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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(a(b(c(a(b(x1))))))
  b(x1) -> x1
  c(c(x1)) -> x1
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> c#(a(b(x1)))
    b#(a(x1)) -> b#(c(a(b(x1))))
    b#(a(x1)) -> a#(b(c(a(b(x1)))))
    b#(a(x1)) -> c#(a(b(c(a(b(x1))))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(a(b(c(a(b(x1))))))
    b(x1) -> x1
    c(c(x1)) -> x1
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(c(a(b(x1))))
     b#(a(x1)) -> a#(b(c(a(b(x1)))))
     b#(a(x1)) -> c#(a(b(c(a(b(x1))))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(a(b(c(a(b(x1))))))
     b(x1) -> x1
     c(c(x1)) -> x1
    graph:
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> c#(a(b(c(a(b(x1))))))
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(c(a(b(x1)))))
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(c(a(b(x1))))
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(c(a(b(x1))))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(a(b(x1)))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(a(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      b#(a(x1)) -> b#(c(a(b(x1))))
      b#(a(x1)) -> b#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(a(b(c(a(b(x1))))))
      b(x1) -> x1
      c(c(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> c(a(b(c(a(b(x1))))))
       b(x1) -> x1
       c(c(x1)) -> x1
      interpretation:
       [b#](x0) = [1 1]x0,
       
                 [0  0 ]  
       [c](x0) = [0  -&]x0,
       
                 [0  1 ]  
       [b](x0) = [-& 0 ]x0,
       
                 [0 1]  
       [a](x0) = [1 2]x0
      orientation:
       b#(a(x1)) = [2 3]x1 >= [2 3]x1 = b#(c(a(b(x1))))
       
       b#(a(x1)) = [2 3]x1 >= [1 1]x1 = b#(x1)
       
               [0 1]             
       a(x1) = [1 2]x1 >= x1 = x1
       
                  [2 3]      [2 3]                         
       b(a(x1)) = [1 2]x1 >= [1 2]x1 = c(a(b(c(a(b(x1))))))
       
               [0  1 ]             
       b(x1) = [-& 0 ]x1 >= x1 = x1
       
                  [0 0]             
       c(c(x1)) = [0 0]x1 >= x1 = x1
      problem:
       DPs:
        b#(a(x1)) -> b#(c(a(b(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(c(a(b(x1))))))
        b(x1) -> x1
        c(c(x1)) -> x1
      Restore Modifier:
       DPs:
        b#(a(x1)) -> b#(c(a(b(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(c(a(b(x1))))))
        b(x1) -> x1
        c(c(x1)) -> x1
       EDG Processor:
        DPs:
         b#(a(x1)) -> b#(c(a(b(x1))))
        TRS:
         a(x1) -> x1
         b(a(x1)) -> c(a(b(c(a(b(x1))))))
         b(x1) -> x1
         c(c(x1)) -> x1
        graph:
         b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(c(a(b(x1))))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(x1)) -> c(a(b(c(a(b(x1))))))
          b(x1) -> x1
          c(c(x1)) -> x1
         interpretation:
          [b#](x0) = [1 0]x0 + [0],
          
                    [-& 0 ]     [0]
          [c](x0) = [0  0 ]x0 + [1],
          
                    [0  -&]     [-&]
          [b](x0) = [1  0 ]x0 + [0 ],
          
                    [2  1 ]     [1]
          [a](x0) = [-& 0 ]x0 + [0]
         orientation:
          b#(a(x1)) = [3 2]x1 + [2] >= [2 1]x1 + [1] = b#(c(a(b(x1))))
          
                  [2  1 ]     [1]           
          a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
          
                     [2 1]     [1]    [2 1]     [1]                       
          b(a(x1)) = [3 2]x1 + [2] >= [3 2]x1 + [2] = c(a(b(c(a(b(x1))))))
          
                  [0  -&]     [-&]           
          b(x1) = [1  0 ]x1 + [0 ] >= x1 = x1
          
                     [0 0]     [1]           
          c(c(x1)) = [0 0]x1 + [1] >= x1 = x1
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           b(a(x1)) -> c(a(b(c(a(b(x1))))))
           b(x1) -> x1
           c(c(x1)) -> x1
         Qed