8.84/2.60	YES
8.84/2.60	
8.84/2.60	Problem:
8.84/2.60	 a(a(x1)) -> b(b(b(x1)))
8.84/2.60	 a(x1) -> d(c(d(x1)))
8.84/2.60	 b(b(b(x1))) -> a(f(x1))
8.84/2.60	 b(b(x1)) -> c(c(c(x1)))
8.84/2.60	 c(c(x1)) -> d(d(d(x1)))
8.84/2.60	 c(d(d(x1))) -> f(x1)
8.84/2.60	 f(f(x1)) -> f(a(x1))
8.84/2.60	
8.84/2.60	Proof:
8.84/2.60	 Bounds Processor:
8.84/2.60	  bound: 3
8.84/2.60	  enrichment: match
8.84/2.60	  automaton:
8.84/2.60	   final states: {15,9,13,10,8,5,1}
8.84/2.60	   transitions:
8.84/2.60	    d1(62) -> 63*
8.84/2.60	    d1(17) -> 18*
8.84/2.60	    d1(154) -> 155*
8.84/2.60	    d1(59) -> 60*
8.84/2.60	    d1(29) -> 30*
8.84/2.60	    d1(19) -> 20*
8.84/2.60	    d1(61) -> 62*
8.84/2.60	    d1(31) -> 32*
8.84/2.60	    d1(153) -> 154*
8.84/2.60	    d1(63) -> 64*
8.84/2.60	    d1(58) -> 59*
8.84/2.60	    d1(155) -> 156*
8.84/2.60	    c1(45) -> 46*
8.84/2.60	    c1(30) -> 31*
8.84/2.60	    c1(47) -> 48*
8.84/2.60	    c1(49) -> 50*
8.84/2.60	    c1(44) -> 45*
8.84/2.60	    c1(48) -> 49*
8.84/2.60	    c1(43) -> 44*
8.84/2.60	    c1(18) -> 19*
8.84/2.60	    a1(122) -> 123*
8.84/2.60	    a1(34) -> 35*
8.84/2.60	    f1(169) -> 170*
8.84/2.60	    f1(109) -> 110*
8.84/2.60	    f1(123) -> 124*
8.84/2.60	    f1(33) -> 34*
8.84/2.60	    d2(85) -> 86*
8.84/2.60	    d2(75) -> 76*
8.84/2.60	    d2(127) -> 128*
8.84/2.60	    d2(97) -> 98*
8.84/2.60	    d2(82) -> 83*
8.84/2.60	    d2(99) -> 100*
8.84/2.60	    d2(101) -> 102*
8.84/2.60	    d2(96) -> 97*
8.84/2.60	    d2(86) -> 87*
8.84/2.60	    d2(81) -> 82*
8.84/2.60	    d2(83) -> 84*
8.84/2.60	    d2(73) -> 74*
8.84/2.60	    d2(125) -> 126*
8.84/2.60	    d2(100) -> 101*
8.84/2.60	    d2(95) -> 96*
8.84/2.60	    c2(74) -> 75*
8.84/2.60	    c2(126) -> 127*
8.84/2.60	    f2(117) -> 118*
8.84/2.60	    f2(149) -> 150*
8.84/2.60	    f2(161) -> 162*
8.84/2.60	    f2(111) -> 112*
8.84/2.60	    f2(165) -> 166*
8.84/2.60	    f50() -> 2*
8.84/2.60	    f3(135) -> 136*
8.84/2.60	    b0(2) -> 3*
8.84/2.60	    b0(4) -> 1*
8.84/2.60	    b0(3) -> 4*
8.84/2.60	    a2(139) -> 140*
8.84/2.60	    d0(7) -> 5*
8.84/2.60	    d0(2) -> 6*
8.84/2.60	    d0(14) -> 13*
8.84/2.60	    d0(6) -> 14*
8.84/2.60	    d3(141) -> 142*
8.84/2.60	    d3(143) -> 144*
8.84/2.60	    c0(12) -> 10*
8.84/2.60	    c0(2) -> 11*
8.84/2.60	    c0(11) -> 12*
8.84/2.60	    c0(6) -> 7*
8.84/2.60	    c3(142) -> 143*
8.84/2.60	    a0(2) -> 16*
8.84/2.60	    a0(9) -> 8*
8.84/2.60	    f0(2) -> 9*
8.84/2.60	    f0(16) -> 15*
8.84/2.60	    1 -> 16*
8.84/2.60	    2 -> 43,33,29
8.84/2.60	    3 -> 47*
8.84/2.60	    6 -> 169*
8.84/2.60	    8 -> 3,47,95,4
8.84/2.60	    9 -> 44,11,61,81,31,7,17
8.84/2.60	    10 -> 3,47,95
8.84/2.60	    11 -> 61*
8.84/2.60	    12 -> 153*
8.84/2.60	    13 -> 44,11,61,81
8.84/2.60	    15 -> 150,143,34,9,17,73
8.84/2.60	    20 -> 8*
8.84/2.60	    29 -> 149*
8.84/2.60	    30 -> 58*
8.84/2.60	    32 -> 16*
8.84/2.60	    34 -> 73*
8.84/2.60	    35 -> 1*
8.84/2.60	    43 -> 99*
8.84/2.60	    44 -> 81*
8.84/2.60	    46 -> 4*
8.84/2.60	    47 -> 95*
8.84/2.60	    48 -> 85*
8.84/2.60	    50 -> 1*
8.84/2.60	    58 -> 109*
8.84/2.60	    60 -> 12*
8.84/2.60	    62 -> 161*
8.84/2.60	    64 -> 10*
8.84/2.60	    76 -> 50,35,1
8.84/2.60	    84 -> 46,4
8.84/2.60	    87 -> 75*
8.84/2.60	    95 -> 135*
8.84/2.60	    96 -> 117*
8.84/2.60	    98 -> 49*
8.84/2.60	    100 -> 111*
8.84/2.60	    102 -> 45*
8.84/2.60	    109 -> 139*
8.84/2.60	    110 -> 10*
8.84/2.60	    112 -> 46,4
8.84/2.60	    117 -> 122*
8.84/2.60	    118 -> 50,1
8.84/2.60	    122 -> 125*
8.84/2.60	    124 -> 15*
8.84/2.60	    128 -> 123*
8.84/2.60	    136 -> 127*
8.84/2.60	    139 -> 141*
8.84/2.60	    140 -> 135*
8.84/2.60	    144 -> 140,135
8.84/2.60	    150 -> 143*
8.84/2.60	    154 -> 165*
8.84/2.60	    156 -> 48*
8.84/2.60	    162 -> 48,85
8.84/2.60	    166 -> 49*
8.84/2.60	    170 -> 45,12
8.84/2.60	  problem:
8.84/2.60	   
8.84/2.60	  Qed
8.84/2.61	EOF