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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(b(x1)))
  b(a(c(x1))) -> c(a(a(x1)))
  b(c(x1)) -> x1
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    b#(a(c(x1))) -> a#(x1)
    b#(a(c(x1))) -> a#(a(x1))
   TRS:
    a(x1) -> c(b(b(x1)))
    b(a(c(x1))) -> c(a(a(x1)))
    b(c(x1)) -> x1
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(x1)
     b#(a(c(x1))) -> a#(a(x1))
    TRS:
     a(x1) -> c(b(b(x1)))
     b(a(c(x1))) -> c(a(a(x1)))
     b(c(x1)) -> x1
    graph:
     b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
     b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
     b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(a(x1))
     a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(a(x1))
     a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> c(b(b(x1)))
      b(a(c(x1))) -> c(a(a(x1)))
      b(c(x1)) -> x1
     interpretation:
      [b#](x0) = [0 0]x0,
      
      [a#](x0) = [0 0]x0,
      
                [0 0]  
      [b](x0) = [0 0]x0,
      
                [0  -&]     [0 ]
      [c](x0) = [0  0 ]x0 + [-&],
      
                [0 1]     [0 ]
      [a](x0) = [0 0]x0 + [-&]
     orientation:
      a#(x1) = [0 0]x1 >= [0 0]x1 = b#(x1)
      
      a#(x1) = [0 0]x1 >= [0 0]x1 = b#(b(x1))
      
      b#(a(c(x1))) = [1 1]x1 + [0] >= [0 0]x1 = a#(x1)
      
      b#(a(c(x1))) = [1 1]x1 + [0] >= [0 1]x1 + [0] = a#(a(x1))
      
              [0 1]     [0 ]    [0 0]     [0 ]              
      a(x1) = [0 0]x1 + [-&] >= [0 0]x1 + [-&] = c(b(b(x1)))
      
                    [1 1]     [0]    [1 1]     [0]              
      b(a(c(x1))) = [1 1]x1 + [0] >= [1 1]x1 + [0] = c(a(a(x1)))
      
                 [0 0]     [0]           
      b(c(x1)) = [0 0]x1 + [0] >= x1 = x1
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       b#(a(c(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> c(b(b(x1)))
       b(a(c(x1))) -> c(a(a(x1)))
       b(c(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       b#(a(c(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> c(b(b(x1)))
       b(a(c(x1))) -> c(a(a(x1)))
       b(c(x1)) -> x1
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(x1))
        b#(a(c(x1))) -> a#(a(x1))
       TRS:
        a(x1) -> c(b(b(x1)))
        b(a(c(x1))) -> c(a(a(x1)))
        b(c(x1)) -> x1
       graph:
        b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
        b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(b(x1))
        a#(x1) -> b#(b(x1)) -> b#(a(c(x1))) -> a#(a(x1))
        a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(a(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> c(b(b(x1)))
         b(a(c(x1))) -> c(a(a(x1)))
         b(c(x1)) -> x1
        interpretation:
         [b#](x0) = [0  -&]x0 + [0],
         
         [a#](x0) = [0 1]x0 + [1],
         
                   [-& 0 ]     [0]
         [b](x0) = [0  0 ]x0 + [1],
         
                   [-& -&]     [1]
         [c](x0) = [0  0 ]x0 + [1],
         
                   [0 1]     [1]
         [a](x0) = [0 0]x0 + [1]
        orientation:
         a#(x1) = [0 1]x1 + [1] >= [0  -&]x1 + [0] = b#(x1)
         
         a#(x1) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(b(x1))
         
         b#(a(c(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a#(a(x1))
         
                 [0 1]     [1]    [-& -&]     [1]              
         a(x1) = [0 0]x1 + [1] >= [0  0 ]x1 + [1] = c(b(b(x1)))
         
                       [0 0]     [1]    [-& -&]     [1]              
         b(a(c(x1))) = [1 1]x1 + [2] >= [1  1 ]x1 + [2] = c(a(a(x1)))
         
                    [0 0]     [1]           
         b(c(x1)) = [0 0]x1 + [1] >= x1 = x1
        problem:
         DPs:
          a#(x1) -> b#(x1)
          b#(a(c(x1))) -> a#(a(x1))
         TRS:
          a(x1) -> c(b(b(x1)))
          b(a(c(x1))) -> c(a(a(x1)))
          b(c(x1)) -> x1
        Restore Modifier:
         DPs:
          a#(x1) -> b#(x1)
          b#(a(c(x1))) -> a#(a(x1))
         TRS:
          a(x1) -> c(b(b(x1)))
          b(a(c(x1))) -> c(a(a(x1)))
          b(c(x1)) -> x1
         EDG Processor:
          DPs:
           a#(x1) -> b#(x1)
           b#(a(c(x1))) -> a#(a(x1))
          TRS:
           a(x1) -> c(b(b(x1)))
           b(a(c(x1))) -> c(a(a(x1)))
           b(c(x1)) -> x1
          graph:
           b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
           a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(a(x1))
          Arctic Interpretation Processor:
           dimension: 2
           usable rules:
            a(x1) -> c(b(b(x1)))
            b(a(c(x1))) -> c(a(a(x1)))
            b(c(x1)) -> x1
           interpretation:
            [b#](x0) = [2  -&]x0,
            
            [a#](x0) = [3  -&]x0 + [0],
            
                      [-& 0 ]     [0]
            [b](x0) = [0  -&]x0 + [0],
            
                      [-& 0 ]     [2]
            [c](x0) = [0  1 ]x0 + [1],
            
                      [-& 2 ]     [2]
            [a](x0) = [0  1 ]x0 + [1]
           orientation:
            a#(x1) = [3  -&]x1 + [0] >= [2  -&]x1 = b#(x1)
            
            b#(a(c(x1))) = [4 5]x1 + [5] >= [-& 5 ]x1 + [5] = a#(a(x1))
            
                    [-& 2 ]     [2]    [-& 0 ]     [2]              
            a(x1) = [0  1 ]x1 + [1] >= [0  1 ]x1 + [1] = c(b(b(x1)))
            
                          [1 2]     [2]    [1 2]     [2]              
            b(a(c(x1))) = [2 3]x1 + [3] >= [2 3]x1 + [3] = c(a(a(x1)))
            
                       [0  1 ]     [1]           
            b(c(x1)) = [-& 0 ]x1 + [2] >= x1 = x1
           problem:
            DPs:
             b#(a(c(x1))) -> a#(a(x1))
            TRS:
             a(x1) -> c(b(b(x1)))
             b(a(c(x1))) -> c(a(a(x1)))
             b(c(x1)) -> x1
           Restore Modifier:
            DPs:
             b#(a(c(x1))) -> a#(a(x1))
            TRS:
             a(x1) -> c(b(b(x1)))
             b(a(c(x1))) -> c(a(a(x1)))
             b(c(x1)) -> x1
            EDG Processor:
             DPs:
              b#(a(c(x1))) -> a#(a(x1))
             TRS:
              a(x1) -> c(b(b(x1)))
              b(a(c(x1))) -> c(a(a(x1)))
              b(c(x1)) -> x1
             graph:
              
             SCC Processor:
              #sccs: 0
              #rules: 0
              #arcs: 0/1