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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(x1) -> b(x1)
  b(x1) -> x1
  c(a(b(x1))) -> a(a(b(c(c(x1)))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    c#(a(b(x1))) -> c#(x1)
    c#(a(b(x1))) -> c#(c(x1))
    c#(a(b(x1))) -> b#(c(c(x1)))
    c#(a(b(x1))) -> a#(b(c(c(x1))))
    c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
   TRS:
    a(x1) -> x1
    a(x1) -> b(x1)
    b(x1) -> x1
    c(a(b(x1))) -> a(a(b(c(c(x1)))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> c#(c(x1))
     c#(a(b(x1))) -> b#(c(c(x1)))
     c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
    TRS:
     a(x1) -> x1
     a(x1) -> b(x1)
     b(x1) -> x1
     c(a(b(x1))) -> a(a(b(c(c(x1)))))
    graph:
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> b#(c(c(x1)))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1))
     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> b#(c(c(x1)))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(c(x1))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> a#(b(c(c(x1)))) -> a#(x1) -> b#(x1)
     c#(a(b(x1))) -> a#(a(b(c(c(x1))))) -> a#(x1) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      c#(a(b(x1))) -> c#(c(x1))
      c#(a(b(x1))) -> c#(x1)
     TRS:
      a(x1) -> x1
      a(x1) -> b(x1)
      b(x1) -> x1
      c(a(b(x1))) -> a(a(b(c(c(x1)))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       a(x1) -> b(x1)
       b(x1) -> x1
       c(a(b(x1))) -> a(a(b(c(c(x1)))))
      interpretation:
       [c#](x0) = [0 2]x0 + [0],
       
                 [0  0 ]     [0 ]
       [c](x0) = [-& 0 ]x0 + [-&],
       
                 [0 0]     [2]
       [b](x0) = [0 0]x0 + [0],
       
                 [0 0]     [2]
       [a](x0) = [2 0]x0 + [0]
      orientation:
       c#(a(b(x1))) = [4 4]x1 + [6] >= [0 2]x1 + [0] = c#(c(x1))
       
       c#(a(b(x1))) = [4 4]x1 + [6] >= [0 2]x1 + [0] = c#(x1)
       
               [0 0]     [2]           
       a(x1) = [2 0]x1 + [0] >= x1 = x1
       
               [0 0]     [2]    [0 0]     [2]        
       a(x1) = [2 0]x1 + [0] >= [0 0]x1 + [0] = b(x1)
       
               [0 0]     [2]           
       b(x1) = [0 0]x1 + [0] >= x1 = x1
       
                     [2 2]     [4]    [2 2]     [4]                    
       c(a(b(x1))) = [2 2]x1 + [4] >= [2 2]x1 + [4] = a(a(b(c(c(x1)))))
      problem:
       DPs:
        
       TRS:
        a(x1) -> x1
        a(x1) -> b(x1)
        b(x1) -> x1
        c(a(b(x1))) -> a(a(b(c(c(x1)))))
      Qed