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

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