, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)))
   A__F(if(c, if(true, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(true, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(false, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(false, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), c, y1), z2)) -> c1(MARK(if(c, if(f(y0), c, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), c, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), c, y3), z2)))
   A__F(if(c, if(false, c, y0), z2)) -> c1(MARK(if(c, if(false, c, y0), z2)))
   A__F(if(c, if(f(y0), true, y1), z2)) -> c1(MARK(if(c, if(f(y0), true, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), true, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), true, y3), z2)))
   A__F(if(c, if(false, true, y0), z2)) -> c1(MARK(if(c, if(false, true, y0), z2)))
   A__F(if(c, if(f(y0), false, y1), z2)) -> c1(MARK(if(c, if(f(y0), false, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), false, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), false, y3), z2)))
   A__F(if(c, if(false, false, y0), z2)) -> c1(MARK(if(c, if(false, false, y0), z2)))
   A__F(if(c, if(f(y0), y1, y2), z2)) -> c1(MARK(if(c, if(f(y0), y1, y2), z2)))
   A__F(if(c, if(f(f(y0)), y1, y2), z2)) -> c1(MARK(if(c, if(f(f(y0)), y1, y2), z2)))
   A__F(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)) -> c1(MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)))
   A__F(if(c, if(f(c), y0, y1), z2)) -> c1(MARK(if(c, if(f(c), y0, y1), z2)))
   A__F(if(c, if(if(y0, f(y1), y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z2)))
   A__F(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)))
   A__F(if(c, if(if(y0, c, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, c, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, true, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, true, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, false, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, false, y1), y2, y3), z2)))
   A__F(if(c, if(if(f(y0), y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z2)))
   A__F(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)))
   A__F(if(c, if(if(c, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(c, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(true, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(true, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(false, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(false, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), y3, y4), z2)))
   A__F(if(c, if(c, f(y0), y1), z2)) -> c1(MARK(if(c, if(c, f(y0), y1), z2)))
   A__F(if(c, if(c, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(c, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(true), y0, y1), z2)) -> c1(MARK(if(c, if(f(true), y0, y1), z2)))
   A__F(if(c, if(f(false), y0, y1), z2)) -> c1(MARK(if(c, if(f(false), y0, y1), z2)))
   A__F(if(c, f(f(true)), z2)) -> c1(MARK(if(c, f(f(true)), z2)))
   A__F(if(c, f(f(false)), z2)) -> c1(MARK(if(c, f(f(false)), z2)))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
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   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
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   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
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   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
   A__F(if(z0, f(f(y1)), z2)) -> c1(MARK(if(z0, f(f(y1)), z2)))
   A__F(if(z0, f(if(y1, y2, y3)), z2)) -> c1(MARK(if(z0, f(if(y1, y2, y3)), z2)))
   A__F(if(z0, f(c), z2)) -> c1(MARK(if(z0, f(c), z2)))
   A__F(if(z0, f(true), z2)) -> c1(MARK(if(z0, f(true), z2)))
   A__F(if(z0, f(false), z2)) -> c1(MARK(if(z0, f(false), z2)))
   A__F(if(f(y0), f(y1), z2)) -> c1(MARK(if(f(y0), f(y1), z2)))
   A__F(if(if(y0, y1, y2), f(y3), z2)) -> c1(MARK(if(if(y0, y1, y2), f(y3), z2)))
   A__F(if(true, f(y0), z2)) -> c1(MARK(if(true, f(y0), z2)))
   A__F(if(false, f(y0), z2)) -> c1(MARK(if(false, f(y0), z2)))
   A__F(if(z0, if(y1, f(y2), y3), z2)) -> c1(MARK(if(z0, if(y1, f(y2), y3), z2)))
   A__F(if(z0, if(y1, if(y2, y3, y4), y5), z2)) -> c1(MARK(if(z0, if(y1, if(y2, y3, y4), y5), z2)))
   A__F(if(z0, if(y1, c, y2), z2)) -> c1(MARK(if(z0, if(y1, c, y2), z2)))
   A__F(if(z0, if(y1, true, y2), z2)) -> c1(MARK(if(z0, if(y1, true, y2), z2)))
   A__F(if(z0, if(y1, false, y2), z2)) -> c1(MARK(if(z0, if(y1, false, y2), z2)))
   A__F(if(z0, if(f(y1), y2, y3), z2)) -> c1(MARK(if(z0, if(f(y1), y2, y3), z2)))
   A__F(if(z0, if(if(y1, y2, y3), y4, y5), z2)) -> c1(MARK(if(z0, if(if(y1, y2, y3), y4, y5), z2)))
   A__F(if(z0, if(c, y1, y2), z2)) -> c1(MARK(if(z0, if(c, y1, y2), z2)))
   A__F(if(z0, if(true, y1, y2), z2)) -> c1(MARK(if(z0, if(true, y1, y2), z2)))
   A__F(if(z0, if(false, y1, y2), z2)) -> c1(MARK(if(z0, if(false, y1, y2), z2)))
   A__F(if(f(y0), if(y1, y2, y3), z2)) -> c1(MARK(if(f(y0), if(y1, y2, y3), z2)))
   A__F(if(if(y0, y1, y2), if(y3, y4, y5), z2)) -> c1(MARK(if(if(y0, y1, y2), if(y3, y4, y5), z2)))
   A__F(if(true, if(y0, y1, y2), z2)) -> c1(MARK(if(true, if(y0, y1, y2), z2)))
   A__F(if(false, if(y0, y1, y2), z2)) -> c1(MARK(if(false, if(y0, y1, y2), z2)))
   A__F(if(f(y0), c, z2)) -> c1(MARK(if(f(y0), c, z2)))
   A__F(if(if(y0, y1, y2), c, z2)) -> c1(MARK(if(if(y0, y1, y2), c, z2)))
   A__F(if(false, c, z2)) -> c1(MARK(if(false, c, z2)))
   A__F(if(f(y0), true, z2)) -> c1(MARK(if(f(y0), true, z2)))
   A__F(if(if(y0, y1, y2), true, z2)) -> c1(MARK(if(if(y0, y1, y2), true, z2)))
   A__F(if(false, true, z2)) -> c1(MARK(if(false, true, z2)))
   A__F(if(f(y0), false, z2)) -> c1(MARK(if(f(y0), false, z2)))
   A__F(if(if(y0, y1, y2), false, z2)) -> c1(MARK(if(if(y0, y1, y2), false, z2)))
   A__F(if(false, false, z2)) -> c1(MARK(if(false, false, z2)))
   A__F(if(f(f(y0)), z1, z2)) -> c1(MARK(if(f(f(y0)), z1, z2)))
   A__F(if(f(if(y0, y1, y2)), z1, z2)) -> c1(MARK(if(f(if(y0, y1, y2)), z1, z2)))
   A__F(if(f(c), z1, z2)) -> c1(MARK(if(f(c), z1, z2)))
   A__F(if(if(y0, f(y1), y2), z1, z2)) -> c1(MARK(if(if(y0, f(y1), y2), z1, z2)))
   A__F(if(if(y0, if(y1, y2, y3), y4), z1, z2)) -> c1(MARK(if(if(y0, if(y1, y2, y3), y4), z1, z2)))
   A__F(if(if(y0, c, y1), z1, z2)) -> c1(MARK(if(if(y0, c, y1), z1, z2)))
   A__F(if(if(y0, true, y1), z1, z2)) -> c1(MARK(if(if(y0, true, y1), z1, z2)))
   A__F(if(if(y0, false, y1), z1, z2)) -> c1(MARK(if(if(y0, false, y1), z1, z2)))
   A__F(if(if(f(y0), y1, y2), z1, z2)) -> c1(MARK(if(if(f(y0), y1, y2), z1, z2)))
   A__F(if(if(if(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(if(if(if(y0, y1, y2), y3, y4), z1, z2)))
   A__F(if(if(c, y0, y1), z1, z2)) -> c1(MARK(if(if(c, y0, y1), z1, z2)))
   A__F(if(if(true, y0, y1), z1, z2)) -> c1(MARK(if(if(true, y0, y1), z1, z2)))
   A__F(if(if(false, y0, y1), z1, z2)) -> c1(MARK(if(if(false, y0, y1), z1, z2)))
   A__F(if(c, f(y0), z2)) -> c1(MARK(if(c, f(y0), z2)))
   A__F(if(c, if(y0, y1, y2), z2)) -> c1(MARK(if(c, if(y0, y1, y2), z2)))
   A__F(if(f(true), z1, z2)) -> c1(MARK(if(f(true), z1, z2)))
   A__F(if(f(false), z1, z2)) -> c1(MARK(if(f(false), z1, z2)))
   A__F(if(c, if(false, y0, y1), z2)) -> c1(MARK(if(c, if(false, y0, y1), z2)))
   A__F(if(c, if(c, y0, y1), z2)) -> c1(MARK(if(c, if(c, y0, y1), z2)))
   A__F(if(c, f(f(y0)), z2)) -> c1(MARK(if(c, f(f(y0)), z2)))
   A__F(if(c, f(f(f(y0))), z2)) -> c1(MARK(if(c, f(f(f(y0))), z2)))
   A__F(if(c, f(f(if(y0, y1, y2))), z2)) -> c1(MARK(if(c, f(f(if(y0, y1, y2))), z2)))
   A__F(if(c, f(f(c)), z2)) -> c1(MARK(if(c, f(f(c)), z2)))
   A__F(if(c, f(if(y0, y1, y2)), z2)) -> c1(MARK(if(c, f(if(y0, y1, y2)), z2)))
   A__F(if(c, f(if(y0, f(y1), y2)), z2)) -> c1(MARK(if(c, f(if(y0, f(y1), y2)), z2)))
   A__F(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)) -> c1(MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)))
   A__F(if(c, f(if(y0, c, y1)), z2)) -> c1(MARK(if(c, f(if(y0, c, y1)), z2)))
   A__F(if(c, f(if(y0, true, y1)), z2)) -> c1(MARK(if(c, f(if(y0, true, y1)), z2)))
   A__F(if(c, f(if(y0, false, y1)), z2)) -> c1(MARK(if(c, f(if(y0, false, y1)), z2)))
   A__F(if(c, f(if(f(y0), y1, y2)), z2)) -> c1(MARK(if(c, f(if(f(y0), y1, y2)), z2)))
   A__F(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)) -> c1(MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)))
   A__F(if(c, f(if(c, y0, y1)), z2)) -> c1(MARK(if(c, f(if(c, y0, y1)), z2)))
   A__F(if(c, f(if(true, y0, y1)), z2)) -> c1(MARK(if(c, f(if(true, y0, y1)), z2)))
   A__F(if(c, f(if(false, y0, y1)), z2)) -> c1(MARK(if(c, f(if(false, y0, y1)), z2)))
   A__F(if(c, if(y0, f(y1), y2), z2)) -> c1(MARK(if(c, if(y0, f(y1), y2), z2)))
   A__F(if(c, if(y0, f(f(y1)), y2), z2)) -> c1(MARK(if(c, if(y0, f(f(y1)), y2), z2)))
   A__F(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)) -> c1(MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)))
   A__F(if(c, if(y0, f(c), y1), z2)) -> c1(MARK(if(c, if(y0, f(c), y1), z2)))
   A__F(if(c, if(y0, f(true), y1), z2)) -> c1(MARK(if(c, if(y0, f(true), y1), z2)))
   A__F(if(c, if(y0, f(false), y1), z2)) -> c1(MARK(if(c, if(y0, f(false), y1), z2)))
   A__F(if(c, if(f(y0), f(y1), y2), z2)) -> c1(MARK(if(c, if(f(y0), f(y1), y2), z2)))
   A__F(if(c, if(if(y0, y1, y2), f(y3), y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z2)))
   A__F(if(c, if(true, f(y0), y1), z2)) -> c1(MARK(if(c, if(true, f(y0), y1), z2)))
   A__F(if(c, if(false, f(y0), y1), z2)) -> c1(MARK(if(c, if(false, f(y0), y1), z2)))
   A__F(if(c, if(y0, if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, f(y2), y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)))
   A__F(if(c, if(y0, if(y1, c, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, c, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, true, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, true, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, false, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, false, y2), y3), z2)))
   A__F(if(c, if(y0, if(f(y1), y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)))
   A__F(if(c, if(y0, if(c, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(c, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(true, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(true, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(false, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(false, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)))
   A__F(if(c, if(true, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(true, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(false, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(false, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), c, y1), z2)) -> c1(MARK(if(c, if(f(y0), c, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), c, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), c, y3), z2)))
   A__F(if(c, if(false, c, y0), z2)) -> c1(MARK(if(c, if(false, c, y0), z2)))
   A__F(if(c, if(f(y0), true, y1), z2)) -> c1(MARK(if(c, if(f(y0), true, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), true, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), true, y3), z2)))
   A__F(if(c, if(false, true, y0), z2)) -> c1(MARK(if(c, if(false, true, y0), z2)))
   A__F(if(c, if(f(y0), false, y1), z2)) -> c1(MARK(if(c, if(f(y0), false, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), false, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), false, y3), z2)))
   A__F(if(c, if(false, false, y0), z2)) -> c1(MARK(if(c, if(false, false, y0), z2)))
   A__F(if(c, if(f(y0), y1, y2), z2)) -> c1(MARK(if(c, if(f(y0), y1, y2), z2)))
   A__F(if(c, if(f(f(y0)), y1, y2), z2)) -> c1(MARK(if(c, if(f(f(y0)), y1, y2), z2)))
   A__F(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)) -> c1(MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)))
   A__F(if(c, if(f(c), y0, y1), z2)) -> c1(MARK(if(c, if(f(c), y0, y1), z2)))
   A__F(if(c, if(if(y0, f(y1), y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z2)))
   A__F(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)))
   A__F(if(c, if(if(y0, c, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, c, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, true, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, true, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, false, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, false, y1), y2, y3), z2)))
   A__F(if(c, if(if(f(y0), y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z2)))
   A__F(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)))
   A__F(if(c, if(if(c, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(c, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(true, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(true, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(false, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(false, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), y3, y4), z2)))
   A__F(if(c, if(c, f(y0), y1), z2)) -> c1(MARK(if(c, if(c, f(y0), y1), z2)))
   A__F(if(c, if(c, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(c, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(true), y0, y1), z2)) -> c1(MARK(if(c, if(f(true), y0, y1), z2)))
   A__F(if(c, if(f(false), y0, y1), z2)) -> c1(MARK(if(c, if(f(false), y0, y1), z2)))
   A__F(if(c, f(f(true)), z2)) -> c1(MARK(if(c, f(f(true)), z2)))
   A__F(if(c, f(f(false)), z2)) -> c1(MARK(if(c, f(f(false)), z2)))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c1_1, c6_2, c6_1, c7_2, c8_1, c3_1, c4_1


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

(171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MARK(if(false, c, x1)) -> c7(A__IF(false, c, x1)) by 
   MARK(if(false, c, if(false, y1, y2))) -> c7(A__IF(false, c, if(false, y1, y2)))
   MARK(if(false, c, if(c, y1, y2))) -> c7(A__IF(false, c, if(c, y1, y2)))
   MARK(if(false, c, f(f(y1)))) -> c7(A__IF(false, c, f(f(y1))))
   MARK(if(false, c, f(f(f(y1))))) -> c7(A__IF(false, c, f(f(f(y1)))))
   MARK(if(false, c, f(f(if(y1, y2, y3))))) -> c7(A__IF(false, c, f(f(if(y1, y2, y3)))))
   MARK(if(false, c, f(f(false)))) -> c7(A__IF(false, c, f(f(false))))
   MARK(if(false, c, f(f(c)))) -> c7(A__IF(false, c, f(f(c))))
   MARK(if(false, c, f(if(y1, y2, y3)))) -> c7(A__IF(false, c, f(if(y1, y2, y3))))
   MARK(if(false, c, f(if(y1, f(y2), y3)))) -> c7(A__IF(false, c, f(if(y1, f(y2), y3))))
   MARK(if(false, c, f(if(y1, if(y2, y3, y4), y5)))) -> c7(A__IF(false, c, f(if(y1, if(y2, y3, y4), y5))))
   MARK(if(false, c, f(if(y1, c, y2)))) -> c7(A__IF(false, c, f(if(y1, c, y2))))
   MARK(if(false, c, f(if(y1, true, y2)))) -> c7(A__IF(false, c, f(if(y1, true, y2))))
   MARK(if(false, c, f(if(y1, false, y2)))) -> c7(A__IF(false, c, f(if(y1, false, y2))))
   MARK(if(false, c, f(if(f(y1), y2, y3)))) -> c7(A__IF(false, c, f(if(f(y1), y2, y3))))
   MARK(if(false, c, f(if(if(y1, y2, y3), y4, y5)))) -> c7(A__IF(false, c, f(if(if(y1, y2, y3), y4, y5))))
   MARK(if(false, c, f(if(c, y1, y2)))) -> c7(A__IF(false, c, f(if(c, y1, y2))))
   MARK(if(false, c, f(if(true, y1, y2)))) -> c7(A__IF(false, c, f(if(true, y1, y2))))
   MARK(if(false, c, f(if(false, y1, y2)))) -> c7(A__IF(false, c, f(if(false, y1, y2))))
   MARK(if(false, c, if(y1, f(y2), y3))) -> c7(A__IF(false, c, if(y1, f(y2), y3)))
   MARK(if(false, c, if(y1, f(f(y2)), y3))) -> c7(A__IF(false, c, if(y1, f(f(y2)), y3)))
   MARK(if(false, c, if(y1, f(if(y2, y3, y4)), y5))) -> c7(A__IF(false, c, if(y1, f(if(y2, y3, y4)), y5)))
   MARK(if(false, c, if(y1, f(c), y2))) -> c7(A__IF(false, c, if(y1, f(c), y2)))
   MARK(if(false, c, if(y1, f(true), y2))) -> c7(A__IF(false, c, if(y1, f(true), y2)))
   MARK(if(false, c, if(y1, f(false), y2))) -> c7(A__IF(false, c, if(y1, f(false), y2)))
   MARK(if(false, c, if(f(y1), f(y2), y3))) -> c7(A__IF(false, c, if(f(y1), f(y2), y3)))
   MARK(if(false, c, if(if(y1, y2, y3), f(y4), y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), f(y4), y5)))
   MARK(if(false, c, if(true, f(y1), y2))) -> c7(A__IF(false, c, if(true, f(y1), y2)))
   MARK(if(false, c, if(false, f(y1), y2))) -> c7(A__IF(false, c, if(false, f(y1), y2)))
   MARK(if(false, c, if(y1, if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, y3, y4), y5)))
   MARK(if(false, c, if(y1, if(y2, f(y3), y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, f(y3), y4), y5)))
   MARK(if(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7))) -> c7(A__IF(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7)))
   MARK(if(false, c, if(y1, if(y2, c, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, c, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, true, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, true, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, false, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, false, y3), y4)))
   MARK(if(false, c, if(y1, if(f(y2), y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(f(y2), y3, y4), y5)))
   MARK(if(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7))) -> c7(A__IF(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7)))
   MARK(if(false, c, if(y1, if(c, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(c, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(true, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(true, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(false, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(false, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(f(y1), if(y2, y3, y4), y5)))
   MARK(if(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7))) -> c7(A__IF(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7)))
   MARK(if(false, c, if(true, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(true, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(false, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(false, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), c, y2))) -> c7(A__IF(false, c, if(f(y1), c, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), c, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), c, y4)))
   MARK(if(false, c, if(false, c, y1))) -> c7(A__IF(false, c, if(false, c, y1)))
   MARK(if(false, c, if(f(y1), true, y2))) -> c7(A__IF(false, c, if(f(y1), true, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), true, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), true, y4)))
   MARK(if(false, c, if(false, true, y1))) -> c7(A__IF(false, c, if(false, true, y1)))
   MARK(if(false, c, if(f(y1), false, y2))) -> c7(A__IF(false, c, if(f(y1), false, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), false, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), false, y4)))
   MARK(if(false, c, if(false, false, y1))) -> c7(A__IF(false, c, if(false, false, y1)))
   MARK(if(false, c, if(f(y1), y2, y3))) -> c7(A__IF(false, c, if(f(y1), y2, y3)))
   MARK(if(false, c, if(f(f(y1)), y2, y3))) -> c7(A__IF(false, c, if(f(f(y1)), y2, y3)))
   MARK(if(false, c, if(f(if(y1, y2, y3)), y4, y5))) -> c7(A__IF(false, c, if(f(if(y1, y2, y3)), y4, y5)))
   MARK(if(false, c, if(f(false), y1, y2))) -> c7(A__IF(false, c, if(f(false), y1, y2)))
   MARK(if(false, c, if(f(c), y1, y2))) -> c7(A__IF(false, c, if(f(c), y1, y2)))
   MARK(if(false, c, if(if(y1, f(y2), y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, f(y2), y3), y4, y5)))
   MARK(if(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7))) -> c7(A__IF(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7)))
   MARK(if(false, c, if(if(y1, c, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, c, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, true, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, true, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, false, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, false, y2), y3, y4)))
   MARK(if(false, c, if(if(f(y1), y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(f(y1), y2, y3), y4, y5)))
   MARK(if(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7))) -> c7(A__IF(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7)))
   MARK(if(false, c, if(if(c, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(c, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(true, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(true, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(false, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(false, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), y4, y5)))
   MARK(if(false, c, if(c, f(y1), y2))) -> c7(A__IF(false, c, if(c, f(y1), y2)))
   MARK(if(false, c, if(c, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(c, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(true), y1, y2))) -> c7(A__IF(false, c, if(f(true), y1, y2)))
   MARK(if(false, c, f(f(true)))) -> c7(A__IF(false, c, f(f(true))))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__f(z0) -> a__if(mark(z0), c, f(true))
   a__f(z0) -> f(z0)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   mark(f(z0)) -> a__f(mark(z0))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), mark(z1), z2)
   mark(c) -> c
   mark(true) -> true
   mark(false) -> false
Tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   A__F(f(x0)) -> c1(MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
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   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
   A__F(if(z0, f(f(y1)), z2)) -> c1(MARK(if(z0, f(f(y1)), z2)))
   A__F(if(z0, f(if(y1, y2, y3)), z2)) -> c1(MARK(if(z0, f(if(y1, y2, y3)), z2)))
   A__F(if(z0, f(c), z2)) -> c1(MARK(if(z0, f(c), z2)))
   A__F(if(z0, f(true), z2)) -> c1(MARK(if(z0, f(true), z2)))
   A__F(if(z0, f(false), z2)) -> c1(MARK(if(z0, f(false), z2)))
   A__F(if(f(y0), f(y1), z2)) -> c1(MARK(if(f(y0), f(y1), z2)))
   A__F(if(if(y0, y1, y2), f(y3), z2)) -> c1(MARK(if(if(y0, y1, y2), f(y3), z2)))
   A__F(if(true, f(y0), z2)) -> c1(MARK(if(true, f(y0), z2)))
   A__F(if(false, f(y0), z2)) -> c1(MARK(if(false, f(y0), z2)))
   A__F(if(z0, if(y1, f(y2), y3), z2)) -> c1(MARK(if(z0, if(y1, f(y2), y3), z2)))
   A__F(if(z0, if(y1, if(y2, y3, y4), y5), z2)) -> c1(MARK(if(z0, if(y1, if(y2, y3, y4), y5), z2)))
   A__F(if(z0, if(y1, c, y2), z2)) -> c1(MARK(if(z0, if(y1, c, y2), z2)))
   A__F(if(z0, if(y1, true, y2), z2)) -> c1(MARK(if(z0, if(y1, true, y2), z2)))
   A__F(if(z0, if(y1, false, y2), z2)) -> c1(MARK(if(z0, if(y1, false, y2), z2)))
   A__F(if(z0, if(f(y1), y2, y3), z2)) -> c1(MARK(if(z0, if(f(y1), y2, y3), z2)))
   A__F(if(z0, if(if(y1, y2, y3), y4, y5), z2)) -> c1(MARK(if(z0, if(if(y1, y2, y3), y4, y5), z2)))
   A__F(if(z0, if(c, y1, y2), z2)) -> c1(MARK(if(z0, if(c, y1, y2), z2)))
   A__F(if(z0, if(true, y1, y2), z2)) -> c1(MARK(if(z0, if(true, y1, y2), z2)))
   A__F(if(z0, if(false, y1, y2), z2)) -> c1(MARK(if(z0, if(false, y1, y2), z2)))
   A__F(if(f(y0), if(y1, y2, y3), z2)) -> c1(MARK(if(f(y0), if(y1, y2, y3), z2)))
   A__F(if(if(y0, y1, y2), if(y3, y4, y5), z2)) -> c1(MARK(if(if(y0, y1, y2), if(y3, y4, y5), z2)))
   A__F(if(true, if(y0, y1, y2), z2)) -> c1(MARK(if(true, if(y0, y1, y2), z2)))
   A__F(if(false, if(y0, y1, y2), z2)) -> c1(MARK(if(false, if(y0, y1, y2), z2)))
   A__F(if(f(y0), c, z2)) -> c1(MARK(if(f(y0), c, z2)))
   A__F(if(if(y0, y1, y2), c, z2)) -> c1(MARK(if(if(y0, y1, y2), c, z2)))
   A__F(if(false, c, z2)) -> c1(MARK(if(false, c, z2)))
   A__F(if(f(y0), true, z2)) -> c1(MARK(if(f(y0), true, z2)))
   A__F(if(if(y0, y1, y2), true, z2)) -> c1(MARK(if(if(y0, y1, y2), true, z2)))
   A__F(if(false, true, z2)) -> c1(MARK(if(false, true, z2)))
   A__F(if(f(y0), false, z2)) -> c1(MARK(if(f(y0), false, z2)))
   A__F(if(if(y0, y1, y2), false, z2)) -> c1(MARK(if(if(y0, y1, y2), false, z2)))
   A__F(if(false, false, z2)) -> c1(MARK(if(false, false, z2)))
   A__F(if(f(f(y0)), z1, z2)) -> c1(MARK(if(f(f(y0)), z1, z2)))
   A__F(if(f(if(y0, y1, y2)), z1, z2)) -> c1(MARK(if(f(if(y0, y1, y2)), z1, z2)))
   A__F(if(f(c), z1, z2)) -> c1(MARK(if(f(c), z1, z2)))
   A__F(if(if(y0, f(y1), y2), z1, z2)) -> c1(MARK(if(if(y0, f(y1), y2), z1, z2)))
   A__F(if(if(y0, if(y1, y2, y3), y4), z1, z2)) -> c1(MARK(if(if(y0, if(y1, y2, y3), y4), z1, z2)))
   A__F(if(if(y0, c, y1), z1, z2)) -> c1(MARK(if(if(y0, c, y1), z1, z2)))
   A__F(if(if(y0, true, y1), z1, z2)) -> c1(MARK(if(if(y0, true, y1), z1, z2)))
   A__F(if(if(y0, false, y1), z1, z2)) -> c1(MARK(if(if(y0, false, y1), z1, z2)))
   A__F(if(if(f(y0), y1, y2), z1, z2)) -> c1(MARK(if(if(f(y0), y1, y2), z1, z2)))
   A__F(if(if(if(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(if(if(if(y0, y1, y2), y3, y4), z1, z2)))
   A__F(if(if(c, y0, y1), z1, z2)) -> c1(MARK(if(if(c, y0, y1), z1, z2)))
   A__F(if(if(true, y0, y1), z1, z2)) -> c1(MARK(if(if(true, y0, y1), z1, z2)))
   A__F(if(if(false, y0, y1), z1, z2)) -> c1(MARK(if(if(false, y0, y1), z1, z2)))
   A__F(if(c, f(y0), z2)) -> c1(MARK(if(c, f(y0), z2)))
   A__F(if(c, if(y0, y1, y2), z2)) -> c1(MARK(if(c, if(y0, y1, y2), z2)))
   A__F(if(f(true), z1, z2)) -> c1(MARK(if(f(true), z1, z2)))
   A__F(if(f(false), z1, z2)) -> c1(MARK(if(f(false), z1, z2)))
   A__F(if(c, if(false, y0, y1), z2)) -> c1(MARK(if(c, if(false, y0, y1), z2)))
   A__F(if(c, if(c, y0, y1), z2)) -> c1(MARK(if(c, if(c, y0, y1), z2)))
   A__F(if(c, f(f(y0)), z2)) -> c1(MARK(if(c, f(f(y0)), z2)))
   A__F(if(c, f(f(f(y0))), z2)) -> c1(MARK(if(c, f(f(f(y0))), z2)))
   A__F(if(c, f(f(if(y0, y1, y2))), z2)) -> c1(MARK(if(c, f(f(if(y0, y1, y2))), z2)))
   A__F(if(c, f(f(c)), z2)) -> c1(MARK(if(c, f(f(c)), z2)))
   A__F(if(c, f(if(y0, y1, y2)), z2)) -> c1(MARK(if(c, f(if(y0, y1, y2)), z2)))
   A__F(if(c, f(if(y0, f(y1), y2)), z2)) -> c1(MARK(if(c, f(if(y0, f(y1), y2)), z2)))
   A__F(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)) -> c1(MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)))
   A__F(if(c, f(if(y0, c, y1)), z2)) -> c1(MARK(if(c, f(if(y0, c, y1)), z2)))
   A__F(if(c, f(if(y0, true, y1)), z2)) -> c1(MARK(if(c, f(if(y0, true, y1)), z2)))
   A__F(if(c, f(if(y0, false, y1)), z2)) -> c1(MARK(if(c, f(if(y0, false, y1)), z2)))
   A__F(if(c, f(if(f(y0), y1, y2)), z2)) -> c1(MARK(if(c, f(if(f(y0), y1, y2)), z2)))
   A__F(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)) -> c1(MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)))
   A__F(if(c, f(if(c, y0, y1)), z2)) -> c1(MARK(if(c, f(if(c, y0, y1)), z2)))
   A__F(if(c, f(if(true, y0, y1)), z2)) -> c1(MARK(if(c, f(if(true, y0, y1)), z2)))
   A__F(if(c, f(if(false, y0, y1)), z2)) -> c1(MARK(if(c, f(if(false, y0, y1)), z2)))
   A__F(if(c, if(y0, f(y1), y2), z2)) -> c1(MARK(if(c, if(y0, f(y1), y2), z2)))
   A__F(if(c, if(y0, f(f(y1)), y2), z2)) -> c1(MARK(if(c, if(y0, f(f(y1)), y2), z2)))
   A__F(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)) -> c1(MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)))
   A__F(if(c, if(y0, f(c), y1), z2)) -> c1(MARK(if(c, if(y0, f(c), y1), z2)))
   A__F(if(c, if(y0, f(true), y1), z2)) -> c1(MARK(if(c, if(y0, f(true), y1), z2)))
   A__F(if(c, if(y0, f(false), y1), z2)) -> c1(MARK(if(c, if(y0, f(false), y1), z2)))
   A__F(if(c, if(f(y0), f(y1), y2), z2)) -> c1(MARK(if(c, if(f(y0), f(y1), y2), z2)))
   A__F(if(c, if(if(y0, y1, y2), f(y3), y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z2)))
   A__F(if(c, if(true, f(y0), y1), z2)) -> c1(MARK(if(c, if(true, f(y0), y1), z2)))
   A__F(if(c, if(false, f(y0), y1), z2)) -> c1(MARK(if(c, if(false, f(y0), y1), z2)))
   A__F(if(c, if(y0, if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, f(y2), y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)))
   A__F(if(c, if(y0, if(y1, c, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, c, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, true, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, true, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, false, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, false, y2), y3), z2)))
   A__F(if(c, if(y0, if(f(y1), y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)))
   A__F(if(c, if(y0, if(c, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(c, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(true, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(true, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(false, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(false, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)))
   A__F(if(c, if(true, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(true, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(false, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(false, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), c, y1), z2)) -> c1(MARK(if(c, if(f(y0), c, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), c, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), c, y3), z2)))
   A__F(if(c, if(false, c, y0), z2)) -> c1(MARK(if(c, if(false, c, y0), z2)))
   A__F(if(c, if(f(y0), true, y1), z2)) -> c1(MARK(if(c, if(f(y0), true, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), true, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), true, y3), z2)))
   A__F(if(c, if(false, true, y0), z2)) -> c1(MARK(if(c, if(false, true, y0), z2)))
   A__F(if(c, if(f(y0), false, y1), z2)) -> c1(MARK(if(c, if(f(y0), false, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), false, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), false, y3), z2)))
   A__F(if(c, if(false, false, y0), z2)) -> c1(MARK(if(c, if(false, false, y0), z2)))
   A__F(if(c, if(f(y0), y1, y2), z2)) -> c1(MARK(if(c, if(f(y0), y1, y2), z2)))
   A__F(if(c, if(f(f(y0)), y1, y2), z2)) -> c1(MARK(if(c, if(f(f(y0)), y1, y2), z2)))
   A__F(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)) -> c1(MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)))
   A__F(if(c, if(f(c), y0, y1), z2)) -> c1(MARK(if(c, if(f(c), y0, y1), z2)))
   A__F(if(c, if(if(y0, f(y1), y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z2)))
   A__F(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)))
   A__F(if(c, if(if(y0, c, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, c, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, true, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, true, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, false, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, false, y1), y2, y3), z2)))
   A__F(if(c, if(if(f(y0), y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z2)))
   A__F(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)))
   A__F(if(c, if(if(c, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(c, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(true, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(true, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(false, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(false, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), y3, y4), z2)))
   A__F(if(c, if(c, f(y0), y1), z2)) -> c1(MARK(if(c, if(c, f(y0), y1), z2)))
   A__F(if(c, if(c, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(c, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(true), y0, y1), z2)) -> c1(MARK(if(c, if(f(true), y0, y1), z2)))
   A__F(if(c, if(f(false), y0, y1), z2)) -> c1(MARK(if(c, if(f(false), y0, y1), z2)))
   A__F(if(c, f(f(true)), z2)) -> c1(MARK(if(c, f(f(true)), z2)))
   A__F(if(c, f(f(false)), z2)) -> c1(MARK(if(c, f(f(false)), z2)))
   MARK(if(false, c, if(false, y1, y2))) -> c7(A__IF(false, c, if(false, y1, y2)))
   MARK(if(false, c, if(c, y1, y2))) -> c7(A__IF(false, c, if(c, y1, y2)))
   MARK(if(false, c, f(f(y1)))) -> c7(A__IF(false, c, f(f(y1))))
   MARK(if(false, c, f(f(f(y1))))) -> c7(A__IF(false, c, f(f(f(y1)))))
   MARK(if(false, c, f(f(if(y1, y2, y3))))) -> c7(A__IF(false, c, f(f(if(y1, y2, y3)))))
   MARK(if(false, c, f(f(false)))) -> c7(A__IF(false, c, f(f(false))))
   MARK(if(false, c, f(f(c)))) -> c7(A__IF(false, c, f(f(c))))
   MARK(if(false, c, f(if(y1, y2, y3)))) -> c7(A__IF(false, c, f(if(y1, y2, y3))))
   MARK(if(false, c, f(if(y1, f(y2), y3)))) -> c7(A__IF(false, c, f(if(y1, f(y2), y3))))
   MARK(if(false, c, f(if(y1, if(y2, y3, y4), y5)))) -> c7(A__IF(false, c, f(if(y1, if(y2, y3, y4), y5))))
   MARK(if(false, c, f(if(y1, c, y2)))) -> c7(A__IF(false, c, f(if(y1, c, y2))))
   MARK(if(false, c, f(if(y1, true, y2)))) -> c7(A__IF(false, c, f(if(y1, true, y2))))
   MARK(if(false, c, f(if(y1, false, y2)))) -> c7(A__IF(false, c, f(if(y1, false, y2))))
   MARK(if(false, c, f(if(f(y1), y2, y3)))) -> c7(A__IF(false, c, f(if(f(y1), y2, y3))))
   MARK(if(false, c, f(if(if(y1, y2, y3), y4, y5)))) -> c7(A__IF(false, c, f(if(if(y1, y2, y3), y4, y5))))
   MARK(if(false, c, f(if(c, y1, y2)))) -> c7(A__IF(false, c, f(if(c, y1, y2))))
   MARK(if(false, c, f(if(true, y1, y2)))) -> c7(A__IF(false, c, f(if(true, y1, y2))))
   MARK(if(false, c, f(if(false, y1, y2)))) -> c7(A__IF(false, c, f(if(false, y1, y2))))
   MARK(if(false, c, if(y1, f(y2), y3))) -> c7(A__IF(false, c, if(y1, f(y2), y3)))
   MARK(if(false, c, if(y1, f(f(y2)), y3))) -> c7(A__IF(false, c, if(y1, f(f(y2)), y3)))
   MARK(if(false, c, if(y1, f(if(y2, y3, y4)), y5))) -> c7(A__IF(false, c, if(y1, f(if(y2, y3, y4)), y5)))
   MARK(if(false, c, if(y1, f(c), y2))) -> c7(A__IF(false, c, if(y1, f(c), y2)))
   MARK(if(false, c, if(y1, f(true), y2))) -> c7(A__IF(false, c, if(y1, f(true), y2)))
   MARK(if(false, c, if(y1, f(false), y2))) -> c7(A__IF(false, c, if(y1, f(false), y2)))
   MARK(if(false, c, if(f(y1), f(y2), y3))) -> c7(A__IF(false, c, if(f(y1), f(y2), y3)))
   MARK(if(false, c, if(if(y1, y2, y3), f(y4), y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), f(y4), y5)))
   MARK(if(false, c, if(true, f(y1), y2))) -> c7(A__IF(false, c, if(true, f(y1), y2)))
   MARK(if(false, c, if(false, f(y1), y2))) -> c7(A__IF(false, c, if(false, f(y1), y2)))
   MARK(if(false, c, if(y1, if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, y3, y4), y5)))
   MARK(if(false, c, if(y1, if(y2, f(y3), y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, f(y3), y4), y5)))
   MARK(if(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7))) -> c7(A__IF(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7)))
   MARK(if(false, c, if(y1, if(y2, c, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, c, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, true, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, true, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, false, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, false, y3), y4)))
   MARK(if(false, c, if(y1, if(f(y2), y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(f(y2), y3, y4), y5)))
   MARK(if(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7))) -> c7(A__IF(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7)))
   MARK(if(false, c, if(y1, if(c, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(c, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(true, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(true, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(false, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(false, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(f(y1), if(y2, y3, y4), y5)))
   MARK(if(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7))) -> c7(A__IF(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7)))
   MARK(if(false, c, if(true, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(true, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(false, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(false, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), c, y2))) -> c7(A__IF(false, c, if(f(y1), c, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), c, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), c, y4)))
   MARK(if(false, c, if(false, c, y1))) -> c7(A__IF(false, c, if(false, c, y1)))
   MARK(if(false, c, if(f(y1), true, y2))) -> c7(A__IF(false, c, if(f(y1), true, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), true, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), true, y4)))
   MARK(if(false, c, if(false, true, y1))) -> c7(A__IF(false, c, if(false, true, y1)))
   MARK(if(false, c, if(f(y1), false, y2))) -> c7(A__IF(false, c, if(f(y1), false, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), false, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), false, y4)))
   MARK(if(false, c, if(false, false, y1))) -> c7(A__IF(false, c, if(false, false, y1)))
   MARK(if(false, c, if(f(y1), y2, y3))) -> c7(A__IF(false, c, if(f(y1), y2, y3)))
   MARK(if(false, c, if(f(f(y1)), y2, y3))) -> c7(A__IF(false, c, if(f(f(y1)), y2, y3)))
   MARK(if(false, c, if(f(if(y1, y2, y3)), y4, y5))) -> c7(A__IF(false, c, if(f(if(y1, y2, y3)), y4, y5)))
   MARK(if(false, c, if(f(false), y1, y2))) -> c7(A__IF(false, c, if(f(false), y1, y2)))
   MARK(if(false, c, if(f(c), y1, y2))) -> c7(A__IF(false, c, if(f(c), y1, y2)))
   MARK(if(false, c, if(if(y1, f(y2), y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, f(y2), y3), y4, y5)))
   MARK(if(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7))) -> c7(A__IF(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7)))
   MARK(if(false, c, if(if(y1, c, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, c, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, true, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, true, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, false, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, false, y2), y3, y4)))
   MARK(if(false, c, if(if(f(y1), y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(f(y1), y2, y3), y4, y5)))
   MARK(if(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7))) -> c7(A__IF(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7)))
   MARK(if(false, c, if(if(c, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(c, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(true, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(true, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(false, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(false, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), y4, y5)))
   MARK(if(false, c, if(c, f(y1), y2))) -> c7(A__IF(false, c, if(c, f(y1), y2)))
   MARK(if(false, c, if(c, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(c, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(true), y1, y2))) -> c7(A__IF(false, c, if(f(true), y1, y2)))
   MARK(if(false, c, f(f(true)))) -> c7(A__IF(false, c, f(f(true))))
S tuples:
   MARK(if(false, x1, x2)) -> c7(A__IF(false, mark(x1), x2))
   MARK(if(false, x1, x2)) -> c8(A__IF(false, mark(x1), x2), MARK(x1))
   MARK(f(f(x0))) -> c6(A__F(a__if(mark(mark(x0)), c, f(true))), MARK(f(x0)))
   MARK(f(f(x0))) -> c6(A__F(f(mark(x0))), MARK(f(x0)))
   MARK(f(f(f(z0)))) -> c6(A__F(a__f(a__f(mark(z0)))), MARK(f(f(z0))))
   MARK(f(f(if(z0, z1, z2)))) -> c6(A__F(a__f(a__if(mark(z0), mark(z1), z2))), MARK(f(if(z0, z1, z2))))
   MARK(f(f(c))) -> c6(A__F(a__f(c)))
   MARK(f(if(x0, x1, z2))) -> c6(A__F(if(mark(x0), mark(x1), z2)), MARK(if(x0, x1, z2)))
   MARK(f(if(x0, f(z0), x2))) -> c6(A__F(a__if(mark(x0), a__f(mark(z0)), x2)), MARK(if(x0, f(z0), x2)))
   MARK(f(if(x0, if(z0, z1, z2), x2))) -> c6(A__F(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2)), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(f(if(x0, c, x2))) -> c6(A__F(a__if(mark(x0), c, x2)), MARK(if(x0, c, x2)))
   MARK(f(if(x0, true, x2))) -> c6(A__F(a__if(mark(x0), true, x2)), MARK(if(x0, true, x2)))
   MARK(f(if(x0, false, x2))) -> c6(A__F(a__if(mark(x0), false, x2)), MARK(if(x0, false, x2)))
   MARK(f(if(f(z0), x1, x2))) -> c6(A__F(a__if(a__f(mark(z0)), mark(x1), x2)), MARK(if(f(z0), x1, x2)))
   MARK(f(if(if(z0, z1, z2), x1, x2))) -> c6(A__F(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2)), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(f(if(c, x1, x2))) -> c6(A__F(a__if(c, mark(x1), x2)), MARK(if(c, x1, x2)))
   MARK(f(if(true, x1, x2))) -> c6(A__F(a__if(true, mark(x1), x2)), MARK(if(true, x1, x2)))
   MARK(f(if(false, x1, x2))) -> c6(A__F(a__if(false, mark(x1), x2)), MARK(if(false, x1, x2)))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(x0))
   MARK(if(x0, f(x1), x2)) -> c7(A__IF(mark(x0), f(mark(x1)), x2), MARK(x0))
   MARK(if(x0, f(f(z0)), x2)) -> c7(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(x0))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c7(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(x0))
   MARK(if(x0, f(c), x2)) -> c7(A__IF(mark(x0), a__f(c), x2), MARK(x0))
   MARK(if(x0, f(true), x2)) -> c7(A__IF(mark(x0), a__f(true), x2), MARK(x0))
   MARK(if(x0, f(false), x2)) -> c7(A__IF(mark(x0), a__f(false), x2), MARK(x0))
   MARK(if(f(z0), f(x1), x2)) -> c7(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(if(z0, z1, z2)))
   MARK(if(true, f(x1), x2)) -> c7(A__IF(true, a__f(mark(x1)), x2))
   MARK(if(false, f(x1), x2)) -> c7(A__IF(false, a__f(mark(x1)), x2))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c7(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(x0))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(x0))
   MARK(if(x0, if(x1, c, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, true, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(x0))
   MARK(if(x0, if(x1, false, x3), x4)) -> c7(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(x0))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(c, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(true, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(x0))
   MARK(if(x0, if(false, x2, x3), x4)) -> c7(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(x0))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c7(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(z0, z1, z2)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c7(A__IF(true, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(false, if(x1, x2, x3), x4)) -> c7(A__IF(false, a__if(mark(x1), mark(x2), x3), x4))
   MARK(if(f(z0), c, x1)) -> c7(A__IF(a__f(mark(z0)), c, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), c, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), c, x1), MARK(if(z0, z1, z2)))
   MARK(if(f(z0), true, x1)) -> c7(A__IF(a__f(mark(z0)), true, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), true, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), true, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, true, x1)) -> c7(A__IF(false, true, x1))
   MARK(if(f(z0), false, x1)) -> c7(A__IF(a__f(mark(z0)), false, x1), MARK(f(z0)))
   MARK(if(if(z0, z1, z2), false, x1)) -> c7(A__IF(a__if(mark(z0), mark(z1), z2), false, x1), MARK(if(z0, z1, z2)))
   MARK(if(false, false, x1)) -> c7(A__IF(false, false, x1))
   MARK(if(f(x0), x1, x2)) -> c7(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(f(x0)))
   MARK(if(f(f(z0)), x1, x2)) -> c7(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(f(f(z0))))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c7(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(x0), x1, x2)) -> c7(MARK(f(x0)))
   MARK(if(f(c), x1, x2)) -> c7(A__IF(a__f(c), mark(x1), x2))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(if(x0, f(z0), x2)))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(if(x0, if(z0, z1, z2), x2)))
   MARK(if(if(x0, c, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(if(x0, c, x2)))
   MARK(if(if(x0, true, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(if(x0, true, x2)))
   MARK(if(if(x0, false, x2), x3, x4)) -> c7(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(if(x0, false, x2)))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(if(f(z0), x1, x2)))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(if(if(z0, z1, z2), x1, x2)))
   MARK(if(if(c, x1, x2), x3, x4)) -> c7(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(if(c, x1, x2)))
   MARK(if(if(true, x1, x2), x3, x4)) -> c7(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(if(true, x1, x2)))
   MARK(if(if(false, x1, x2), x3, x4)) -> c7(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(if(false, x1, x2)))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c7(MARK(if(x0, x1, z2)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), a__if(mark(mark(x1)), c, f(true)), x2), MARK(f(x1)))
   MARK(if(x0, f(x1), x2)) -> c8(A__IF(mark(x0), f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(f(z0)), x2)) -> c8(A__IF(mark(x0), a__f(a__f(mark(z0))), x2), MARK(f(f(z0))))
   MARK(if(x0, f(if(z0, z1, z2)), x2)) -> c8(A__IF(mark(x0), a__f(a__if(mark(z0), mark(z1), z2)), x2), MARK(f(if(z0, z1, z2))))
   MARK(if(f(z0), f(x1), x2)) -> c8(A__IF(a__f(mark(z0)), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(if(z0, z1, z2), f(x1), x2)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(true, f(x1), x2)) -> c8(A__IF(true, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(false, f(x1), x2)) -> c8(A__IF(false, a__f(mark(x1)), x2), MARK(f(x1)))
   MARK(if(x0, f(c), x2)) -> c8(A__IF(mark(x0), a__f(c), x2))
   MARK(if(c, f(x1), x2)) -> c8(MARK(f(x1)))
   MARK(if(x0, if(x1, x2, z2), x4)) -> c8(A__IF(mark(x0), if(mark(x1), mark(x2), z2), x4), MARK(if(x1, x2, z2)))
   MARK(if(x0, if(x1, f(z0), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__f(mark(z0)), x3), x4), MARK(if(x1, f(z0), x3)))
   MARK(if(x0, if(x1, if(z0, z1, z2), x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), a__if(mark(z0), mark(z1), z2), x3), x4), MARK(if(x1, if(z0, z1, z2), x3)))
   MARK(if(x0, if(x1, c, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), c, x3), x4), MARK(if(x1, c, x3)))
   MARK(if(x0, if(x1, true, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), true, x3), x4), MARK(if(x1, true, x3)))
   MARK(if(x0, if(x1, false, x3), x4)) -> c8(A__IF(mark(x0), a__if(mark(x1), false, x3), x4), MARK(if(x1, false, x3)))
   MARK(if(x0, if(f(z0), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__f(mark(z0)), mark(x2), x3), x4), MARK(if(f(z0), x2, x3)))
   MARK(if(x0, if(if(z0, z1, z2), x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(a__if(mark(z0), mark(z1), z2), mark(x2), x3), x4), MARK(if(if(z0, z1, z2), x2, x3)))
   MARK(if(x0, if(c, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(c, mark(x2), x3), x4), MARK(if(c, x2, x3)))
   MARK(if(x0, if(true, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(true, mark(x2), x3), x4), MARK(if(true, x2, x3)))
   MARK(if(x0, if(false, x2, x3), x4)) -> c8(A__IF(mark(x0), a__if(false, mark(x2), x3), x4), MARK(if(false, x2, x3)))
   MARK(if(f(z0), if(x1, x2, x3), x4)) -> c8(A__IF(a__f(mark(z0)), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(if(z0, z1, z2), if(x1, x2, x3), x4)) -> c8(A__IF(a__if(mark(z0), mark(z1), z2), a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(true, if(x1, x2, x3), x4)) -> c8(A__IF(true, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(false, if(x1, x2, x3), x4)) -> c8(A__IF(false, a__if(mark(x1), mark(x2), x3), x4), MARK(if(x1, x2, x3)))
   MARK(if(c, if(x1, x2, x3), x4)) -> c8(MARK(if(x1, x2, x3)))
   MARK(if(f(x0), x1, x2)) -> c8(A__IF(a__if(mark(mark(x0)), c, f(true)), mark(x1), x2), MARK(x1))
   MARK(if(f(f(z0)), x1, x2)) -> c8(A__IF(a__f(a__f(mark(z0))), mark(x1), x2), MARK(x1))
   MARK(if(f(if(z0, z1, z2)), x1, x2)) -> c8(A__IF(a__f(a__if(mark(z0), mark(z1), z2)), mark(x1), x2), MARK(x1))
   MARK(if(f(c), x1, x2)) -> c8(A__IF(a__f(c), mark(x1), x2), MARK(x1))
   MARK(if(f(true), x1, x2)) -> c8(A__IF(a__f(true), mark(x1), x2), MARK(x1))
   MARK(if(f(false), x1, x2)) -> c8(A__IF(a__f(false), mark(x1), x2), MARK(x1))
   MARK(if(f(x0), c, x2)) -> c8(A__IF(a__f(mark(x0)), c, x2))
   MARK(if(f(x0), true, x2)) -> c8(A__IF(a__f(mark(x0)), true, x2))
   MARK(if(f(x0), false, x2)) -> c8(A__IF(a__f(mark(x0)), false, x2))
   MARK(if(f(x0), x1, x2)) -> c8(MARK(x1))
   MARK(if(if(x0, f(z0), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__f(mark(z0)), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, if(z0, z1, z2), x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), a__if(mark(z0), mark(z1), z2), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, c, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), c, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, true, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), true, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, false, x2), x3, x4)) -> c8(A__IF(a__if(mark(x0), false, x2), mark(x3), x4), MARK(x3))
   MARK(if(if(f(z0), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__f(mark(z0)), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(if(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__IF(a__if(a__if(mark(z0), mark(z1), z2), mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(c, x1, x2), x3, x4)) -> c8(A__IF(a__if(c, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(true, x1, x2), x3, x4)) -> c8(A__IF(a__if(true, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(false, x1, x2), x3, x4)) -> c8(A__IF(a__if(false, mark(x1), x2), mark(x3), x4), MARK(x3))
   MARK(if(if(x0, x1, x2), c, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), c, x4))
   MARK(if(if(x0, x1, x2), true, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), true, x4))
   MARK(if(if(x0, x1, x2), false, x4)) -> c8(A__IF(a__if(mark(x0), mark(x1), x2), false, x4))
   MARK(if(if(x0, x1, z2), x3, x4)) -> c8(MARK(x3))
   MARK(if(false, c, x1)) -> c8(A__IF(false, c, x1))
   MARK(if(false, true, x1)) -> c8(A__IF(false, true, x1))
   MARK(if(false, false, x1)) -> c8(A__IF(false, false, x1))
   A__IF(true, if(true, y0, y1), z1) -> c3(MARK(if(true, y0, y1)))
   A__IF(true, if(false, y0, y1), z1) -> c3(MARK(if(false, y0, y1)))
   A__IF(true, if(c, y0, y1), z1) -> c3(MARK(if(c, y0, y1)))
   A__IF(true, f(f(y0)), z1) -> c3(MARK(f(f(y0))))
   A__IF(true, f(f(f(y0))), z1) -> c3(MARK(f(f(f(y0)))))
   A__IF(true, f(f(if(y0, y1, y2))), z1) -> c3(MARK(f(f(if(y0, y1, y2)))))
   A__IF(true, f(f(true)), z1) -> c3(MARK(f(f(true))))
   A__IF(true, f(f(false)), z1) -> c3(MARK(f(f(false))))
   A__IF(true, f(f(c)), z1) -> c3(MARK(f(f(c))))
   A__IF(true, f(if(y0, y1, y2)), z1) -> c3(MARK(f(if(y0, y1, y2))))
   A__IF(true, f(if(y0, f(y1), y2)), z1) -> c3(MARK(f(if(y0, f(y1), y2))))
   A__IF(true, f(if(y0, if(y1, y2, y3), y4)), z1) -> c3(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(true, f(if(y0, c, y1)), z1) -> c3(MARK(f(if(y0, c, y1))))
   A__IF(true, f(if(y0, true, y1)), z1) -> c3(MARK(f(if(y0, true, y1))))
   A__IF(true, f(if(y0, false, y1)), z1) -> c3(MARK(f(if(y0, false, y1))))
   A__IF(true, f(if(f(y0), y1, y2)), z1) -> c3(MARK(f(if(f(y0), y1, y2))))
   A__IF(true, f(if(if(y0, y1, y2), y3, y4)), z1) -> c3(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(true, f(if(c, y0, y1)), z1) -> c3(MARK(f(if(c, y0, y1))))
   A__IF(true, f(if(true, y0, y1)), z1) -> c3(MARK(f(if(true, y0, y1))))
   A__IF(true, f(if(false, y0, y1)), z1) -> c3(MARK(f(if(false, y0, y1))))
   A__IF(true, if(y0, f(y1), y2), z1) -> c3(MARK(if(y0, f(y1), y2)))
   A__IF(true, if(y0, f(f(y1)), y2), z1) -> c3(MARK(if(y0, f(f(y1)), y2)))
   A__IF(true, if(y0, f(if(y1, y2, y3)), y4), z1) -> c3(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(true, if(y0, f(c), y1), z1) -> c3(MARK(if(y0, f(c), y1)))
   A__IF(true, if(y0, f(true), y1), z1) -> c3(MARK(if(y0, f(true), y1)))
   A__IF(true, if(y0, f(false), y1), z1) -> c3(MARK(if(y0, f(false), y1)))
   A__IF(true, if(f(y0), f(y1), y2), z1) -> c3(MARK(if(f(y0), f(y1), y2)))
   A__IF(true, if(if(y0, y1, y2), f(y3), y4), z1) -> c3(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(true, if(true, f(y0), y1), z1) -> c3(MARK(if(true, f(y0), y1)))
   A__IF(true, if(false, f(y0), y1), z1) -> c3(MARK(if(false, f(y0), y1)))
   A__IF(true, if(y0, if(y1, y2, y3), y4), z1) -> c3(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(true, if(y0, if(y1, f(y2), y3), y4), z1) -> c3(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(true, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1) -> c3(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(true, if(y0, if(y1, c, y2), y3), z1) -> c3(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(true, if(y0, if(y1, true, y2), y3), z1) -> c3(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(true, if(y0, if(y1, false, y2), y3), z1) -> c3(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(true, if(y0, if(f(y1), y2, y3), y4), z1) -> c3(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(true, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1) -> c3(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(true, if(y0, if(c, y1, y2), y3), z1) -> c3(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(true, if(y0, if(true, y1, y2), y3), z1) -> c3(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(true, if(y0, if(false, y1, y2), y3), z1) -> c3(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(true, if(f(y0), if(y1, y2, y3), y4), z1) -> c3(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(true, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1) -> c3(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(true, if(true, if(y0, y1, y2), y3), z1) -> c3(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(true, if(false, if(y0, y1, y2), y3), z1) -> c3(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(true, if(f(y0), c, y1), z1) -> c3(MARK(if(f(y0), c, y1)))
   A__IF(true, if(if(y0, y1, y2), c, y3), z1) -> c3(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(true, if(false, c, y0), z1) -> c3(MARK(if(false, c, y0)))
   A__IF(true, if(f(y0), true, y1), z1) -> c3(MARK(if(f(y0), true, y1)))
   A__IF(true, if(if(y0, y1, y2), true, y3), z1) -> c3(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(true, if(false, true, y0), z1) -> c3(MARK(if(false, true, y0)))
   A__IF(true, if(f(y0), false, y1), z1) -> c3(MARK(if(f(y0), false, y1)))
   A__IF(true, if(if(y0, y1, y2), false, y3), z1) -> c3(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(true, if(false, false, y0), z1) -> c3(MARK(if(false, false, y0)))
   A__IF(true, if(f(y0), y1, y2), z1) -> c3(MARK(if(f(y0), y1, y2)))
   A__IF(true, if(f(f(y0)), y1, y2), z1) -> c3(MARK(if(f(f(y0)), y1, y2)))
   A__IF(true, if(f(if(y0, y1, y2)), y3, y4), z1) -> c3(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(true, if(f(true), y0, y1), z1) -> c3(MARK(if(f(true), y0, y1)))
   A__IF(true, if(f(false), y0, y1), z1) -> c3(MARK(if(f(false), y0, y1)))
   A__IF(true, if(f(c), y0, y1), z1) -> c3(MARK(if(f(c), y0, y1)))
   A__IF(true, if(if(y0, f(y1), y2), y3, y4), z1) -> c3(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(true, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1) -> c3(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(true, if(if(y0, c, y1), y2, y3), z1) -> c3(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(true, if(if(y0, true, y1), y2, y3), z1) -> c3(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(true, if(if(y0, false, y1), y2, y3), z1) -> c3(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(true, if(if(f(y0), y1, y2), y3, y4), z1) -> c3(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(true, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1) -> c3(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(true, if(if(c, y0, y1), y2, y3), z1) -> c3(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(true, if(if(true, y0, y1), y2, y3), z1) -> c3(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(true, if(if(false, y0, y1), y2, y3), z1) -> c3(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(true, if(if(y0, y1, y2), y3, y4), z1) -> c3(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(true, if(c, f(y0), y1), z1) -> c3(MARK(if(c, f(y0), y1)))
   A__IF(true, if(c, if(y0, y1, y2), y3), z1) -> c3(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(f(f(true))) -> c6(A__F(a__f(true)))
   MARK(if(f(true), x1, x2)) -> c7(A__IF(a__f(true), mark(x1), x2))
   MARK(if(x0, f(true), x2)) -> c8(A__IF(mark(x0), a__f(true), x2))
   A__IF(false, z0, if(false, y0, y1)) -> c4(MARK(if(false, y0, y1)))
   A__IF(false, z0, if(c, y0, y1)) -> c4(MARK(if(c, y0, y1)))
   A__IF(false, z0, f(f(y0))) -> c4(MARK(f(f(y0))))
   A__IF(false, z0, f(f(f(y0)))) -> c4(MARK(f(f(f(y0)))))
   A__IF(false, z0, f(f(if(y0, y1, y2)))) -> c4(MARK(f(f(if(y0, y1, y2)))))
   A__IF(false, z0, f(f(false))) -> c4(MARK(f(f(false))))
   A__IF(false, z0, f(f(c))) -> c4(MARK(f(f(c))))
   A__IF(false, z0, f(if(y0, y1, y2))) -> c4(MARK(f(if(y0, y1, y2))))
   A__IF(false, z0, f(if(y0, f(y1), y2))) -> c4(MARK(f(if(y0, f(y1), y2))))
   A__IF(false, z0, f(if(y0, if(y1, y2, y3), y4))) -> c4(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__IF(false, z0, f(if(y0, c, y1))) -> c4(MARK(f(if(y0, c, y1))))
   A__IF(false, z0, f(if(y0, true, y1))) -> c4(MARK(f(if(y0, true, y1))))
   A__IF(false, z0, f(if(y0, false, y1))) -> c4(MARK(f(if(y0, false, y1))))
   A__IF(false, z0, f(if(f(y0), y1, y2))) -> c4(MARK(f(if(f(y0), y1, y2))))
   A__IF(false, z0, f(if(if(y0, y1, y2), y3, y4))) -> c4(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__IF(false, z0, f(if(c, y0, y1))) -> c4(MARK(f(if(c, y0, y1))))
   A__IF(false, z0, f(if(true, y0, y1))) -> c4(MARK(f(if(true, y0, y1))))
   A__IF(false, z0, f(if(false, y0, y1))) -> c4(MARK(f(if(false, y0, y1))))
   A__IF(false, z0, if(y0, f(y1), y2)) -> c4(MARK(if(y0, f(y1), y2)))
   A__IF(false, z0, if(y0, f(f(y1)), y2)) -> c4(MARK(if(y0, f(f(y1)), y2)))
   A__IF(false, z0, if(y0, f(if(y1, y2, y3)), y4)) -> c4(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   A__IF(false, z0, if(y0, f(c), y1)) -> c4(MARK(if(y0, f(c), y1)))
   A__IF(false, z0, if(y0, f(true), y1)) -> c4(MARK(if(y0, f(true), y1)))
   A__IF(false, z0, if(y0, f(false), y1)) -> c4(MARK(if(y0, f(false), y1)))
   A__IF(false, z0, if(f(y0), f(y1), y2)) -> c4(MARK(if(f(y0), f(y1), y2)))
   A__IF(false, z0, if(if(y0, y1, y2), f(y3), y4)) -> c4(MARK(if(if(y0, y1, y2), f(y3), y4)))
   A__IF(false, z0, if(true, f(y0), y1)) -> c4(MARK(if(true, f(y0), y1)))
   A__IF(false, z0, if(false, f(y0), y1)) -> c4(MARK(if(false, f(y0), y1)))
   A__IF(false, z0, if(y0, if(y1, y2, y3), y4)) -> c4(MARK(if(y0, if(y1, y2, y3), y4)))
   A__IF(false, z0, if(y0, if(y1, f(y2), y3), y4)) -> c4(MARK(if(y0, if(y1, f(y2), y3), y4)))
   A__IF(false, z0, if(y0, if(y1, if(y2, y3, y4), y5), y6)) -> c4(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   A__IF(false, z0, if(y0, if(y1, c, y2), y3)) -> c4(MARK(if(y0, if(y1, c, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, true, y2), y3)) -> c4(MARK(if(y0, if(y1, true, y2), y3)))
   A__IF(false, z0, if(y0, if(y1, false, y2), y3)) -> c4(MARK(if(y0, if(y1, false, y2), y3)))
   A__IF(false, z0, if(y0, if(f(y1), y2, y3), y4)) -> c4(MARK(if(y0, if(f(y1), y2, y3), y4)))
   A__IF(false, z0, if(y0, if(if(y1, y2, y3), y4, y5), y6)) -> c4(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   A__IF(false, z0, if(y0, if(c, y1, y2), y3)) -> c4(MARK(if(y0, if(c, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(true, y1, y2), y3)) -> c4(MARK(if(y0, if(true, y1, y2), y3)))
   A__IF(false, z0, if(y0, if(false, y1, y2), y3)) -> c4(MARK(if(y0, if(false, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), if(y1, y2, y3), y4)) -> c4(MARK(if(f(y0), if(y1, y2, y3), y4)))
   A__IF(false, z0, if(if(y0, y1, y2), if(y3, y4, y5), y6)) -> c4(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   A__IF(false, z0, if(true, if(y0, y1, y2), y3)) -> c4(MARK(if(true, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(false, if(y0, y1, y2), y3)) -> c4(MARK(if(false, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(y0), c, y1)) -> c4(MARK(if(f(y0), c, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), c, y3)) -> c4(MARK(if(if(y0, y1, y2), c, y3)))
   A__IF(false, z0, if(false, c, y0)) -> c4(MARK(if(false, c, y0)))
   A__IF(false, z0, if(f(y0), true, y1)) -> c4(MARK(if(f(y0), true, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), true, y3)) -> c4(MARK(if(if(y0, y1, y2), true, y3)))
   A__IF(false, z0, if(false, true, y0)) -> c4(MARK(if(false, true, y0)))
   A__IF(false, z0, if(f(y0), false, y1)) -> c4(MARK(if(f(y0), false, y1)))
   A__IF(false, z0, if(if(y0, y1, y2), false, y3)) -> c4(MARK(if(if(y0, y1, y2), false, y3)))
   A__IF(false, z0, if(false, false, y0)) -> c4(MARK(if(false, false, y0)))
   A__IF(false, z0, if(f(y0), y1, y2)) -> c4(MARK(if(f(y0), y1, y2)))
   A__IF(false, z0, if(f(f(y0)), y1, y2)) -> c4(MARK(if(f(f(y0)), y1, y2)))
   A__IF(false, z0, if(f(if(y0, y1, y2)), y3, y4)) -> c4(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   A__IF(false, z0, if(f(false), y0, y1)) -> c4(MARK(if(f(false), y0, y1)))
   A__IF(false, z0, if(f(c), y0, y1)) -> c4(MARK(if(f(c), y0, y1)))
   A__IF(false, z0, if(if(y0, f(y1), y2), y3, y4)) -> c4(MARK(if(if(y0, f(y1), y2), y3, y4)))
   A__IF(false, z0, if(if(y0, if(y1, y2, y3), y4), y5, y6)) -> c4(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   A__IF(false, z0, if(if(y0, c, y1), y2, y3)) -> c4(MARK(if(if(y0, c, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, true, y1), y2, y3)) -> c4(MARK(if(if(y0, true, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, false, y1), y2, y3)) -> c4(MARK(if(if(y0, false, y1), y2, y3)))
   A__IF(false, z0, if(if(f(y0), y1, y2), y3, y4)) -> c4(MARK(if(if(f(y0), y1, y2), y3, y4)))
   A__IF(false, z0, if(if(if(y0, y1, y2), y3, y4), y5, y6)) -> c4(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   A__IF(false, z0, if(if(c, y0, y1), y2, y3)) -> c4(MARK(if(if(c, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(true, y0, y1), y2, y3)) -> c4(MARK(if(if(true, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(false, y0, y1), y2, y3)) -> c4(MARK(if(if(false, y0, y1), y2, y3)))
   A__IF(false, z0, if(if(y0, y1, y2), y3, y4)) -> c4(MARK(if(if(y0, y1, y2), y3, y4)))
   A__IF(false, z0, if(c, f(y0), y1)) -> c4(MARK(if(c, f(y0), y1)))
   A__IF(false, z0, if(c, if(y0, y1, y2), y3)) -> c4(MARK(if(c, if(y0, y1, y2), y3)))
   A__IF(false, z0, if(f(true), y0, y1)) -> c4(MARK(if(f(true), y0, y1)))
   A__IF(false, z0, f(f(true))) -> c4(MARK(f(f(true))))
   A__F(f(f(z0))) -> c1(MARK(f(f(z0))))
   A__F(f(if(z0, z1, z2))) -> c1(MARK(f(if(z0, z1, z2))))
   A__F(if(x0, f(z0), x2)) -> c1(MARK(if(x0, f(z0), x2)))
   A__F(if(x0, if(z0, z1, z2), x2)) -> c1(MARK(if(x0, if(z0, z1, z2), x2)))
   A__F(if(x0, c, x2)) -> c1(MARK(if(x0, c, x2)))
   A__F(if(x0, true, x2)) -> c1(MARK(if(x0, true, x2)))
   A__F(if(x0, false, x2)) -> c1(MARK(if(x0, false, x2)))
   A__F(if(f(z0), x1, x2)) -> c1(MARK(if(f(z0), x1, x2)))
   A__F(if(if(z0, z1, z2), x1, x2)) -> c1(MARK(if(if(z0, z1, z2), x1, x2)))
   A__F(if(c, x1, x2)) -> c1(MARK(if(c, x1, x2)))
   A__F(if(true, x1, x2)) -> c1(MARK(if(true, x1, x2)))
   A__F(if(false, x1, x2)) -> c1(MARK(if(false, x1, x2)))
   MARK(f(f(false))) -> c6(A__F(a__f(false)))
   MARK(if(f(false), x1, x2)) -> c7(A__IF(a__f(false), mark(x1), x2))
   MARK(if(x0, f(false), x2)) -> c8(A__IF(mark(x0), a__f(false), x2))
   MARK(if(c, if(false, y0, y1), z1)) -> c8(MARK(if(false, y0, y1)))
   MARK(if(c, if(c, y0, y1), z1)) -> c8(MARK(if(c, y0, y1)))
   MARK(if(c, f(f(y0)), z1)) -> c8(MARK(f(f(y0))))
   MARK(if(c, f(f(f(y0))), z1)) -> c8(MARK(f(f(f(y0)))))
   MARK(if(c, f(f(if(y0, y1, y2))), z1)) -> c8(MARK(f(f(if(y0, y1, y2)))))
   MARK(if(c, f(f(c)), z1)) -> c8(MARK(f(f(c))))
   MARK(if(c, f(if(y0, y1, y2)), z1)) -> c8(MARK(f(if(y0, y1, y2))))
   MARK(if(c, f(if(y0, f(y1), y2)), z1)) -> c8(MARK(f(if(y0, f(y1), y2))))
   MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z1)) -> c8(MARK(f(if(y0, if(y1, y2, y3), y4))))
   MARK(if(c, f(if(y0, c, y1)), z1)) -> c8(MARK(f(if(y0, c, y1))))
   MARK(if(c, f(if(y0, true, y1)), z1)) -> c8(MARK(f(if(y0, true, y1))))
   MARK(if(c, f(if(y0, false, y1)), z1)) -> c8(MARK(f(if(y0, false, y1))))
   MARK(if(c, f(if(f(y0), y1, y2)), z1)) -> c8(MARK(f(if(f(y0), y1, y2))))
   MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z1)) -> c8(MARK(f(if(if(y0, y1, y2), y3, y4))))
   MARK(if(c, f(if(c, y0, y1)), z1)) -> c8(MARK(f(if(c, y0, y1))))
   MARK(if(c, f(if(true, y0, y1)), z1)) -> c8(MARK(f(if(true, y0, y1))))
   MARK(if(c, f(if(false, y0, y1)), z1)) -> c8(MARK(f(if(false, y0, y1))))
   MARK(if(c, if(y0, f(y1), y2), z1)) -> c8(MARK(if(y0, f(y1), y2)))
   MARK(if(c, if(y0, f(f(y1)), y2), z1)) -> c8(MARK(if(y0, f(f(y1)), y2)))
   MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z1)) -> c8(MARK(if(y0, f(if(y1, y2, y3)), y4)))
   MARK(if(c, if(y0, f(c), y1), z1)) -> c8(MARK(if(y0, f(c), y1)))
   MARK(if(c, if(y0, f(true), y1), z1)) -> c8(MARK(if(y0, f(true), y1)))
   MARK(if(c, if(y0, f(false), y1), z1)) -> c8(MARK(if(y0, f(false), y1)))
   MARK(if(c, if(f(y0), f(y1), y2), z1)) -> c8(MARK(if(f(y0), f(y1), y2)))
   MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z1)) -> c8(MARK(if(if(y0, y1, y2), f(y3), y4)))
   MARK(if(c, if(true, f(y0), y1), z1)) -> c8(MARK(if(true, f(y0), y1)))
   MARK(if(c, if(false, f(y0), y1), z1)) -> c8(MARK(if(false, f(y0), y1)))
   MARK(if(c, if(y0, if(y1, y2, y3), y4), z1)) -> c8(MARK(if(y0, if(y1, y2, y3), y4)))
   MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z1)) -> c8(MARK(if(y0, if(y1, f(y2), y3), y4)))
   MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z1)) -> c8(MARK(if(y0, if(y1, if(y2, y3, y4), y5), y6)))
   MARK(if(c, if(y0, if(y1, c, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, c, y2), y3)))
   MARK(if(c, if(y0, if(y1, true, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, true, y2), y3)))
   MARK(if(c, if(y0, if(y1, false, y2), y3), z1)) -> c8(MARK(if(y0, if(y1, false, y2), y3)))
   MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z1)) -> c8(MARK(if(y0, if(f(y1), y2, y3), y4)))
   MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z1)) -> c8(MARK(if(y0, if(if(y1, y2, y3), y4, y5), y6)))
   MARK(if(c, if(y0, if(c, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(c, y1, y2), y3)))
   MARK(if(c, if(y0, if(true, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(true, y1, y2), y3)))
   MARK(if(c, if(y0, if(false, y1, y2), y3), z1)) -> c8(MARK(if(y0, if(false, y1, y2), y3)))
   MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z1)) -> c8(MARK(if(f(y0), if(y1, y2, y3), y4)))
   MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z1)) -> c8(MARK(if(if(y0, y1, y2), if(y3, y4, y5), y6)))
   MARK(if(c, if(true, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(true, if(y0, y1, y2), y3)))
   MARK(if(c, if(false, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(false, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(y0), c, y1), z1)) -> c8(MARK(if(f(y0), c, y1)))
   MARK(if(c, if(if(y0, y1, y2), c, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), c, y3)))
   MARK(if(c, if(false, c, y0), z1)) -> c8(MARK(if(false, c, y0)))
   MARK(if(c, if(f(y0), true, y1), z1)) -> c8(MARK(if(f(y0), true, y1)))
   MARK(if(c, if(if(y0, y1, y2), true, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), true, y3)))
   MARK(if(c, if(false, true, y0), z1)) -> c8(MARK(if(false, true, y0)))
   MARK(if(c, if(f(y0), false, y1), z1)) -> c8(MARK(if(f(y0), false, y1)))
   MARK(if(c, if(if(y0, y1, y2), false, y3), z1)) -> c8(MARK(if(if(y0, y1, y2), false, y3)))
   MARK(if(c, if(false, false, y0), z1)) -> c8(MARK(if(false, false, y0)))
   MARK(if(c, if(f(y0), y1, y2), z1)) -> c8(MARK(if(f(y0), y1, y2)))
   MARK(if(c, if(f(f(y0)), y1, y2), z1)) -> c8(MARK(if(f(f(y0)), y1, y2)))
   MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z1)) -> c8(MARK(if(f(if(y0, y1, y2)), y3, y4)))
   MARK(if(c, if(f(c), y0, y1), z1)) -> c8(MARK(if(f(c), y0, y1)))
   MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z1)) -> c8(MARK(if(if(y0, f(y1), y2), y3, y4)))
   MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z1)) -> c8(MARK(if(if(y0, if(y1, y2, y3), y4), y5, y6)))
   MARK(if(c, if(if(y0, c, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, c, y1), y2, y3)))
   MARK(if(c, if(if(y0, true, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, true, y1), y2, y3)))
   MARK(if(c, if(if(y0, false, y1), y2, y3), z1)) -> c8(MARK(if(if(y0, false, y1), y2, y3)))
   MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z1)) -> c8(MARK(if(if(f(y0), y1, y2), y3, y4)))
   MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z1)) -> c8(MARK(if(if(if(y0, y1, y2), y3, y4), y5, y6)))
   MARK(if(c, if(if(c, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(c, y0, y1), y2, y3)))
   MARK(if(c, if(if(true, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(true, y0, y1), y2, y3)))
   MARK(if(c, if(if(false, y0, y1), y2, y3), z1)) -> c8(MARK(if(if(false, y0, y1), y2, y3)))
   MARK(if(c, if(if(y0, y1, y2), y3, y4), z1)) -> c8(MARK(if(if(y0, y1, y2), y3, y4)))
   MARK(if(c, if(c, f(y0), y1), z1)) -> c8(MARK(if(c, f(y0), y1)))
   MARK(if(c, if(c, if(y0, y1, y2), y3), z1)) -> c8(MARK(if(c, if(y0, y1, y2), y3)))
   MARK(if(c, if(f(true), y0, y1), z1)) -> c8(MARK(if(f(true), y0, y1)))
   MARK(if(c, if(f(false), y0, y1), z1)) -> c8(MARK(if(f(false), y0, y1)))
   MARK(if(c, f(f(true)), z1)) -> c8(MARK(f(f(true))))
   MARK(if(c, f(f(false)), z1)) -> c8(MARK(f(f(false))))
   A__F(f(f(f(y0)))) -> c1(MARK(f(f(f(y0)))))
   A__F(f(f(if(y0, y1, y2)))) -> c1(MARK(f(f(if(y0, y1, y2)))))
   A__F(f(f(c))) -> c1(MARK(f(f(c))))
   A__F(f(if(y0, f(y1), y2))) -> c1(MARK(f(if(y0, f(y1), y2))))
   A__F(f(if(y0, if(y1, y2, y3), y4))) -> c1(MARK(f(if(y0, if(y1, y2, y3), y4))))
   A__F(f(if(y0, c, y1))) -> c1(MARK(f(if(y0, c, y1))))
   A__F(f(if(y0, true, y1))) -> c1(MARK(f(if(y0, true, y1))))
   A__F(f(if(y0, false, y1))) -> c1(MARK(f(if(y0, false, y1))))
   A__F(f(if(f(y0), y1, y2))) -> c1(MARK(f(if(f(y0), y1, y2))))
   A__F(f(if(if(y0, y1, y2), y3, y4))) -> c1(MARK(f(if(if(y0, y1, y2), y3, y4))))
   A__F(f(if(c, y0, y1))) -> c1(MARK(f(if(c, y0, y1))))
   A__F(f(if(true, y0, y1))) -> c1(MARK(f(if(true, y0, y1))))
   A__F(f(if(false, y0, y1))) -> c1(MARK(f(if(false, y0, y1))))
   A__F(f(f(true))) -> c1(MARK(f(f(true))))
   A__F(f(f(false))) -> c1(MARK(f(f(false))))
   A__F(if(z0, f(f(y1)), z2)) -> c1(MARK(if(z0, f(f(y1)), z2)))
   A__F(if(z0, f(if(y1, y2, y3)), z2)) -> c1(MARK(if(z0, f(if(y1, y2, y3)), z2)))
   A__F(if(z0, f(c), z2)) -> c1(MARK(if(z0, f(c), z2)))
   A__F(if(z0, f(true), z2)) -> c1(MARK(if(z0, f(true), z2)))
   A__F(if(z0, f(false), z2)) -> c1(MARK(if(z0, f(false), z2)))
   A__F(if(f(y0), f(y1), z2)) -> c1(MARK(if(f(y0), f(y1), z2)))
   A__F(if(if(y0, y1, y2), f(y3), z2)) -> c1(MARK(if(if(y0, y1, y2), f(y3), z2)))
   A__F(if(true, f(y0), z2)) -> c1(MARK(if(true, f(y0), z2)))
   A__F(if(false, f(y0), z2)) -> c1(MARK(if(false, f(y0), z2)))
   A__F(if(z0, if(y1, f(y2), y3), z2)) -> c1(MARK(if(z0, if(y1, f(y2), y3), z2)))
   A__F(if(z0, if(y1, if(y2, y3, y4), y5), z2)) -> c1(MARK(if(z0, if(y1, if(y2, y3, y4), y5), z2)))
   A__F(if(z0, if(y1, c, y2), z2)) -> c1(MARK(if(z0, if(y1, c, y2), z2)))
   A__F(if(z0, if(y1, true, y2), z2)) -> c1(MARK(if(z0, if(y1, true, y2), z2)))
   A__F(if(z0, if(y1, false, y2), z2)) -> c1(MARK(if(z0, if(y1, false, y2), z2)))
   A__F(if(z0, if(f(y1), y2, y3), z2)) -> c1(MARK(if(z0, if(f(y1), y2, y3), z2)))
   A__F(if(z0, if(if(y1, y2, y3), y4, y5), z2)) -> c1(MARK(if(z0, if(if(y1, y2, y3), y4, y5), z2)))
   A__F(if(z0, if(c, y1, y2), z2)) -> c1(MARK(if(z0, if(c, y1, y2), z2)))
   A__F(if(z0, if(true, y1, y2), z2)) -> c1(MARK(if(z0, if(true, y1, y2), z2)))
   A__F(if(z0, if(false, y1, y2), z2)) -> c1(MARK(if(z0, if(false, y1, y2), z2)))
   A__F(if(f(y0), if(y1, y2, y3), z2)) -> c1(MARK(if(f(y0), if(y1, y2, y3), z2)))
   A__F(if(if(y0, y1, y2), if(y3, y4, y5), z2)) -> c1(MARK(if(if(y0, y1, y2), if(y3, y4, y5), z2)))
   A__F(if(true, if(y0, y1, y2), z2)) -> c1(MARK(if(true, if(y0, y1, y2), z2)))
   A__F(if(false, if(y0, y1, y2), z2)) -> c1(MARK(if(false, if(y0, y1, y2), z2)))
   A__F(if(f(y0), c, z2)) -> c1(MARK(if(f(y0), c, z2)))
   A__F(if(if(y0, y1, y2), c, z2)) -> c1(MARK(if(if(y0, y1, y2), c, z2)))
   A__F(if(false, c, z2)) -> c1(MARK(if(false, c, z2)))
   A__F(if(f(y0), true, z2)) -> c1(MARK(if(f(y0), true, z2)))
   A__F(if(if(y0, y1, y2), true, z2)) -> c1(MARK(if(if(y0, y1, y2), true, z2)))
   A__F(if(false, true, z2)) -> c1(MARK(if(false, true, z2)))
   A__F(if(f(y0), false, z2)) -> c1(MARK(if(f(y0), false, z2)))
   A__F(if(if(y0, y1, y2), false, z2)) -> c1(MARK(if(if(y0, y1, y2), false, z2)))
   A__F(if(false, false, z2)) -> c1(MARK(if(false, false, z2)))
   A__F(if(f(f(y0)), z1, z2)) -> c1(MARK(if(f(f(y0)), z1, z2)))
   A__F(if(f(if(y0, y1, y2)), z1, z2)) -> c1(MARK(if(f(if(y0, y1, y2)), z1, z2)))
   A__F(if(f(c), z1, z2)) -> c1(MARK(if(f(c), z1, z2)))
   A__F(if(if(y0, f(y1), y2), z1, z2)) -> c1(MARK(if(if(y0, f(y1), y2), z1, z2)))
   A__F(if(if(y0, if(y1, y2, y3), y4), z1, z2)) -> c1(MARK(if(if(y0, if(y1, y2, y3), y4), z1, z2)))
   A__F(if(if(y0, c, y1), z1, z2)) -> c1(MARK(if(if(y0, c, y1), z1, z2)))
   A__F(if(if(y0, true, y1), z1, z2)) -> c1(MARK(if(if(y0, true, y1), z1, z2)))
   A__F(if(if(y0, false, y1), z1, z2)) -> c1(MARK(if(if(y0, false, y1), z1, z2)))
   A__F(if(if(f(y0), y1, y2), z1, z2)) -> c1(MARK(if(if(f(y0), y1, y2), z1, z2)))
   A__F(if(if(if(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(if(if(if(y0, y1, y2), y3, y4), z1, z2)))
   A__F(if(if(c, y0, y1), z1, z2)) -> c1(MARK(if(if(c, y0, y1), z1, z2)))
   A__F(if(if(true, y0, y1), z1, z2)) -> c1(MARK(if(if(true, y0, y1), z1, z2)))
   A__F(if(if(false, y0, y1), z1, z2)) -> c1(MARK(if(if(false, y0, y1), z1, z2)))
   A__F(if(c, f(y0), z2)) -> c1(MARK(if(c, f(y0), z2)))
   A__F(if(c, if(y0, y1, y2), z2)) -> c1(MARK(if(c, if(y0, y1, y2), z2)))
   A__F(if(f(true), z1, z2)) -> c1(MARK(if(f(true), z1, z2)))
   A__F(if(f(false), z1, z2)) -> c1(MARK(if(f(false), z1, z2)))
   A__F(if(c, if(false, y0, y1), z2)) -> c1(MARK(if(c, if(false, y0, y1), z2)))
   A__F(if(c, if(c, y0, y1), z2)) -> c1(MARK(if(c, if(c, y0, y1), z2)))
   A__F(if(c, f(f(y0)), z2)) -> c1(MARK(if(c, f(f(y0)), z2)))
   A__F(if(c, f(f(f(y0))), z2)) -> c1(MARK(if(c, f(f(f(y0))), z2)))
   A__F(if(c, f(f(if(y0, y1, y2))), z2)) -> c1(MARK(if(c, f(f(if(y0, y1, y2))), z2)))
   A__F(if(c, f(f(c)), z2)) -> c1(MARK(if(c, f(f(c)), z2)))
   A__F(if(c, f(if(y0, y1, y2)), z2)) -> c1(MARK(if(c, f(if(y0, y1, y2)), z2)))
   A__F(if(c, f(if(y0, f(y1), y2)), z2)) -> c1(MARK(if(c, f(if(y0, f(y1), y2)), z2)))
   A__F(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)) -> c1(MARK(if(c, f(if(y0, if(y1, y2, y3), y4)), z2)))
   A__F(if(c, f(if(y0, c, y1)), z2)) -> c1(MARK(if(c, f(if(y0, c, y1)), z2)))
   A__F(if(c, f(if(y0, true, y1)), z2)) -> c1(MARK(if(c, f(if(y0, true, y1)), z2)))
   A__F(if(c, f(if(y0, false, y1)), z2)) -> c1(MARK(if(c, f(if(y0, false, y1)), z2)))
   A__F(if(c, f(if(f(y0), y1, y2)), z2)) -> c1(MARK(if(c, f(if(f(y0), y1, y2)), z2)))
   A__F(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)) -> c1(MARK(if(c, f(if(if(y0, y1, y2), y3, y4)), z2)))
   A__F(if(c, f(if(c, y0, y1)), z2)) -> c1(MARK(if(c, f(if(c, y0, y1)), z2)))
   A__F(if(c, f(if(true, y0, y1)), z2)) -> c1(MARK(if(c, f(if(true, y0, y1)), z2)))
   A__F(if(c, f(if(false, y0, y1)), z2)) -> c1(MARK(if(c, f(if(false, y0, y1)), z2)))
   A__F(if(c, if(y0, f(y1), y2), z2)) -> c1(MARK(if(c, if(y0, f(y1), y2), z2)))
   A__F(if(c, if(y0, f(f(y1)), y2), z2)) -> c1(MARK(if(c, if(y0, f(f(y1)), y2), z2)))
   A__F(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)) -> c1(MARK(if(c, if(y0, f(if(y1, y2, y3)), y4), z2)))
   A__F(if(c, if(y0, f(c), y1), z2)) -> c1(MARK(if(c, if(y0, f(c), y1), z2)))
   A__F(if(c, if(y0, f(true), y1), z2)) -> c1(MARK(if(c, if(y0, f(true), y1), z2)))
   A__F(if(c, if(y0, f(false), y1), z2)) -> c1(MARK(if(c, if(y0, f(false), y1), z2)))
   A__F(if(c, if(f(y0), f(y1), y2), z2)) -> c1(MARK(if(c, if(f(y0), f(y1), y2), z2)))
   A__F(if(c, if(if(y0, y1, y2), f(y3), y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), f(y3), y4), z2)))
   A__F(if(c, if(true, f(y0), y1), z2)) -> c1(MARK(if(c, if(true, f(y0), y1), z2)))
   A__F(if(c, if(false, f(y0), y1), z2)) -> c1(MARK(if(c, if(false, f(y0), y1), z2)))
   A__F(if(c, if(y0, if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, f(y2), y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(y1, f(y2), y3), y4), z2)))
   A__F(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(y1, if(y2, y3, y4), y5), y6), z2)))
   A__F(if(c, if(y0, if(y1, c, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, c, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, true, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, true, y2), y3), z2)))
   A__F(if(c, if(y0, if(y1, false, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(y1, false, y2), y3), z2)))
   A__F(if(c, if(y0, if(f(y1), y2, y3), y4), z2)) -> c1(MARK(if(c, if(y0, if(f(y1), y2, y3), y4), z2)))
   A__F(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)) -> c1(MARK(if(c, if(y0, if(if(y1, y2, y3), y4, y5), y6), z2)))
   A__F(if(c, if(y0, if(c, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(c, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(true, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(true, y1, y2), y3), z2)))
   A__F(if(c, if(y0, if(false, y1, y2), y3), z2)) -> c1(MARK(if(c, if(y0, if(false, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), if(y1, y2, y3), y4), z2)) -> c1(MARK(if(c, if(f(y0), if(y1, y2, y3), y4), z2)))
   A__F(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), if(y3, y4, y5), y6), z2)))
   A__F(if(c, if(true, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(true, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(false, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(false, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(y0), c, y1), z2)) -> c1(MARK(if(c, if(f(y0), c, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), c, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), c, y3), z2)))
   A__F(if(c, if(false, c, y0), z2)) -> c1(MARK(if(c, if(false, c, y0), z2)))
   A__F(if(c, if(f(y0), true, y1), z2)) -> c1(MARK(if(c, if(f(y0), true, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), true, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), true, y3), z2)))
   A__F(if(c, if(false, true, y0), z2)) -> c1(MARK(if(c, if(false, true, y0), z2)))
   A__F(if(c, if(f(y0), false, y1), z2)) -> c1(MARK(if(c, if(f(y0), false, y1), z2)))
   A__F(if(c, if(if(y0, y1, y2), false, y3), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), false, y3), z2)))
   A__F(if(c, if(false, false, y0), z2)) -> c1(MARK(if(c, if(false, false, y0), z2)))
   A__F(if(c, if(f(y0), y1, y2), z2)) -> c1(MARK(if(c, if(f(y0), y1, y2), z2)))
   A__F(if(c, if(f(f(y0)), y1, y2), z2)) -> c1(MARK(if(c, if(f(f(y0)), y1, y2), z2)))
   A__F(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)) -> c1(MARK(if(c, if(f(if(y0, y1, y2)), y3, y4), z2)))
   A__F(if(c, if(f(c), y0, y1), z2)) -> c1(MARK(if(c, if(f(c), y0, y1), z2)))
   A__F(if(c, if(if(y0, f(y1), y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, f(y1), y2), y3, y4), z2)))
   A__F(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(y0, if(y1, y2, y3), y4), y5, y6), z2)))
   A__F(if(c, if(if(y0, c, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, c, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, true, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, true, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, false, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(y0, false, y1), y2, y3), z2)))
   A__F(if(c, if(if(f(y0), y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(f(y0), y1, y2), y3, y4), z2)))
   A__F(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)) -> c1(MARK(if(c, if(if(if(y0, y1, y2), y3, y4), y5, y6), z2)))
   A__F(if(c, if(if(c, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(c, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(true, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(true, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(false, y0, y1), y2, y3), z2)) -> c1(MARK(if(c, if(if(false, y0, y1), y2, y3), z2)))
   A__F(if(c, if(if(y0, y1, y2), y3, y4), z2)) -> c1(MARK(if(c, if(if(y0, y1, y2), y3, y4), z2)))
   A__F(if(c, if(c, f(y0), y1), z2)) -> c1(MARK(if(c, if(c, f(y0), y1), z2)))
   A__F(if(c, if(c, if(y0, y1, y2), y3), z2)) -> c1(MARK(if(c, if(c, if(y0, y1, y2), y3), z2)))
   A__F(if(c, if(f(true), y0, y1), z2)) -> c1(MARK(if(c, if(f(true), y0, y1), z2)))
   A__F(if(c, if(f(false), y0, y1), z2)) -> c1(MARK(if(c, if(f(false), y0, y1), z2)))
   A__F(if(c, f(f(true)), z2)) -> c1(MARK(if(c, f(f(true)), z2)))
   A__F(if(c, f(f(false)), z2)) -> c1(MARK(if(c, f(f(false)), z2)))
   MARK(if(false, c, if(false, y1, y2))) -> c7(A__IF(false, c, if(false, y1, y2)))
   MARK(if(false, c, if(c, y1, y2))) -> c7(A__IF(false, c, if(c, y1, y2)))
   MARK(if(false, c, f(f(y1)))) -> c7(A__IF(false, c, f(f(y1))))
   MARK(if(false, c, f(f(f(y1))))) -> c7(A__IF(false, c, f(f(f(y1)))))
   MARK(if(false, c, f(f(if(y1, y2, y3))))) -> c7(A__IF(false, c, f(f(if(y1, y2, y3)))))
   MARK(if(false, c, f(f(false)))) -> c7(A__IF(false, c, f(f(false))))
   MARK(if(false, c, f(f(c)))) -> c7(A__IF(false, c, f(f(c))))
   MARK(if(false, c, f(if(y1, y2, y3)))) -> c7(A__IF(false, c, f(if(y1, y2, y3))))
   MARK(if(false, c, f(if(y1, f(y2), y3)))) -> c7(A__IF(false, c, f(if(y1, f(y2), y3))))
   MARK(if(false, c, f(if(y1, if(y2, y3, y4), y5)))) -> c7(A__IF(false, c, f(if(y1, if(y2, y3, y4), y5))))
   MARK(if(false, c, f(if(y1, c, y2)))) -> c7(A__IF(false, c, f(if(y1, c, y2))))
   MARK(if(false, c, f(if(y1, true, y2)))) -> c7(A__IF(false, c, f(if(y1, true, y2))))
   MARK(if(false, c, f(if(y1, false, y2)))) -> c7(A__IF(false, c, f(if(y1, false, y2))))
   MARK(if(false, c, f(if(f(y1), y2, y3)))) -> c7(A__IF(false, c, f(if(f(y1), y2, y3))))
   MARK(if(false, c, f(if(if(y1, y2, y3), y4, y5)))) -> c7(A__IF(false, c, f(if(if(y1, y2, y3), y4, y5))))
   MARK(if(false, c, f(if(c, y1, y2)))) -> c7(A__IF(false, c, f(if(c, y1, y2))))
   MARK(if(false, c, f(if(true, y1, y2)))) -> c7(A__IF(false, c, f(if(true, y1, y2))))
   MARK(if(false, c, f(if(false, y1, y2)))) -> c7(A__IF(false, c, f(if(false, y1, y2))))
   MARK(if(false, c, if(y1, f(y2), y3))) -> c7(A__IF(false, c, if(y1, f(y2), y3)))
   MARK(if(false, c, if(y1, f(f(y2)), y3))) -> c7(A__IF(false, c, if(y1, f(f(y2)), y3)))
   MARK(if(false, c, if(y1, f(if(y2, y3, y4)), y5))) -> c7(A__IF(false, c, if(y1, f(if(y2, y3, y4)), y5)))
   MARK(if(false, c, if(y1, f(c), y2))) -> c7(A__IF(false, c, if(y1, f(c), y2)))
   MARK(if(false, c, if(y1, f(true), y2))) -> c7(A__IF(false, c, if(y1, f(true), y2)))
   MARK(if(false, c, if(y1, f(false), y2))) -> c7(A__IF(false, c, if(y1, f(false), y2)))
   MARK(if(false, c, if(f(y1), f(y2), y3))) -> c7(A__IF(false, c, if(f(y1), f(y2), y3)))
   MARK(if(false, c, if(if(y1, y2, y3), f(y4), y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), f(y4), y5)))
   MARK(if(false, c, if(true, f(y1), y2))) -> c7(A__IF(false, c, if(true, f(y1), y2)))
   MARK(if(false, c, if(false, f(y1), y2))) -> c7(A__IF(false, c, if(false, f(y1), y2)))
   MARK(if(false, c, if(y1, if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, y3, y4), y5)))
   MARK(if(false, c, if(y1, if(y2, f(y3), y4), y5))) -> c7(A__IF(false, c, if(y1, if(y2, f(y3), y4), y5)))
   MARK(if(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7))) -> c7(A__IF(false, c, if(y1, if(y2, if(y3, y4, y5), y6), y7)))
   MARK(if(false, c, if(y1, if(y2, c, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, c, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, true, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, true, y3), y4)))
   MARK(if(false, c, if(y1, if(y2, false, y3), y4))) -> c7(A__IF(false, c, if(y1, if(y2, false, y3), y4)))
   MARK(if(false, c, if(y1, if(f(y2), y3, y4), y5))) -> c7(A__IF(false, c, if(y1, if(f(y2), y3, y4), y5)))
   MARK(if(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7))) -> c7(A__IF(false, c, if(y1, if(if(y2, y3, y4), y5, y6), y7)))
   MARK(if(false, c, if(y1, if(c, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(c, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(true, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(true, y2, y3), y4)))
   MARK(if(false, c, if(y1, if(false, y2, y3), y4))) -> c7(A__IF(false, c, if(y1, if(false, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), if(y2, y3, y4), y5))) -> c7(A__IF(false, c, if(f(y1), if(y2, y3, y4), y5)))
   MARK(if(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7))) -> c7(A__IF(false, c, if(if(y1, y2, y3), if(y4, y5, y6), y7)))
   MARK(if(false, c, if(true, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(true, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(false, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(false, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(y1), c, y2))) -> c7(A__IF(false, c, if(f(y1), c, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), c, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), c, y4)))
   MARK(if(false, c, if(false, c, y1))) -> c7(A__IF(false, c, if(false, c, y1)))
   MARK(if(false, c, if(f(y1), true, y2))) -> c7(A__IF(false, c, if(f(y1), true, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), true, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), true, y4)))
   MARK(if(false, c, if(false, true, y1))) -> c7(A__IF(false, c, if(false, true, y1)))
   MARK(if(false, c, if(f(y1), false, y2))) -> c7(A__IF(false, c, if(f(y1), false, y2)))
   MARK(if(false, c, if(if(y1, y2, y3), false, y4))) -> c7(A__IF(false, c, if(if(y1, y2, y3), false, y4)))
   MARK(if(false, c, if(false, false, y1))) -> c7(A__IF(false, c, if(false, false, y1)))
   MARK(if(false, c, if(f(y1), y2, y3))) -> c7(A__IF(false, c, if(f(y1), y2, y3)))
   MARK(if(false, c, if(f(f(y1)), y2, y3))) -> c7(A__IF(false, c, if(f(f(y1)), y2, y3)))
   MARK(if(false, c, if(f(if(y1, y2, y3)), y4, y5))) -> c7(A__IF(false, c, if(f(if(y1, y2, y3)), y4, y5)))
   MARK(if(false, c, if(f(false), y1, y2))) -> c7(A__IF(false, c, if(f(false), y1, y2)))
   MARK(if(false, c, if(f(c), y1, y2))) -> c7(A__IF(false, c, if(f(c), y1, y2)))
   MARK(if(false, c, if(if(y1, f(y2), y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, f(y2), y3), y4, y5)))
   MARK(if(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7))) -> c7(A__IF(false, c, if(if(y1, if(y2, y3, y4), y5), y6, y7)))
   MARK(if(false, c, if(if(y1, c, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, c, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, true, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, true, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, false, y2), y3, y4))) -> c7(A__IF(false, c, if(if(y1, false, y2), y3, y4)))
   MARK(if(false, c, if(if(f(y1), y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(f(y1), y2, y3), y4, y5)))
   MARK(if(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7))) -> c7(A__IF(false, c, if(if(if(y1, y2, y3), y4, y5), y6, y7)))
   MARK(if(false, c, if(if(c, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(c, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(true, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(true, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(false, y1, y2), y3, y4))) -> c7(A__IF(false, c, if(if(false, y1, y2), y3, y4)))
   MARK(if(false, c, if(if(y1, y2, y3), y4, y5))) -> c7(A__IF(false, c, if(if(y1, y2, y3), y4, y5)))
   MARK(if(false, c, if(c, f(y1), y2))) -> c7(A__IF(false, c, if(c, f(y1), y2)))
   MARK(if(false, c, if(c, if(y1, y2, y3), y4))) -> c7(A__IF(false, c, if(c, if(y1, y2, y3), y4)))
   MARK(if(false, c, if(f(true), y1, y2))) -> c7(A__IF(false, c, if(f(true), y1, y2)))
   MARK(if(false, c, f(f(true)))) -> c7(A__IF(false, c, f(f(true))))
K tuples:none
Defined Rule Symbols:   a__f_1, a__if_3, mark_1

Defined Pair Symbols:   MARK_1, A__F_1, A__IF_3

Compound Symbols:   c7_1, c8_2, c1_1, c6_2, c6_1, c7_2, c8_1, c3_1, c4_1


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

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

(174)
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:

   a__f(X) -> a__if(mark(X), c, f(true)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   mark(f(X)) -> a__f(mark(X)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3) [1]
   mark(c) -> c [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__f(X) -> f(X) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]

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

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

(176)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__f(X) -> a__if(mark(X), c, f(true)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   mark(f(X)) -> a__f(mark(X)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3) [1]
   mark(c) -> c [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__f(X) -> f(X) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]

The TRS has the following type information:
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
false :: c:true:f:false:if
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if

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

(177) 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:
none

(c) The following functions are completely defined:

   mark_1
   a__if_3
   a__f_1

Due to the following rules being added:
none

And the following fresh constants: none

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

(178)
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:

   a__f(X) -> a__if(mark(X), c, f(true)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   mark(f(X)) -> a__f(mark(X)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3) [1]
   mark(c) -> c [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__f(X) -> f(X) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]

The TRS has the following type information:
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
false :: c:true:f:false:if
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if

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

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

(180)
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:

   a__f(f(X')) -> a__if(a__f(mark(X')), c, f(true)) [2]
   a__f(if(X1', X2', X3')) -> a__if(a__if(mark(X1'), mark(X2'), X3'), c, f(true)) [2]
   a__f(c) -> a__if(c, c, f(true)) [2]
   a__f(true) -> a__if(true, c, f(true)) [2]
   a__f(false) -> a__if(false, c, f(true)) [2]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   mark(f(f(X''))) -> a__f(a__f(mark(X''))) [2]
   mark(f(if(X1'', X2'', X3''))) -> a__f(a__if(mark(X1''), mark(X2''), X3'')) [2]
   mark(f(c)) -> a__f(c) [2]
   mark(f(true)) -> a__f(true) [2]
   mark(f(false)) -> a__f(false) [2]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3) [1]
   mark(c) -> c [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__f(X) -> f(X) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]

The TRS has the following type information:
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
false :: c:true:f:false:if
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if

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

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

   c => 0
   true => 2
   false => 1

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

(182)
Obligation:
Complexity RNTS consisting of the following rules:

   a__f(z) -{ 2 }-> a__if(a__if(mark(X1'), mark(X2'), X3'), 0, 1 + 2) :|: X3' >= 0, X2' >= 0, z = 1 + X1' + X2' + X3', X1' >= 0
   a__f(z) -{ 2 }-> a__if(a__f(mark(X')), 0, 1 + 2) :|: X' >= 0, z = 1 + X'
   a__f(z) -{ 2 }-> a__if(2, 0, 1 + 2) :|: z = 2
   a__f(z) -{ 2 }-> a__if(1, 0, 1 + 2) :|: z = 1
   a__f(z) -{ 2 }-> a__if(0, 0, 1 + 2) :|: z = 0
   a__f(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   mark(z) -{ 1 }-> a__if(mark(X1), mark(X2), X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__f(a__if(mark(X1''), mark(X2''), X3'')) :|: X1'' >= 0, X3'' >= 0, X2'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'')
   mark(z) -{ 2 }-> a__f(a__f(mark(X''))) :|: z = 1 + (1 + X''), X'' >= 0
   mark(z) -{ 2 }-> a__f(2) :|: z = 1 + 2
   mark(z) -{ 2 }-> a__f(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__f(0) :|: z = 1 + 0
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0


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

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

(184)
Obligation:
Complexity RNTS consisting of the following rules:

   a__f(z) -{ 2 }-> a__if(a__if(mark(X1'), mark(X2'), X3'), 0, 1 + 2) :|: X3' >= 0, X2' >= 0, z = 1 + X1' + X2' + X3', X1' >= 0
   a__f(z) -{ 2 }-> a__if(a__f(mark(z - 1)), 0, 1 + 2) :|: z - 1 >= 0
   a__f(z) -{ 2 }-> a__if(2, 0, 1 + 2) :|: z = 2
   a__f(z) -{ 2 }-> a__if(1, 0, 1 + 2) :|: z = 1
   a__f(z) -{ 2 }-> a__if(0, 0, 1 + 2) :|: z = 0
   a__f(z) -{ 1 }-> 1 + z :|: z >= 0
   a__if(z, z', z'') -{ 1 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0
   a__if(z, z', z'') -{ 1 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   mark(z) -{ 1 }-> a__if(mark(X1), mark(X2), X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__f(a__if(mark(X1''), mark(X2''), X3'')) :|: X1'' >= 0, X3'' >= 0, X2'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'')
   mark(z) -{ 2 }-> a__f(a__f(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__f(2) :|: z = 1 + 2
   mark(z) -{ 2 }-> a__f(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__f(0) :|: z = 1 + 0
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0


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

(185) 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:
none

And the following fresh constants: none

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

(186)
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:

   a__f(X) -> a__if(mark(X), c, f(true)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   mark(f(X)) -> a__f(mark(X)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), mark(X2), X3) [1]
   mark(c) -> c [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__f(X) -> f(X) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]

The TRS has the following type information:
a__f :: c:true:f:false:if -> c:true:f:false:if
a__if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if
mark :: c:true:f:false:if -> c:true:f:false:if
c :: c:true:f:false:if
f :: c:true:f:false:if -> c:true:f:false:if
true :: c:true:f:false:if
false :: c:true:f:false:if
if :: c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if -> c:true:f:false:if

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

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

   c => 0
   true => 2
   false => 1

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

(188)
Obligation:
Complexity RNTS consisting of the following rules:

   a__f(z) -{ 1 }-> a__if(mark(X), 0, 1 + 2) :|: X >= 0, z = X
   a__f(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   mark(z) -{ 1 }-> a__if(mark(X1), mark(X2), X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__f(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0

Only complete derivations are relevant for the runtime complexity.