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

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