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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(a(b(b(x1)))))
  c(b(x1)) -> a(x1)
  DP Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(a(b(b(x1)))))
    c(b(x1)) -> a(x1)
   TDG Processor:
    DPs:
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     c#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(a(b(b(x1)))))
     c(b(x1)) -> a(x1)
    graph:
     b#(b(a(x1))) -> c#(b(a(b(b(x1))))) -> c#(b(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
     b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
     b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 16/36
     DPs:
      b#(b(a(x1))) -> b#(b(x1))
      b#(b(a(x1))) -> b#(x1)
      b#(b(a(x1))) -> b#(a(b(b(x1))))
     TRS:
      a(x1) -> x1
      b(b(a(x1))) -> c(b(a(b(b(x1)))))
      c(b(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(b(a(x1))) -> c(b(a(b(b(x1)))))
       c(b(x1)) -> a(x1)
      interpretation:
       [b#](x0) = [0 1]x0 + [0],
       
                 [1  0 ]     [0]
       [c](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [b](x0) = [0  -&]x0 + [0],
       
                 [0  1 ]     [1]
       [a](x0) = [-& 0 ]x0 + [0]
      orientation:
       b#(b(a(x1))) = [1 2]x1 + [2] >= [1 0]x1 + [1] = b#(b(x1))
       
       b#(b(a(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [0] = b#(x1)
       
       b#(b(a(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [1] = b#(a(b(b(x1))))
       
               [0  1 ]     [1]           
       a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
       
                     [0  1 ]     [1]    [0  1 ]     [1]                    
       b(b(a(x1))) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(b(a(b(b(x1)))))
       
                  [0  1 ]     [1]    [0  1 ]     [1]        
       c(b(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = a(x1)
      problem:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(a(b(b(x1)))))
        c(b(x1)) -> a(x1)
      Restore Modifier:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(a(b(b(x1)))))
        c(b(x1)) -> a(x1)
       EDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         b(b(a(x1))) -> c(b(a(b(b(x1)))))
         c(b(x1)) -> a(x1)
        graph:
         b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
        Matrix Interpretation Processor: dim=1
         
         usable rules:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(a(b(b(x1)))))
          c(b(x1)) -> a(x1)
         interpretation:
          [b#](x0) = 4x0 + 1/2,
          
          [c](x0) = 1/2x0 + 3/2,
          
          [b](x0) = 2x0,
          
          [a](x0) = x0 + 1/2
         orientation:
          b#(b(a(x1))) = 8x1 + 9/2 >= 8x1 + 1/2 = b#(b(x1))
          
          a(x1) = x1 + 1/2 >= x1 = x1
          
          b(b(a(x1))) = 4x1 + 2 >= 4x1 + 2 = c(b(a(b(b(x1)))))
          
          c(b(x1)) = x1 + 3/2 >= x1 + 1/2 = a(x1)
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           b(b(a(x1))) -> c(b(a(b(b(x1)))))
           c(b(x1)) -> a(x1)
         Qed