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


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YES

Problem:
 a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
 a(d(x1)) -> c(x1)
 a(f(f(x1))) -> g(x1)
 b(g(x1)) -> g(b(x1))
 c(x1) -> f(f(x1))
 c(a(c(x1))) -> b(c(a(b(c(x1)))))
 c(d(x1)) -> a(a(x1))
 g(x1) -> c(a(x1))
 g(x1) -> d(d(d(d(x1))))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0) = x0 + 4,
   
   [c](x0) = x0 + 8,
   
   [d](x0) = x0 + 3,
   
   [g](x0) = x0 + 13,
   
   [a](x0) = x0 + 5,
   
   [b](x0) = x0
  orientation:
   a(b(c(a(x1)))) = x1 + 18 >= x1 + 18 = b(a(c(b(a(b(x1))))))
   
   a(d(x1)) = x1 + 8 >= x1 + 8 = c(x1)
   
   a(f(f(x1))) = x1 + 13 >= x1 + 13 = g(x1)
   
   b(g(x1)) = x1 + 13 >= x1 + 13 = g(b(x1))
   
   c(x1) = x1 + 8 >= x1 + 8 = f(f(x1))
   
   c(a(c(x1))) = x1 + 21 >= x1 + 21 = b(c(a(b(c(x1)))))
   
   c(d(x1)) = x1 + 11 >= x1 + 10 = a(a(x1))
   
   g(x1) = x1 + 13 >= x1 + 13 = c(a(x1))
   
   g(x1) = x1 + 13 >= x1 + 12 = d(d(d(d(x1))))
  problem:
   a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
   a(d(x1)) -> c(x1)
   a(f(f(x1))) -> g(x1)
   b(g(x1)) -> g(b(x1))
   c(x1) -> f(f(x1))
   c(a(c(x1))) -> b(c(a(b(c(x1)))))
   g(x1) -> c(a(x1))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0) = x0 + 1,
    
    [c](x0) = x0 + 4,
    
    [d](x0) = 4x0 + 4,
    
    [g](x0) = 4x0 + 8,
    
    [a](x0) = 4x0 + 1,
    
    [b](x0) = x0
   orientation:
    a(b(c(a(x1)))) = 16x1 + 21 >= 16x1 + 21 = b(a(c(b(a(b(x1))))))
    
    a(d(x1)) = 16x1 + 17 >= x1 + 4 = c(x1)
    
    a(f(f(x1))) = 4x1 + 9 >= 4x1 + 8 = g(x1)
    
    b(g(x1)) = 4x1 + 8 >= 4x1 + 8 = g(b(x1))
    
    c(x1) = x1 + 4 >= x1 + 2 = f(f(x1))
    
    c(a(c(x1))) = 4x1 + 21 >= 4x1 + 21 = b(c(a(b(c(x1)))))
    
    g(x1) = 4x1 + 8 >= 4x1 + 5 = c(a(x1))
   problem:
    a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
    b(g(x1)) -> g(b(x1))
    c(a(c(x1))) -> b(c(a(b(c(x1)))))
   Bounds Processor:
    bound: 0
    enrichment: match
    automaton:
     final states: {9,8,1}
     transitions:
      b0(13) -> 9*
      b0(7) -> 1*
      b0(4) -> 5*
      b0(10) -> 11*
      b0(2) -> 3*
      g0(3) -> 8*
      c0(12) -> 13*
      c0(2) -> 10*
      c0(5) -> 6*
      a0(3) -> 4*
      a0(6) -> 7*
      a0(11) -> 12*
      f60() -> 2*
      8 -> 3*
      1 -> 4,12
      9 -> 10*
    problem:
     
    Qed