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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(x1))
  b(a(x1)) -> a(c(x1))
  c(c(c(x1))) -> b(a(x1))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> a#(c(x1))
    c#(c(c(x1))) -> a#(x1)
    c#(c(c(x1))) -> b#(a(x1))
   TRS:
    a(x1) -> c(b(x1))
    b(a(x1)) -> a(c(x1))
    c(c(c(x1))) -> b(a(x1))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1))
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> a#(c(x1))
     c#(c(c(x1))) -> a#(x1)
     c#(c(c(x1))) -> b#(a(x1))
    TRS:
     a(x1) -> c(b(x1))
     b(a(x1)) -> a(c(x1))
     c(c(c(x1))) -> b(a(x1))
    graph:
     c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
     c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> c#(x1)
     c#(c(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1))
     c#(c(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(c(x1))) -> b#(a(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(c(x1))) -> a#(x1)
     b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1))
     b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(a(x1))
     a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(x1) -> c(b(x1))
      b(a(x1)) -> a(c(x1))
      c(c(c(x1))) -> b(a(x1))
     interpretation:
      [c#](x0) = x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = 1x0,
      
      [b](x0) = 1x0,
      
      [c](x0) = 1x0,
      
      [a](x0) = 2x0
     orientation:
      a#(x1) = 1x1 >= x1 = b#(x1)
      
      a#(x1) = 1x1 >= 1x1 = c#(b(x1))
      
      b#(a(x1)) = 2x1 >= x1 = c#(x1)
      
      b#(a(x1)) = 2x1 >= 2x1 = a#(c(x1))
      
      c#(c(c(x1))) = 2x1 >= 1x1 = a#(x1)
      
      c#(c(c(x1))) = 2x1 >= 2x1 = b#(a(x1))
      
      a(x1) = 2x1 >= 2x1 = c(b(x1))
      
      b(a(x1)) = 3x1 >= 3x1 = a(c(x1))
      
      c(c(c(x1))) = 3x1 >= 3x1 = b(a(x1))
     problem:
      DPs:
       a#(x1) -> c#(b(x1))
       b#(a(x1)) -> a#(c(x1))
       c#(c(c(x1))) -> b#(a(x1))
      TRS:
       a(x1) -> c(b(x1))
       b(a(x1)) -> a(c(x1))
       c(c(c(x1))) -> b(a(x1))
     Restore Modifier:
      DPs:
       a#(x1) -> c#(b(x1))
       b#(a(x1)) -> a#(c(x1))
       c#(c(c(x1))) -> b#(a(x1))
      TRS:
       a(x1) -> c(b(x1))
       b(a(x1)) -> a(c(x1))
       c(c(c(x1))) -> b(a(x1))
      EDG Processor:
       DPs:
        a#(x1) -> c#(b(x1))
        b#(a(x1)) -> a#(c(x1))
        c#(c(c(x1))) -> b#(a(x1))
       TRS:
        a(x1) -> c(b(x1))
        b(a(x1)) -> a(c(x1))
        c(c(c(x1))) -> b(a(x1))
       graph:
        c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
        b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1))
        a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(a(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> c(b(x1))
         b(a(x1)) -> a(c(x1))
         c(c(c(x1))) -> b(a(x1))
        interpretation:
         [c#](x0) = [0 0]x0 + [0],
         
         [b#](x0) = [0  -&]x0 + [0],
         
         [a#](x0) = [2 0]x0 + [0],
         
                   [2  -&]     [-&]
         [b](x0) = [0  -&]x0 + [0 ],
         
                   [-& 0 ]     [0]
         [c](x0) = [0  2 ]x0 + [2],
         
                   [0  2 ]     [2]
         [a](x0) = [2  -&]x0 + [2]
        orientation:
         a#(x1) = [2 0]x1 + [0] >= [2  -&]x1 + [0] = c#(b(x1))
         
         b#(a(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = a#(c(x1))
         
         c#(c(c(x1))) = [2 4]x1 + [4] >= [0 2]x1 + [2] = b#(a(x1))
         
                 [0  2 ]     [2]    [0  -&]     [0]           
         a(x1) = [2  -&]x1 + [2] >= [2  -&]x1 + [2] = c(b(x1))
         
                    [2 4]     [4]    [2  4 ]     [4]           
         b(a(x1)) = [0 2]x1 + [2] >= [-& 2 ]x1 + [2] = a(c(x1))
         
                       [2 4]     [4]    [2 4]     [4]           
         c(c(c(x1))) = [4 6]x1 + [6] >= [0 2]x1 + [2] = b(a(x1))
        problem:
         DPs:
          a#(x1) -> c#(b(x1))
          b#(a(x1)) -> a#(c(x1))
         TRS:
          a(x1) -> c(b(x1))
          b(a(x1)) -> a(c(x1))
          c(c(c(x1))) -> b(a(x1))
        Restore Modifier:
         DPs:
          a#(x1) -> c#(b(x1))
          b#(a(x1)) -> a#(c(x1))
         TRS:
          a(x1) -> c(b(x1))
          b(a(x1)) -> a(c(x1))
          c(c(c(x1))) -> b(a(x1))
         EDG Processor:
          DPs:
           a#(x1) -> c#(b(x1))
           b#(a(x1)) -> a#(c(x1))
          TRS:
           a(x1) -> c(b(x1))
           b(a(x1)) -> a(c(x1))
           c(c(c(x1))) -> b(a(x1))
          graph:
           b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1))
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4