/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)))
 a(c(x1)) -> c(a(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))
   a#(c(x1)) -> b#(x1)
   a#(c(x1)) -> a#(b(x1))
  TRS:
   a(b(x1)) -> b(c(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   a(c(x1)) -> c(a(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))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1))
   TRS:
    a(b(x1)) -> b(c(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    a(c(x1)) -> c(a(b(x1)))
   graph:
    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#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1))
    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(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#(c(x1)) -> a#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(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)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 16/36
    DPs:
     a#(c(x1)) -> a#(b(x1))
     a#(b(x1)) -> a#(x1)
    TRS:
     a(b(x1)) -> b(c(a(x1)))
     b(c(x1)) -> c(b(b(x1)))
     a(c(x1)) -> c(a(b(x1)))
    Usable Rule Processor:
     DPs:
      a#(c(x1)) -> a#(b(x1))
      a#(b(x1)) -> a#(x1)
     TRS:
      b(c(x1)) -> c(b(b(x1)))
     Polynomial Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0,
       
       [c](x0) = x0 + 1,
       
       [b](x0) = x0
      orientation:
       a#(c(x1)) = x1 + 1 >= x1 = a#(b(x1))
       
       a#(b(x1)) = x1 >= x1 = a#(x1)
       
       b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1)))
      problem:
       DPs:
        a#(b(x1)) -> a#(x1)
       TRS:
        b(c(x1)) -> c(b(b(x1)))
      Usable Rule Processor:
       DPs:
        a#(b(x1)) -> a#(x1)
       TRS:
        
       Polynomial Interpretation Processor:
        dimension: 1
        interpretation:
         [a#](x0) = x0,
         
         [b](x0) = x0 + 1
        orientation:
         a#(b(x1)) = x1 + 1 >= x1 = a#(x1)
        problem:
         DPs:
          
         TRS:
          
        Qed
    
    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)))
     a(c(x1)) -> c(a(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)))
     Polynomial Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0 + 1,
       
       [c](x0) = x0 + 1,
       
       [b](x0) = x0
      orientation:
       b#(c(x1)) = x1 + 2 >= x1 + 1 = b#(b(x1))
       
       b#(c(x1)) = x1 + 2 >= x1 + 1 = b#(x1)
       
       b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1)))
      problem:
       DPs:
        
       TRS:
        b(c(x1)) -> c(b(b(x1)))
      Qed