/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(x1))
  c(c(x1)) -> a(b(c(b(x1))))
  DP Processor:
   DPs:
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> a#(c(x1))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> c#(b(x1))
    c#(c(x1)) -> b#(c(b(x1)))
    c#(c(x1)) -> a#(b(c(b(x1))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(x1))
    c(c(x1)) -> a(b(c(b(x1))))
   TDG Processor:
    DPs:
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> c#(b(x1))
     c#(c(x1)) -> b#(c(b(x1)))
     c#(c(x1)) -> a#(b(c(b(x1))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(x1))
     c(c(x1)) -> a(b(c(b(x1))))
    graph:
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(b(c(b(x1))))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(c(b(x1)))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
     c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(c(x1)) -> c#(b(x1))
      c#(c(x1)) -> b#(x1)
      b#(a(x1)) -> c#(x1)
      c#(c(x1)) -> b#(c(b(x1)))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(x1))
      c(c(x1)) -> a(b(c(b(x1))))
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> a(c(x1))
       c(c(x1)) -> a(b(c(b(x1))))
      interpretation:
       [c#](x0) = [0 0 0]x0 + [1],
       
       [b#](x0) = [-& -& 0 ]x0 + [0],
       
                 [-& 0  -&]     [0 ]
       [c](x0) = [0  0  1 ]x0 + [1 ]
                 [-& 0  -&]     [-&],
       
                 [0  -& 1 ]     [0 ]
       [b](x0) = [-& -& 0 ]x0 + [-&]
                 [0  -& 0 ]     [0 ],
       
                 [0 1 0]     [0]
       [a](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [1]
      orientation:
       c#(c(x1)) = [0 0 1]x1 + [1] >= [0  -& 1 ]x1 + [1] = c#(b(x1))
       
       c#(c(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = b#(x1)
       
       b#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 0]x1 + [1] = c#(x1)
       
       c#(c(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = b#(c(b(x1)))
       
               [0 1 0]     [0]           
       a(x1) = [0 0 0]x1 + [0] >= x1 = x1
               [0 0 1]     [1]           
       
                  [1 1 2]     [2]    [1 1 2]     [2]           
       b(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(c(x1))
                  [0 1 1]     [1]    [0 1 1]     [1]           
       
                  [0 0 1]     [1]    [-& -& 1 ]     [0]                 
       c(c(x1)) = [0 1 1]x1 + [1] >= [-& -& 1 ]x1 + [0] = a(b(c(b(x1))))
                  [0 0 1]     [1]    [-& -& 1 ]     [1]                 
      problem:
       DPs:
        c#(c(x1)) -> c#(b(x1))
        b#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(x1))
        c(c(x1)) -> a(b(c(b(x1))))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> c#(b(x1))
        b#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(x1))
        c(c(x1)) -> a(b(c(b(x1))))
       EDG Processor:
        DPs:
         c#(c(x1)) -> c#(b(x1))
         b#(a(x1)) -> c#(x1)
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(c(x1))
         c(c(x1)) -> a(b(c(b(x1))))
        graph:
         c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1))
         b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          c#(c(x1)) -> c#(b(x1))
         TRS:
          a(x1) -> x1
          b(a(x1)) -> a(c(x1))
          c(c(x1)) -> a(b(c(b(x1))))
         Arctic Interpretation Processor:
          dimension: 3
          usable rules:
           a(x1) -> x1
           b(a(x1)) -> a(c(x1))
           c(c(x1)) -> a(b(c(b(x1))))
          interpretation:
           [c#](x0) = [0  -& -&]x0 + [0],
           
                     [0  1  0 ]     [1]
           [c](x0) = [0  -& -&]x0 + [0]
                     [0  -& -&]     [0],
           
                     [-& 0  -&]     [0]
           [b](x0) = [-& 0  0 ]x0 + [0]
                     [-& 1  0 ]     [0],
           
                     [0 0 0]     [0]
           [a](x0) = [0 1 0]x0 + [1]
                     [1 0 0]     [1]
          orientation:
           c#(c(x1)) = [0 1 0]x1 + [1] >= [-& 0  -&]x1 + [0] = c#(b(x1))
           
                   [0 0 0]     [0]           
           a(x1) = [0 1 0]x1 + [1] >= x1 = x1
                   [1 0 0]     [1]           
           
                      [0 1 0]     [1]    [0 1 0]     [1]           
           b(a(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = a(c(x1))
                      [1 2 1]     [2]    [1 2 1]     [2]           
           
                      [1 1 0]     [1]    [-& 1  -&]     [1]                 
           c(c(x1)) = [0 1 0]x1 + [1] >= [-& 1  -&]x1 + [1] = a(b(c(b(x1))))
                      [0 1 0]     [1]    [-& 1  -&]     [1]                 
          problem:
           DPs:
            
           TRS:
            a(x1) -> x1
            b(a(x1)) -> a(c(x1))
            c(c(x1)) -> a(b(c(b(x1))))
          Qed