Problem:
 a__g(X) -> a__h(X)
 a__c() -> d()
 a__h(d()) -> a__g(c())
 mark(g(X)) -> a__g(X)
 mark(h(X)) -> a__h(X)
 mark(c()) -> a__c()
 mark(d()) -> d()
 a__g(X) -> g(X)
 a__h(X) -> h(X)
 a__c() -> c()

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {8,7,6,5}
   transitions:
    c1() -> 29*
    h1(65) -> 66*
    h1(79) -> 80*
    h1(71) -> 72*
    h1(73) -> 74*
    g1(55) -> 56*
    g1(57) -> 58*
    g1(49) -> 50*
    g1(63) -> 64*
    d1() -> 25*
    a__c1() -> 47*
    a__h1(15) -> 16*
    a__h1(17) -> 18*
    a__h1(9) -> 10*
    a__h1(23) -> 24*
    a__g1(45) -> 46*
    a__g1(37) -> 38*
    a__g1(39) -> 40*
    a__g1(29) -> 30*
    a__g1(31) -> 32*
    c2() -> 139*
    h2(137) -> 138*
    h2(129) -> 130*
    h2(131) -> 132*
    h2(123) -> 124*
    a__g0(2) -> 5*
    a__g0(4) -> 5*
    a__g0(1) -> 5*
    a__g0(3) -> 5*
    g2(107) -> 108*
    g2(121) -> 122*
    g2(113) -> 114*
    g2(115) -> 116*
    g2(105) -> 106*
    a__h0(2) -> 7*
    a__h0(4) -> 7*
    a__h0(1) -> 7*
    a__h0(3) -> 7*
    d2() -> 101*
    a__c0() -> 6*
    a__h2(85) -> 86*
    a__h2(99) -> 100*
    a__h2(91) -> 92*
    a__h2(93) -> 94*
    a__h2(83) -> 84*
    d0() -> 1*
    h3(147) -> 148*
    h3(159) -> 160*
    h3(141) -> 142*
    h3(153) -> 154*
    h3(155) -> 156*
    c0() -> 2*
    mark0(2) -> 8*
    mark0(4) -> 8*
    mark0(1) -> 8*
    mark0(3) -> 8*
    g0(2) -> 3*
    g0(4) -> 3*
    g0(1) -> 3*
    g0(3) -> 3*
    h0(2) -> 4*
    h0(4) -> 4*
    h0(1) -> 4*
    h0(3) -> 4*
    1 -> 71,55,39,15
    2 -> 79,63,31,23
    3 -> 65,49,45,9
    4 -> 73,57,37,17
    9 -> 131*
    10 -> 8,5
    15 -> 137*
    16 -> 8,5
    17 -> 123*
    18 -> 8,5
    23 -> 129*
    24 -> 8,5
    25 -> 8,6
    29 -> 107,85,6
    30 -> 94,40,16,5,8,7
    31 -> 113,91
    32 -> 8*
    37 -> 105,83
    38 -> 8*
    39 -> 115,93
    40 -> 8*
    45 -> 121,99
    46 -> 8*
    47 -> 8*
    50 -> 5*
    56 -> 5*
    58 -> 5*
    64 -> 5*
    66 -> 7*
    72 -> 7*
    74 -> 7*
    80 -> 7*
    83 -> 159*
    84 -> 38*
    85 -> 141*
    86 -> 30*
    91 -> 153*
    92 -> 32*
    93 -> 155*
    94 -> 40,8
    99 -> 147*
    100 -> 46,8
    101 -> 47,8
    106 -> 38*
    108 -> 30*
    114 -> 32*
    116 -> 40,8
    122 -> 46,8
    124 -> 18*
    130 -> 24*
    132 -> 10,8,5
    138 -> 16,8,5
    139 -> 47,8
    142 -> 86,30,16
    148 -> 100,46
    154 -> 92,32
    156 -> 94,40
    160 -> 84,38
  problem:
   
  Qed