/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:
 f(f(x1)) -> b(b(b(x1)))
 a(f(x1)) -> f(a(a(x1)))
 b(b(x1)) -> c(c(a(c(x1))))
 d(b(x1)) -> d(a(b(x1)))
 c(c(x1)) -> d(d(d(x1)))
 b(d(x1)) -> d(b(x1))
 c(d(d(x1))) -> f(x1)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [d](x0) = x0 + 4,
   
   [b](x0) = x0 + 9,
   
   [c](x0) = x0 + 6,
   
   [f](x0) = x0 + 14,
   
   [a](x0) = x0
  orientation:
   f(f(x1)) = x1 + 28 >= x1 + 27 = b(b(b(x1)))
   
   a(f(x1)) = x1 + 14 >= x1 + 14 = f(a(a(x1)))
   
   b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(a(c(x1))))
   
   d(b(x1)) = x1 + 13 >= x1 + 13 = d(a(b(x1)))
   
   c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
   
   b(d(x1)) = x1 + 13 >= x1 + 13 = d(b(x1))
   
   c(d(d(x1))) = x1 + 14 >= x1 + 14 = f(x1)
  problem:
   a(f(x1)) -> f(a(a(x1)))
   b(b(x1)) -> c(c(a(c(x1))))
   d(b(x1)) -> d(a(b(x1)))
   c(c(x1)) -> d(d(d(x1)))
   b(d(x1)) -> d(b(x1))
   c(d(d(x1))) -> f(x1)
  String Reversal Processor:
   f(a(x1)) -> a(a(f(x1)))
   b(b(x1)) -> c(a(c(c(x1))))
   b(d(x1)) -> b(a(d(x1)))
   c(c(x1)) -> d(d(d(x1)))
   d(b(x1)) -> b(d(x1))
   d(d(c(x1))) -> f(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [d](x0) = x0,
     
     [b](x0) = 4x0 + 1,
     
     [c](x0) = x0,
     
     [f](x0) = x0,
     
     [a](x0) = x0
    orientation:
     f(a(x1)) = x1 >= x1 = a(a(f(x1)))
     
     b(b(x1)) = 16x1 + 5 >= x1 = c(a(c(c(x1))))
     
     b(d(x1)) = 4x1 + 1 >= 4x1 + 1 = b(a(d(x1)))
     
     c(c(x1)) = x1 >= x1 = d(d(d(x1)))
     
     d(b(x1)) = 4x1 + 1 >= 4x1 + 1 = b(d(x1))
     
     d(d(c(x1))) = x1 >= x1 = f(x1)
    problem:
     f(a(x1)) -> a(a(f(x1)))
     b(d(x1)) -> b(a(d(x1)))
     c(c(x1)) -> d(d(d(x1)))
     d(b(x1)) -> b(d(x1))
     d(d(c(x1))) -> f(x1)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [d](x0) = x0 + 2,
      
      [b](x0) = x0 + 8,
      
      [c](x0) = x0 + 3,
      
      [f](x0) = x0,
      
      [a](x0) = x0
     orientation:
      f(a(x1)) = x1 >= x1 = a(a(f(x1)))
      
      b(d(x1)) = x1 + 10 >= x1 + 10 = b(a(d(x1)))
      
      c(c(x1)) = x1 + 6 >= x1 + 6 = d(d(d(x1)))
      
      d(b(x1)) = x1 + 10 >= x1 + 10 = b(d(x1))
      
      d(d(c(x1))) = x1 + 7 >= x1 = f(x1)
     problem:
      f(a(x1)) -> a(a(f(x1)))
      b(d(x1)) -> b(a(d(x1)))
      c(c(x1)) -> d(d(d(x1)))
      d(b(x1)) -> b(d(x1))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [d](x0) = x0,
       
       [b](x0) = 8x0 + 4,
       
       [c](x0) = x0 + 1,
       
       [f](x0) = x0 + 4,
       
       [a](x0) = x0
      orientation:
       f(a(x1)) = x1 + 4 >= x1 + 4 = a(a(f(x1)))
       
       b(d(x1)) = 8x1 + 4 >= 8x1 + 4 = b(a(d(x1)))
       
       c(c(x1)) = x1 + 2 >= x1 = d(d(d(x1)))
       
       d(b(x1)) = 8x1 + 4 >= 8x1 + 4 = b(d(x1))
      problem:
       f(a(x1)) -> a(a(f(x1)))
       b(d(x1)) -> b(a(d(x1)))
       d(b(x1)) -> b(d(x1))
      Bounds Processor:
       bound: 1
       enrichment: match
       automaton:
        final states: {8,5,1}
        transitions:
         f50() -> 2*
         a1(14) -> 15*
         f0(2) -> 3*
         b1(15) -> 16*
         d0(2) -> 6*
         b0(6) -> 8*
         b0(7) -> 5*
         d1(13) -> 14*
         a0(6) -> 7*
         a0(4) -> 1*
         a0(3) -> 4*
         16 -> 8*
         2 -> 13*
         8 -> 14,6
         1 -> 3*
       problem:
        
       Qed