/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 g(h(x1)) -> g(f(s(x1)))
 f(s(s(s(x1)))) -> h(f(s(h(x1))))
 f(h(x1)) -> h(f(s(h(x1))))
 h(x1) -> x1
 f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
 b(a(x1)) -> a(b(x1))
 a(a(a(x1))) -> b(a(a(b(x1))))
 b(b(b(b(x1)))) -> a(x1)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0) = x0 + 6,
   
   [g](x0) = x0 + 2,
   
   [f](x0) = x0,
   
   [b](x0) = x0 + 3,
   
   [h](x0) = x0,
   
   [s](x0) = x0
  orientation:
   g(h(x1)) = x1 + 2 >= x1 + 2 = g(f(s(x1)))
   
   f(s(s(s(x1)))) = x1 >= x1 = h(f(s(h(x1))))
   
   f(h(x1)) = x1 >= x1 = h(f(s(h(x1))))
   
   h(x1) = x1 >= x1 = x1
   
   f(f(s(s(x1)))) = x1 >= x1 = s(s(s(f(f(x1)))))
   
   b(a(x1)) = x1 + 9 >= x1 + 9 = a(b(x1))
   
   a(a(a(x1))) = x1 + 18 >= x1 + 18 = b(a(a(b(x1))))
   
   b(b(b(b(x1)))) = x1 + 12 >= x1 + 6 = a(x1)
  problem:
   g(h(x1)) -> g(f(s(x1)))
   f(s(s(s(x1)))) -> h(f(s(h(x1))))
   f(h(x1)) -> h(f(s(h(x1))))
   h(x1) -> x1
   f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
   b(a(x1)) -> a(b(x1))
   a(a(a(x1))) -> b(a(a(b(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a](x0) = x0 + 4,
    
    [g](x0) = x0,
    
    [f](x0) = x0,
    
    [b](x0) = x0,
    
    [h](x0) = x0,
    
    [s](x0) = x0
   orientation:
    g(h(x1)) = x1 >= x1 = g(f(s(x1)))
    
    f(s(s(s(x1)))) = x1 >= x1 = h(f(s(h(x1))))
    
    f(h(x1)) = x1 >= x1 = h(f(s(h(x1))))
    
    h(x1) = x1 >= x1 = x1
    
    f(f(s(s(x1)))) = x1 >= x1 = s(s(s(f(f(x1)))))
    
    b(a(x1)) = x1 + 4 >= x1 + 4 = a(b(x1))
    
    a(a(a(x1))) = x1 + 12 >= x1 + 8 = b(a(a(b(x1))))
   problem:
    g(h(x1)) -> g(f(s(x1)))
    f(s(s(s(x1)))) -> h(f(s(h(x1))))
    f(h(x1)) -> h(f(s(h(x1))))
    h(x1) -> x1
    f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
    b(a(x1)) -> a(b(x1))
   Bounds Processor:
    bound: 1
    enrichment: match
    automaton:
     final states: {14,9,2,5,1}
     transitions:
      g1(18) -> 19*
      s1(25) -> 26*
      s1(16) -> 17*
      g0(4) -> 1*
      f60() -> 2*
      b0(2) -> 15*
      a0(15) -> 14*
      f0(2) -> 10*
      f0(10) -> 11*
      f0(3) -> 4*
      f0(7) -> 8*
      h0(8) -> 5*
      h0(2) -> 6*
      s0(12) -> 13*
      s0(2) -> 3*
      s0(13) -> 9*
      s0(6) -> 7*
      s0(11) -> 12*
      h1(34) -> 35*
      h1(27) -> 28*
      h1(44) -> 45*
      h1(24) -> 25*
      h1(40) -> 41*
      f1(26) -> 27*
      f1(17) -> 18*
      27 -> 28,11
      19 -> 1*
      24 -> 25*
      35 -> 25*
      12 -> 40*
      14 -> 15*
      45 -> 25*
      28 -> 27,11
      11 -> 34*
      2 -> 6*
      44 -> 45,25
      13 -> 44*
      8 -> 24,16,5
      40 -> 41,25
      34 -> 35,25
      5 -> 10,4,8
      9 -> 10,11
      41 -> 25*
    problem:
     
    Qed