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


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YES

Problem:
 p(0(x1)) -> 0(s(s(p(x1))))
 p(s(x1)) -> x1
 p(p(s(x1))) -> p(x1)
 f(s(x1)) -> p(s(g(p(s(s(x1))))))
 g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
 j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
 half(0(x1)) -> 0(s(s(half(p(s(p(s(x1))))))))
 half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
 rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [rd](x0) = 7x0,
   
   [half](x0) = x0,
   
   [j](x0) = x0,
   
   [g](x0) = x0,
   
   [f](x0) = x0,
   
   [s](x0) = x0,
   
   [p](x0) = x0,
   
   [0](x0) = x0 + 4
  orientation:
   p(0(x1)) = x1 + 4 >= x1 + 4 = 0(s(s(p(x1))))
   
   p(s(x1)) = x1 >= x1 = x1
   
   p(p(s(x1))) = x1 >= x1 = p(x1)
   
   f(s(x1)) = x1 >= x1 = p(s(g(p(s(s(x1))))))
   
   g(s(x1)) = x1 >= x1 = p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
   
   j(s(x1)) = x1 >= x1 = p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
   
   half(0(x1)) = x1 + 4 >= x1 + 4 = 0(s(s(half(p(s(p(s(x1))))))))
   
   half(s(s(x1))) = x1 >= x1 = s(half(p(p(s(s(x1))))))
   
   rd(0(x1)) = 7x1 + 28 >= 7x1 + 24 = 0(s(0(0(0(0(s(0(rd(x1)))))))))
  problem:
   p(0(x1)) -> 0(s(s(p(x1))))
   p(s(x1)) -> x1
   p(p(s(x1))) -> p(x1)
   f(s(x1)) -> p(s(g(p(s(s(x1))))))
   g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
   j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
   half(0(x1)) -> 0(s(s(half(p(s(p(s(x1))))))))
   half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [half](x0) = 10x0 + 6,
    
    [j](x0) = x0 + 4,
    
    [g](x0) = x0 + 4,
    
    [f](x0) = x0 + 4,
    
    [s](x0) = x0,
    
    [p](x0) = x0,
    
    [0](x0) = x0 + 1
   orientation:
    p(0(x1)) = x1 + 1 >= x1 + 1 = 0(s(s(p(x1))))
    
    p(s(x1)) = x1 >= x1 = x1
    
    p(p(s(x1))) = x1 >= x1 = p(x1)
    
    f(s(x1)) = x1 + 4 >= x1 + 4 = p(s(g(p(s(s(x1))))))
    
    g(s(x1)) = x1 + 4 >= x1 + 4 = p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
    
    j(s(x1)) = x1 + 4 >= x1 + 4 = p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
    
    half(0(x1)) = 10x1 + 16 >= 10x1 + 7 = 0(s(s(half(p(s(p(s(x1))))))))
    
    half(s(s(x1))) = 10x1 + 6 >= 10x1 + 6 = s(half(p(p(s(s(x1))))))
   problem:
    p(0(x1)) -> 0(s(s(p(x1))))
    p(s(x1)) -> x1
    p(p(s(x1))) -> p(x1)
    f(s(x1)) -> p(s(g(p(s(s(x1))))))
    g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
    j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
    half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
   Bounds Processor:
    bound: 3
    enrichment: match
    automaton:
     final states: {31,22,12,6,3,2,1}
     transitions:
      half0(32) -> 33*
      p1(85) -> 86*
      p1(65) -> 66*
      p1(60) -> 61*
      p1(40) -> 41*
      p1(92) -> 93*
      p1(62) -> 63*
      p1(42) -> 43*
      p1(59) -> 60*
      p1(34) -> 35*
      p1(91) -> 92*
      p1(68) -> 69*
      s1(67) -> 68*
      s1(89) -> 90*
      s1(84) -> 85*
      s1(64) -> 65*
      s1(86) -> 87*
      s1(66) -> 67*
      s1(61) -> 62*
      s1(88) -> 89*
      s1(58) -> 59*
      s1(90) -> 91*
      f1(63) -> 64*
      j1(87) -> 88*
      p2(117) -> 118*
      p2(112) -> 113*
      p2(82) -> 83*
      p2(114) -> 115*
      p2(111) -> 112*
      p2(96) -> 97*
      p2(120) -> 121*
      s2(119) -> 120*
      s2(116) -> 117*
      s2(118) -> 119*
      s2(113) -> 114*
      s2(110) -> 111*
      f2(115) -> 116*
      p3(122) -> 123*
      f80() -> 2*
      00(5) -> 1*
      s0(15) -> 16*
      s0(10) -> 11*
      s0(17) -> 18*
      s0(7) -> 8*
      s0(2) -> 7*
      s0(29) -> 30*
      s0(19) -> 20*
      s0(4) -> 5*
      s0(26) -> 27*
      s0(33) -> 31*
      s0(28) -> 29*
      s0(23) -> 24*
      s0(18) -> 19*
      s0(13) -> 14*
      s0(3) -> 4*
      p0(30) -> 22*
      p0(20) -> 21*
      p0(27) -> 28*
      p0(7) -> 13*
      p0(2) -> 3*
      p0(24) -> 25*
      p0(14) -> 15*
      p0(9) -> 32*
      p0(21) -> 12*
      p0(11) -> 6*
      p0(13) -> 23*
      p0(8) -> 9*
      g0(9) -> 10*
      j0(16) -> 17*
      f0(25) -> 26*
      1 -> 123,41,23,25,3,83,113
      2 -> 123,41,23,25,3,83,113,43,32,40,13
      6 -> 116,64,26,28,66,118
      7 -> 42,9
      10 -> 6*
      13 -> 15*
      15 -> 58*
      18 -> 35,12
      19 -> 34,21
      23 -> 25*
      26 -> 28*
      29 -> 22*
      31 -> 33*
      35 -> 12*
      41 -> 23*
      43 -> 32*
      58 -> 82,60
      60 -> 84*
      61 -> 63*
      64 -> 66*
      67 -> 69,17
      69 -> 17*
      83 -> 61*
      84 -> 86*
      86 -> 110*
      89 -> 97*
      90 -> 96,92
      93 -> 10,6
      97 -> 93*
      110 -> 122,112
      113 -> 115*
      116 -> 118*
      119 -> 121*
      121 -> 88*
      123 -> 113*
    problem:
     
    Qed