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

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