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

Proof:
 String Reversal Processor:
  a(b(a(x1))) -> c(b(x1))
  b(b(b(x1))) -> b(c(x1))
  c(x1) -> b(a(x1))
  d(c(x1)) -> a(b(c(d(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [d](x0) = 3x0,
    
    [c](x0) = x0 + 8,
    
    [b](x0) = x0 + 4,
    
    [a](x0) = x0 + 4
   orientation:
    a(b(a(x1))) = x1 + 12 >= x1 + 12 = c(b(x1))
    
    b(b(b(x1))) = x1 + 12 >= x1 + 12 = b(c(x1))
    
    c(x1) = x1 + 8 >= x1 + 8 = b(a(x1))
    
    d(c(x1)) = 3x1 + 24 >= 3x1 + 16 = a(b(c(d(x1))))
   problem:
    a(b(a(x1))) -> c(b(x1))
    b(b(b(x1))) -> b(c(x1))
    c(x1) -> b(a(x1))
   DP Processor:
    DPs:
     a#(b(a(x1))) -> b#(x1)
     a#(b(a(x1))) -> c#(b(x1))
     b#(b(b(x1))) -> c#(x1)
     b#(b(b(x1))) -> b#(c(x1))
     c#(x1) -> a#(x1)
     c#(x1) -> b#(a(x1))
    TRS:
     a(b(a(x1))) -> c(b(x1))
     b(b(b(x1))) -> b(c(x1))
     c(x1) -> b(a(x1))
    TDG Processor:
     DPs:
      a#(b(a(x1))) -> b#(x1)
      a#(b(a(x1))) -> c#(b(x1))
      b#(b(b(x1))) -> c#(x1)
      b#(b(b(x1))) -> b#(c(x1))
      c#(x1) -> a#(x1)
      c#(x1) -> b#(a(x1))
     TRS:
      a(b(a(x1))) -> c(b(x1))
      b(b(b(x1))) -> b(c(x1))
      c(x1) -> b(a(x1))
     graph:
      c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(c(x1))
      c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> c#(x1)
      c#(x1) -> a#(x1) -> a#(b(a(x1))) -> c#(b(x1))
      c#(x1) -> a#(x1) -> a#(b(a(x1))) -> b#(x1)
      b#(b(b(x1))) -> c#(x1) -> c#(x1) -> b#(a(x1))
      b#(b(b(x1))) -> c#(x1) -> c#(x1) -> a#(x1)
      b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> b#(c(x1))
      b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(x1)
      a#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> b#(a(x1))
      a#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> a#(x1)
      a#(b(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> b#(c(x1))
      a#(b(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       a(b(a(x1))) -> c(b(x1))
       b(b(b(x1))) -> b(c(x1))
       c(x1) -> b(a(x1))
      interpretation:
       [c#](x0) = 8x0 + 0,
       
       [b#](x0) = x0 + 0,
       
       [a#](x0) = 8x0,
       
       [c](x0) = 8x0 + 4,
       
       [b](x0) = 4x0 + 0,
       
       [a](x0) = 4x0 + 0
      orientation:
       a#(b(a(x1))) = 16x1 + 12 >= x1 + 0 = b#(x1)
       
       a#(b(a(x1))) = 16x1 + 12 >= 12x1 + 8 = c#(b(x1))
       
       b#(b(b(x1))) = 8x1 + 4 >= 8x1 + 0 = c#(x1)
       
       b#(b(b(x1))) = 8x1 + 4 >= 8x1 + 4 = b#(c(x1))
       
       c#(x1) = 8x1 + 0 >= 8x1 = a#(x1)
       
       c#(x1) = 8x1 + 0 >= 4x1 + 0 = b#(a(x1))
       
       a(b(a(x1))) = 12x1 + 8 >= 12x1 + 8 = c(b(x1))
       
       b(b(b(x1))) = 12x1 + 8 >= 12x1 + 8 = b(c(x1))
       
       c(x1) = 8x1 + 4 >= 8x1 + 4 = b(a(x1))
      problem:
       DPs:
        b#(b(b(x1))) -> c#(x1)
        b#(b(b(x1))) -> b#(c(x1))
        c#(x1) -> a#(x1)
        c#(x1) -> b#(a(x1))
       TRS:
        a(b(a(x1))) -> c(b(x1))
        b(b(b(x1))) -> b(c(x1))
        c(x1) -> b(a(x1))
      Restore Modifier:
       DPs:
        b#(b(b(x1))) -> c#(x1)
        b#(b(b(x1))) -> b#(c(x1))
        c#(x1) -> a#(x1)
        c#(x1) -> b#(a(x1))
       TRS:
        a(b(a(x1))) -> c(b(x1))
        b(b(b(x1))) -> b(c(x1))
        c(x1) -> b(a(x1))
       EDG Processor:
        DPs:
         b#(b(b(x1))) -> c#(x1)
         b#(b(b(x1))) -> b#(c(x1))
         c#(x1) -> a#(x1)
         c#(x1) -> b#(a(x1))
        TRS:
         a(b(a(x1))) -> c(b(x1))
         b(b(b(x1))) -> b(c(x1))
         c(x1) -> b(a(x1))
        graph:
         c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> c#(x1)
         c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(c(x1))
         b#(b(b(x1))) -> c#(x1) -> c#(x1) -> a#(x1)
         b#(b(b(x1))) -> c#(x1) -> c#(x1) -> b#(a(x1))
         b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> c#(x1)
         b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> b#(c(x1))
        SCC Processor:
         #sccs: 1
         #rules: 3
         #arcs: 6/16
         DPs:
          c#(x1) -> b#(a(x1))
          b#(b(b(x1))) -> b#(c(x1))
          b#(b(b(x1))) -> c#(x1)
         TRS:
          a(b(a(x1))) -> c(b(x1))
          b(b(b(x1))) -> b(c(x1))
          c(x1) -> b(a(x1))
         Arctic Interpretation Processor:
          dimension: 1
          usable rules:
           a(b(a(x1))) -> c(b(x1))
           b(b(b(x1))) -> b(c(x1))
           c(x1) -> b(a(x1))
          interpretation:
           [c#](x0) = 2x0,
           
           [b#](x0) = x0,
           
           [c](x0) = 4x0,
           
           [b](x0) = 2x0,
           
           [a](x0) = 2x0
          orientation:
           c#(x1) = 2x1 >= 2x1 = b#(a(x1))
           
           b#(b(b(x1))) = 4x1 >= 4x1 = b#(c(x1))
           
           b#(b(b(x1))) = 4x1 >= 2x1 = c#(x1)
           
           a(b(a(x1))) = 6x1 >= 6x1 = c(b(x1))
           
           b(b(b(x1))) = 6x1 >= 6x1 = b(c(x1))
           
           c(x1) = 4x1 >= 4x1 = b(a(x1))
          problem:
           DPs:
            c#(x1) -> b#(a(x1))
            b#(b(b(x1))) -> b#(c(x1))
           TRS:
            a(b(a(x1))) -> c(b(x1))
            b(b(b(x1))) -> b(c(x1))
            c(x1) -> b(a(x1))
          Restore Modifier:
           DPs:
            c#(x1) -> b#(a(x1))
            b#(b(b(x1))) -> b#(c(x1))
           TRS:
            a(b(a(x1))) -> c(b(x1))
            b(b(b(x1))) -> b(c(x1))
            c(x1) -> b(a(x1))
           EDG Processor:
            DPs:
             c#(x1) -> b#(a(x1))
             b#(b(b(x1))) -> b#(c(x1))
            TRS:
             a(b(a(x1))) -> c(b(x1))
             b(b(b(x1))) -> b(c(x1))
             c(x1) -> b(a(x1))
            graph:
             c#(x1) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(c(x1))
             b#(b(b(x1))) -> b#(c(x1)) -> b#(b(b(x1))) -> b#(c(x1))
            SCC Processor:
             #sccs: 1
             #rules: 1
             #arcs: 2/4
             DPs:
              b#(b(b(x1))) -> b#(c(x1))
             TRS:
              a(b(a(x1))) -> c(b(x1))
              b(b(b(x1))) -> b(c(x1))
              c(x1) -> b(a(x1))
             Arctic Interpretation Processor:
              dimension: 3
              usable rules:
               a(b(a(x1))) -> c(b(x1))
               b(b(b(x1))) -> b(c(x1))
               c(x1) -> b(a(x1))
              interpretation:
               [b#](x0) = [0  0  -&]x0 + [0],
               
                         [-& 0  1 ]     [1 ]
               [c](x0) = [-& -& -&]x0 + [-&]
                         [-& 1  0 ]     [1 ],
               
                         [1  -& 1 ]     [1 ]
               [b](x0) = [-& -& -&]x0 + [-&]
                         [-& 0  -&]     [0 ],
               
                         [-& -& 0 ]     [0]
               [a](x0) = [-& 1  0 ]x0 + [1]
                         [-& -& 0 ]     [0]
              orientation:
               b#(b(b(x1))) = [2 1 2]x1 + [2] >= [-& 0  1 ]x1 + [1] = b#(c(x1))
               
                             [-& 1  0 ]     [1]    [-& 1  -&]     [1 ]           
               a(b(a(x1))) = [-& 1  0 ]x1 + [1] >= [-& -& -&]x1 + [-&] = c(b(x1))
                             [-& 1  0 ]     [1]    [-& 0  -&]     [1 ]           
               
                             [3  2  3 ]     [3 ]    [-& 2  2 ]     [2 ]           
               b(b(b(x1))) = [-& -& -&]x1 + [-&] >= [-& -& -&]x1 + [-&] = b(c(x1))
                             [-& -& -&]     [0 ]    [-& -& -&]     [0 ]           
               
                       [-& 0  1 ]     [1 ]    [-& -& 1 ]     [1 ]           
               c(x1) = [-& -& -&]x1 + [-&] >= [-& -& -&]x1 + [-&] = b(a(x1))
                       [-& 1  0 ]     [1 ]    [-& 1  0 ]     [1 ]           
              problem:
               DPs:
                
               TRS:
                a(b(a(x1))) -> c(b(x1))
                b(b(b(x1))) -> b(c(x1))
                c(x1) -> b(a(x1))
              Qed