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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(x1) -> b(x1)
  c(b(a(x1))) -> a(b(a(c(c(x1)))))
  c(x1) -> x1
  DP Processor:
   DPs:
    c#(b(a(x1))) -> c#(x1)
    c#(b(a(x1))) -> c#(c(x1))
    c#(b(a(x1))) -> a#(c(c(x1)))
    c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
   TRS:
    a(x1) -> x1
    a(x1) -> b(x1)
    c(b(a(x1))) -> a(b(a(c(c(x1)))))
    c(x1) -> x1
   TDG Processor:
    DPs:
     c#(b(a(x1))) -> c#(x1)
     c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> a#(c(c(x1)))
     c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
    TRS:
     a(x1) -> x1
     a(x1) -> b(x1)
     c(b(a(x1))) -> a(b(a(c(c(x1)))))
     c(x1) -> x1
    graph:
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(c(c(x1)))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1)
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(c(c(x1)))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 8/16
     DPs:
      c#(b(a(x1))) -> c#(c(x1))
      c#(b(a(x1))) -> c#(x1)
     TRS:
      a(x1) -> x1
      a(x1) -> b(x1)
      c(b(a(x1))) -> a(b(a(c(c(x1)))))
      c(x1) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       a(x1) -> b(x1)
       c(b(a(x1))) -> a(b(a(c(c(x1)))))
       c(x1) -> x1
      interpretation:
       [c#](x0) = [0 3]x0,
       
                 [0 0]     [0]
       [c](x0) = [0 0]x0 + [2],
       
                 [0  -&]     [-&]
       [b](x0) = [1  0 ]x0 + [0 ],
       
                 [0 0]     [-&]
       [a](x0) = [1 0]x0 + [3 ]
      orientation:
       c#(b(a(x1))) = [4 4]x1 + [6] >= [3 3]x1 + [5] = c#(c(x1))
       
       c#(b(a(x1))) = [4 4]x1 + [6] >= [0 3]x1 = c#(x1)
       
               [0 0]     [-&]           
       a(x1) = [1 0]x1 + [3 ] >= x1 = x1
       
               [0 0]     [-&]    [0  -&]     [-&]        
       a(x1) = [1 0]x1 + [3 ] >= [1  0 ]x1 + [0 ] = b(x1)
       
                     [1 1]     [3]    [1 1]     [3]                    
       c(b(a(x1))) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(a(c(c(x1)))))
       
               [0 0]     [0]           
       c(x1) = [0 0]x1 + [2] >= x1 = x1
      problem:
       DPs:
        
       TRS:
        a(x1) -> x1
        a(x1) -> b(x1)
        c(b(a(x1))) -> a(b(a(c(c(x1)))))
        c(x1) -> x1
      Qed