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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(x1))
  c(c(x1)) -> a(b(c(b(c(x1)))))
  DP Processor:
   DPs:
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> a#(c(x1))
    c#(c(x1)) -> b#(c(x1))
    c#(c(x1)) -> c#(b(c(x1)))
    c#(c(x1)) -> b#(c(b(c(x1))))
    c#(c(x1)) -> a#(b(c(b(c(x1)))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(x1))
    c(c(x1)) -> a(b(c(b(c(x1)))))
   TDG Processor:
    DPs:
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(c(x1))
     c#(c(x1)) -> c#(b(c(x1)))
     c#(c(x1)) -> b#(c(b(c(x1))))
     c#(c(x1)) -> a#(b(c(b(c(x1)))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(x1))
     c(c(x1)) -> a(b(c(b(c(x1)))))
    graph:
     c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(b(c(b(c(x1)))))
     c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(b(c(x1))))
     c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> c#(b(c(x1)))
     c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(x1))
     c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(b(c(x1)))))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(c(x1))))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(c(x1)))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(c(x1)) -> c#(b(c(x1)))
      c#(c(x1)) -> b#(c(x1))
      b#(a(x1)) -> c#(x1)
      c#(c(x1)) -> b#(c(b(c(x1))))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(x1))
      c(c(x1)) -> a(b(c(b(c(x1)))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> a(c(x1))
       c(c(x1)) -> a(b(c(b(c(x1)))))
      interpretation:
       [c#](x0) = [1 0]x0 + [0],
       
       [b#](x0) = [1 0]x0 + [0],
       
                 [1  0 ]     [1]
       [c](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [b](x0) = [0  1 ]x0 + [0],
       
                 [0 1]     [0]
       [a](x0) = [1 0]x0 + [1]
      orientation:
       c#(c(x1)) = [2 1]x1 + [2] >= [1 0]x1 + [1] = c#(b(c(x1)))
       
       c#(c(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = b#(c(x1))
       
       b#(a(x1)) = [1 2]x1 + [1] >= [1 0]x1 + [0] = c#(x1)
       
       c#(c(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = b#(c(b(c(x1))))
       
               [0 1]     [0]           
       a(x1) = [1 0]x1 + [1] >= x1 = x1
       
                  [1 0]     [1]    [1 0]     [1]           
       b(a(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = a(c(x1))
       
                  [2 1]     [2]    [2 1]     [2]                    
       c(c(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(b(c(b(c(x1)))))
      problem:
       DPs:
        c#(c(x1)) -> b#(c(x1))
        b#(a(x1)) -> c#(x1)
        c#(c(x1)) -> b#(c(b(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(x1))
        c(c(x1)) -> a(b(c(b(c(x1)))))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> b#(c(x1))
        b#(a(x1)) -> c#(x1)
        c#(c(x1)) -> b#(c(b(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(x1))
        c(c(x1)) -> a(b(c(b(c(x1)))))
       EDG Processor:
        DPs:
         c#(c(x1)) -> b#(c(x1))
         b#(a(x1)) -> c#(x1)
         c#(c(x1)) -> b#(c(b(c(x1))))
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(c(x1))
         c(c(x1)) -> a(b(c(b(c(x1)))))
        graph:
         c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1)
         c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
         b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1))
         b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(c(x1))))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(x1)) -> a(c(x1))
          c(c(x1)) -> a(b(c(b(c(x1)))))
         interpretation:
          [c#](x0) = [1 0]x0 + [2],
          
          [b#](x0) = [0 0]x0 + [0],
          
                    [1  0 ]     [2]
          [c](x0) = [0  -&]x0 + [0],
          
                    [-& 0 ]     [1]
          [b](x0) = [0  1 ]x0 + [0],
          
                    [0 0]     [0]
          [a](x0) = [1 0]x0 + [2]
         orientation:
          c#(c(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = b#(c(x1))
          
          b#(a(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = c#(x1)
          
          c#(c(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = b#(c(b(c(x1))))
          
                  [0 0]     [0]           
          a(x1) = [1 0]x1 + [2] >= x1 = x1
          
                     [1 0]     [2]    [1 0]     [2]           
          b(a(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(c(x1))
          
                     [2 1]     [3]    [1 0]     [2]                    
          c(c(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(b(c(b(c(x1)))))
         problem:
          DPs:
           b#(a(x1)) -> c#(x1)
          TRS:
           a(x1) -> x1
           b(a(x1)) -> a(c(x1))
           c(c(x1)) -> a(b(c(b(c(x1)))))
         Restore Modifier:
          DPs:
           b#(a(x1)) -> c#(x1)
          TRS:
           a(x1) -> x1
           b(a(x1)) -> a(c(x1))
           c(c(x1)) -> a(b(c(b(c(x1)))))
          EDG Processor:
           DPs:
            b#(a(x1)) -> c#(x1)
           TRS:
            a(x1) -> x1
            b(a(x1)) -> a(c(x1))
            c(c(x1)) -> a(b(c(b(c(x1)))))
           graph:
            
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 0/1