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

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