10.25/2.97	YES
10.25/2.98	
10.25/2.98	Problem:
10.25/2.98	 p(0(x1)) -> 0(s(s(p(x1))))
10.25/2.98	 p(s(x1)) -> x1
10.25/2.98	 p(p(s(x1))) -> p(x1)
10.25/2.98	 f(s(x1)) -> p(s(g(p(s(s(x1))))))
10.25/2.98	 g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
10.25/2.98	 j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
10.25/2.98	 half(0(x1)) -> 0(s(s(half(p(s(p(s(x1))))))))
10.25/2.98	 half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
10.25/2.98	 rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))
10.25/2.98	
10.25/2.98	Proof:
10.25/2.98	 Bounds Processor:
10.25/2.98	  bound: 3
10.25/2.98	  enrichment: match
10.25/2.98	  automaton:
10.25/2.98	   final states: {38,35,31,22,12,6,3,2,1}
10.25/2.98	   transitions:
10.25/2.98	    p1(75) -> 76*
10.25/2.98	    p1(55) -> 56*
10.25/2.98	    p1(72) -> 73*
10.25/2.98	    p1(47) -> 48*
10.25/2.98	    p1(94) -> 95*
10.25/2.98	    p1(81) -> 82*
10.25/2.98	    p1(88) -> 89*
10.25/2.98	    p1(78) -> 79*
10.25/2.98	    p1(73) -> 74*
10.25/2.98	    p1(53) -> 54*
10.25/2.98	    p1(95) -> 96*
10.25/2.98	    s1(80) -> 81*
10.25/2.98	    s1(92) -> 93*
10.25/2.98	    s1(87) -> 88*
10.25/2.98	    s1(77) -> 78*
10.25/2.98	    s1(89) -> 90*
10.25/2.98	    s1(79) -> 80*
10.25/2.98	    s1(74) -> 75*
10.25/2.98	    s1(91) -> 92*
10.25/2.98	    s1(71) -> 72*
10.25/2.98	    s1(93) -> 94*
10.25/2.98	    f1(76) -> 77*
10.25/2.98	    j1(90) -> 91*
10.25/2.98	    p2(107) -> 108*
10.25/2.98	    p2(119) -> 120*
10.25/2.98	    p2(116) -> 117*
10.25/2.98	    p2(111) -> 112*
10.25/2.98	    p2(113) -> 114*
10.25/2.98	    p2(83) -> 84*
10.25/2.98	    p2(110) -> 111*
10.25/2.98	    s2(117) -> 118*
10.25/2.98	    s2(112) -> 113*
10.25/2.98	    s2(109) -> 110*
10.25/2.98	    s2(118) -> 119*
10.25/2.98	    s2(115) -> 116*
10.25/2.98	    f2(114) -> 115*
10.25/2.98	    p3(135) -> 136*
10.25/2.98	    f80() -> 2*
10.25/2.98	    00(5) -> 1*
10.25/2.98	    00(42) -> 43*
10.25/2.98	    00(44) -> 45*
10.25/2.98	    00(39) -> 40*
10.25/2.98	    00(34) -> 31*
10.25/2.98	    00(46) -> 38*
10.25/2.98	    00(41) -> 42*
10.25/2.98	    00(43) -> 44*
10.25/2.98	    s0(45) -> 46*
10.25/2.98	    s0(40) -> 41*
10.25/2.98	    s0(15) -> 16*
10.25/2.98	    s0(10) -> 11*
10.25/2.98	    s0(37) -> 35*
10.25/2.98	    s0(32) -> 33*
10.25/2.98	    s0(17) -> 18*
10.25/2.98	    s0(7) -> 8*
10.25/2.98	    s0(2) -> 7*
10.25/2.98	    s0(29) -> 30*
10.25/2.98	    s0(19) -> 20*
10.25/2.98	    s0(4) -> 5*
10.25/2.98	    s0(26) -> 27*
10.25/2.98	    s0(33) -> 34*
10.25/2.98	    s0(28) -> 29*
10.25/2.98	    s0(23) -> 24*
10.25/2.98	    s0(18) -> 19*
10.25/2.98	    s0(13) -> 14*
10.25/2.98	    s0(3) -> 4*
10.25/2.98	    p0(30) -> 22*
10.25/2.98	    p0(20) -> 21*
10.25/2.98	    p0(27) -> 28*
10.25/2.98	    p0(7) -> 13*
10.25/2.98	    p0(2) -> 3*
10.25/2.98	    p0(24) -> 25*
10.25/2.98	    p0(14) -> 15*
10.25/2.98	    p0(9) -> 36*
10.25/2.98	    p0(21) -> 12*
10.25/2.98	    p0(11) -> 6*
10.25/2.98	    p0(13) -> 23*
10.25/2.98	    p0(8) -> 9*
10.25/2.98	    g0(9) -> 10*
10.25/2.98	    j0(16) -> 17*
10.25/2.98	    f0(25) -> 26*
10.25/2.98	    half0(15) -> 32*
10.25/2.98	    half0(36) -> 37*
10.25/2.98	    rd0(2) -> 39*
10.25/2.98	    1 -> 136,54,23,25,3,84,112
10.25/2.98	    2 -> 136,54,23,25,3,84,112,56,53,13
10.25/2.98	    6 -> 115,77,26,28,79,117
10.25/2.98	    7 -> 55,9
10.25/2.98	    10 -> 6*
10.25/2.98	    13 -> 15*
10.25/2.98	    15 -> 71*
10.25/2.98	    18 -> 48*
10.25/2.98	    19 -> 47,21
10.25/2.98	    23 -> 25*
10.25/2.98	    26 -> 28*
10.25/2.98	    29 -> 22*
10.25/2.98	    31 -> 32,37
10.25/2.98	    35 -> 32,37
10.25/2.98	    38 -> 39*
10.25/2.98	    48 -> 12*
10.25/2.98	    54 -> 23*
10.25/2.98	    56 -> 36*
10.25/2.98	    71 -> 83,73
10.25/2.98	    73 -> 87*
10.25/2.98	    74 -> 76*
10.25/2.98	    77 -> 79*
10.25/2.98	    80 -> 82*
10.25/2.98	    82 -> 17*
10.25/2.98	    84 -> 74*
10.25/2.98	    87 -> 89*
10.25/2.98	    89 -> 109*
10.25/2.98	    92 -> 108,96
10.25/2.98	    93 -> 107,95
10.25/2.98	    96 -> 10,6
10.25/2.98	    108 -> 96*
10.25/2.98	    109 -> 135,111
10.25/2.98	    112 -> 114*
10.25/2.98	    115 -> 117*
10.25/2.98	    118 -> 120,91
10.25/2.98	    120 -> 91*
10.25/2.98	    136 -> 112*
10.25/2.98	  problem:
10.25/2.98	   
10.25/2.98	  Qed
10.25/2.98	EOF