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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(c(a(x1)))
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(c(b(x1)))
  TRS:
   a(b(x1)) -> b(c(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   b(a(x1)) -> a(c(b(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1)))
   TRS:
    a(b(x1)) -> b(c(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    b(a(x1)) -> a(c(b(x1)))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> b#(c(a(x1)))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> a#(c(b(x1)))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   Polynomial Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = x0,
     
     [a#](x0) = x0 + 1,
     
     [c](x0) = x0,
     
     [a](x0) = x0 + 1,
     
     [b](x0) = x0
    orientation:
     a#(b(x1)) = x1 + 1 >= x1 + 1 = a#(x1)
     
     a#(b(x1)) = x1 + 1 >= x1 + 1 = b#(c(a(x1)))
     
     b#(c(x1)) = x1 >= x1 = b#(x1)
     
     b#(c(x1)) = x1 >= x1 = b#(b(x1))
     
     b#(a(x1)) = x1 + 1 >= x1 = b#(x1)
     
     b#(a(x1)) = x1 + 1 >= x1 + 1 = a#(c(b(x1)))
     
     a(b(x1)) = x1 + 1 >= x1 + 1 = b(c(a(x1)))
     
     b(c(x1)) = x1 >= x1 = c(b(b(x1)))
     
     b(a(x1)) = x1 + 1 >= x1 + 1 = a(c(b(x1)))
    problem:
     DPs:
      a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> b#(c(a(x1)))
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1))
      b#(a(x1)) -> a#(c(b(x1)))
     TRS:
      a(b(x1)) -> b(c(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      b(a(x1)) -> a(c(b(x1)))
    Polynomial Interpretation Processor:
     dimension: 1
     usable rules:
      
     interpretation:
      [b#](x0) = 1,
      
      [a#](x0) = x0 + 1,
      
      [c](x0) = 0,
      
      [a](x0) = 0,
      
      [b](x0) = x0 + 1
     orientation:
      a#(b(x1)) = x1 + 2 >= x1 + 1 = a#(x1)
      
      a#(b(x1)) = x1 + 2 >= 1 = b#(c(a(x1)))
      
      b#(c(x1)) = 1 >= 1 = b#(x1)
      
      b#(c(x1)) = 1 >= 1 = b#(b(x1))
      
      b#(a(x1)) = 1 >= 1 = a#(c(b(x1)))
      
      a(b(x1)) = 0 >= 1 = b(c(a(x1)))
      
      b(c(x1)) = 1 >= 0 = c(b(b(x1)))
      
      b(a(x1)) = 1 >= 0 = a(c(b(x1)))
     problem:
      DPs:
       b#(c(x1)) -> b#(x1)
       b#(c(x1)) -> b#(b(x1))
       b#(a(x1)) -> a#(c(b(x1)))
      TRS:
       a(b(x1)) -> b(c(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       b(a(x1)) -> a(c(b(x1)))
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 20/9
      DPs:
       b#(c(x1)) -> b#(b(x1))
       b#(c(x1)) -> b#(x1)
      TRS:
       a(b(x1)) -> b(c(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       b(a(x1)) -> a(c(b(x1)))
      Usable Rule Processor:
       DPs:
        b#(c(x1)) -> b#(b(x1))
        b#(c(x1)) -> b#(x1)
       TRS:
        b(c(x1)) -> c(b(b(x1)))
        b(a(x1)) -> a(c(b(x1)))
       Polynomial Interpretation Processor:
        dimension: 1
        usable rules:
         b(c(x1)) -> c(b(b(x1)))
         b(a(x1)) -> a(c(b(x1)))
        interpretation:
         [b#](x0) = x0,
         
         [c](x0) = x0 + 1,
         
         [a](x0) = 1,
         
         [b](x0) = x0
        orientation:
         b#(c(x1)) = x1 + 1 >= x1 = b#(b(x1))
         
         b#(c(x1)) = x1 + 1 >= x1 = b#(x1)
         
         b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1)))
         
         b(a(x1)) = 1 >= 1 = a(c(b(x1)))
        problem:
         DPs:
          
         TRS:
          b(c(x1)) -> c(b(b(x1)))
          b(a(x1)) -> a(c(b(x1)))
        Qed