/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 twoto(0(x1)) -> p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1))))))))))))))))
 twoto(s(x1)) ->
 p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
 twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
 twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(s(p(s(x1)))))))
 0(x1) -> x1

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [twice](x0) = x0,
   
   [p](x0) = x0,
   
   [s](x0) = x0,
   
   [twoto](x0) = 4x0,
   
   [0](x0) = 4x0 + 2
  orientation:
   twoto(0(x1)) = 16x1 + 8 >= 4x1 + 2 = p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1))))))))))))))))
   
   twoto(s(x1)) = 4x1 >= 4x1 = p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
   
   twice(0(x1)) = 4x1 + 2 >= 4x1 + 2 = p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
   
   twice(s(x1)) = x1 >= x1 = s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
   
   p(p(s(x1))) = x1 >= x1 = p(x1)
   
   p(s(x1)) = x1 >= x1 = x1
   
   p(0(x1)) = 4x1 + 2 >= 4x1 + 2 = 0(s(s(s(s(p(s(x1)))))))
   
   0(x1) = 4x1 + 2 >= x1 = x1
  problem:
   twoto(s(x1)) ->
   p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
   twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
   twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
   p(p(s(x1))) -> p(x1)
   p(s(x1)) -> x1
   p(0(x1)) -> 0(s(s(s(s(p(s(x1)))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {54,2,53,38,28,1}
    transitions:
     p1(55) -> 56*
     p1(87) -> 88*
     p1(77) -> 78*
     p1(79) -> 80*
     p1(69) -> 70*
     p1(71) -> 72*
     p1(61) -> 62*
     p1(63) -> 64*
     p1(85) -> 86*
     f50() -> 2*
     p0(50) -> 51*
     p0(35) -> 36*
     p0(15) -> 16*
     p0(10) -> 11*
     p0(5) -> 6*
     p0(37) -> 28*
     p0(27) -> 1*
     p0(22) -> 23*
     p0(12) -> 13*
     p0(2) -> 53*
     p0(49) -> 50*
     p0(39) -> 40*
     p0(51) -> 52*
     p0(41) -> 42*
     p0(31) -> 32*
     p0(26) -> 27*
     p0(21) -> 22*
     p0(16) -> 17*
     p0(11) -> 12*
     p0(48) -> 49*
     p0(23) -> 24*
     p0(3) -> 4*
     s0(45) -> 46*
     s0(40) -> 41*
     s0(30) -> 31*
     s0(25) -> 26*
     s0(20) -> 21*
     s0(5) -> 29*
     s0(52) -> 38*
     s0(47) -> 48*
     s0(32) -> 33*
     s0(7) -> 8*
     s0(2) -> 3*
     s0(44) -> 45*
     s0(34) -> 35*
     s0(29) -> 30*
     s0(24) -> 25*
     s0(19) -> 20*
     s0(14) -> 15*
     s0(9) -> 10*
     s0(4) -> 5*
     s0(46) -> 47*
     s0(36) -> 37*
     s0(6) -> 39*
     s0(43) -> 44*
     s0(18) -> 19*
     s0(13) -> 14*
     s0(8) -> 9*
     twice0(42) -> 43*
     twice0(17) -> 18*
     twoto0(6) -> 7*
     00(31) -> 54*
     00(33) -> 34*
     1 -> 7,78,13,17
     2 -> 53,4
     4 -> 6*
     6 -> 40*
     7 -> 78*
     8 -> 64,12,77
     9 -> 11,63
     13 -> 62*
     14 -> 16,61
     18 -> 80,24,72
     19 -> 56,23,79
     20 -> 22,55
     24 -> 72,1
     25 -> 27,71
     28 -> 43*
     30 -> 32*
     34 -> 53,36
     36 -> 28*
     38 -> 43*
     40 -> 42*
     44 -> 88*
     45 -> 86,87
     46 -> 70,85
     47 -> 49,69
     56 -> 23*
     62 -> 17*
     64 -> 12*
     70 -> 50*
     72 -> 1*
     78 -> 13*
     80 -> 24*
     86 -> 51*
     88 -> 52*
   problem:
    
   Qed