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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(x1)) -> c(x1)
  c(a(c(x1))) -> a(c(b(a(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(x1)) -> c#(x1)
    c#(a(c(x1))) -> a#(x1)
    c#(a(c(x1))) -> b#(a(x1))
    c#(a(c(x1))) -> c#(b(a(x1)))
    c#(a(c(x1))) -> a#(c(b(a(x1))))
   TRS:
    a(x1) -> b(x1)
    b(b(x1)) -> c(x1)
    c(a(c(x1))) -> a(c(b(a(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(x1)) -> c#(x1)
     c#(a(c(x1))) -> a#(x1)
     c#(a(c(x1))) -> b#(a(x1))
     c#(a(c(x1))) -> c#(b(a(x1)))
     c#(a(c(x1))) -> a#(c(b(a(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(x1)) -> c(x1)
     c(a(c(x1))) -> a(c(b(a(x1))))
    graph:
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> c#(b(a(x1)))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> b#(a(x1))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(x1)
     c#(a(c(x1))) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1)
     c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1)
     c#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> c#(b(a(x1)))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> b#(a(x1))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(x1) -> b(x1)
      b(b(x1)) -> c(x1)
      c(a(c(x1))) -> a(c(b(a(x1))))
     interpretation:
      [c#](x0) = 15x0,
      
      [b#](x0) = 14x0,
      
      [a#](x0) = 14x0,
      
      [c](x0) = 2x0,
      
      [b](x0) = 1x0,
      
      [a](x0) = 1x0
     orientation:
      a#(x1) = 14x1 >= 14x1 = b#(x1)
      
      b#(b(x1)) = 15x1 >= 15x1 = c#(x1)
      
      c#(a(c(x1))) = 18x1 >= 14x1 = a#(x1)
      
      c#(a(c(x1))) = 18x1 >= 15x1 = b#(a(x1))
      
      c#(a(c(x1))) = 18x1 >= 17x1 = c#(b(a(x1)))
      
      c#(a(c(x1))) = 18x1 >= 18x1 = a#(c(b(a(x1))))
      
      a(x1) = 1x1 >= 1x1 = b(x1)
      
      b(b(x1)) = 2x1 >= 2x1 = c(x1)
      
      c(a(c(x1))) = 5x1 >= 5x1 = a(c(b(a(x1))))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(x1)) -> c#(x1)
       c#(a(c(x1))) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(x1)) -> c(x1)
       c(a(c(x1))) -> a(c(b(a(x1))))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(x1)) -> c#(x1)
       c#(a(c(x1))) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(x1)) -> c(x1)
       c(a(c(x1))) -> a(c(b(a(x1))))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        b#(b(x1)) -> c#(x1)
        c#(a(c(x1))) -> a#(c(b(a(x1))))
       TRS:
        a(x1) -> b(x1)
        b(b(x1)) -> c(x1)
        c(a(c(x1))) -> a(c(b(a(x1))))
       graph:
        c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1)
        b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
        a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(x1) -> b(x1)
         b(b(x1)) -> c(x1)
         c(a(c(x1))) -> a(c(b(a(x1))))
        interpretation:
         [c#](x0) = [1 0 0]x0 + [0],
         
         [b#](x0) = [-& 0  0 ]x0 + [0],
         
         [a#](x0) = [0 1 1]x0 + [1],
         
                   [1  -& 0 ]     [-&]
         [c](x0) = [1  -& 1 ]x0 + [0 ]
                   [0  -& 1 ]     [1 ],
         
                   [0  -& 1 ]     [1]
         [b](x0) = [1  0  0 ]x0 + [0]
                   [0  -& -&]     [0],
         
                   [1  -& 1 ]     [1]
         [a](x0) = [1  0  0 ]x0 + [0]
                   [0  -& -&]     [0]
        orientation:
         a#(x1) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = b#(x1)
         
         b#(b(x1)) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = c#(x1)
         
         c#(a(c(x1))) = [3  -& 3 ]x1 + [3] >= [3  -& 3 ]x1 + [3] = a#(c(b(a(x1))))
         
                 [1  -& 1 ]     [1]    [0  -& 1 ]     [1]        
         a(x1) = [1  0  0 ]x1 + [0] >= [1  0  0 ]x1 + [0] = b(x1)
                 [0  -& -&]     [0]    [0  -& -&]     [0]        
         
                    [1  -& 1 ]     [1]    [1  -& 0 ]     [-&]        
         b(b(x1)) = [1  0  2 ]x1 + [2] >= [1  -& 1 ]x1 + [0 ] = c(x1)
                    [0  -& 1 ]     [1]    [0  -& 1 ]     [1 ]        
         
                       [3  -& 3 ]     [3]    [3  -& 3 ]     [3]                 
         c(a(c(x1))) = [3  -& 3 ]x1 + [3] >= [3  -& 3 ]x1 + [3] = a(c(b(a(x1))))
                       [2  -& 2 ]     [2]    [2  -& 2 ]     [2]                 
        problem:
         DPs:
          b#(b(x1)) -> c#(x1)
          c#(a(c(x1))) -> a#(c(b(a(x1))))
         TRS:
          a(x1) -> b(x1)
          b(b(x1)) -> c(x1)
          c(a(c(x1))) -> a(c(b(a(x1))))
        Restore Modifier:
         DPs:
          b#(b(x1)) -> c#(x1)
          c#(a(c(x1))) -> a#(c(b(a(x1))))
         TRS:
          a(x1) -> b(x1)
          b(b(x1)) -> c(x1)
          c(a(c(x1))) -> a(c(b(a(x1))))
         EDG Processor:
          DPs:
           b#(b(x1)) -> c#(x1)
           c#(a(c(x1))) -> a#(c(b(a(x1))))
          TRS:
           a(x1) -> b(x1)
           b(b(x1)) -> c(x1)
           c(a(c(x1))) -> a(c(b(a(x1))))
          graph:
           b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4