/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 a(x1) -> x1
 a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
 c(b(x1)) -> x1

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> c#(a(x1))
   a#(a(b(x1))) -> a#(c(a(x1)))
   a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
   c(b(x1)) -> x1
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(c(a(x1)))
    a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
    c(b(x1)) -> x1
   graph:
    a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
    a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(c(a(x1)))
    a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(b(a(c(a(x1))))) ->
    a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
    a#(a(b(x1))) -> a#(b(a(c(a(x1))))) ->
    a#(a(b(x1))) -> a#(c(a(x1)))
    a#(a(b(x1))) -> a#(b(a(c(a(x1))))) ->
    a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(b(a(c(a(x1))))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(c(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   EDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> c#(a(x1))
     a#(a(b(x1))) -> a#(c(a(x1)))
     a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
     c(b(x1)) -> x1
    graph:
     a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> c#(a(x1))
     a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(c(a(x1)))
     a#(a(b(x1))) -> a#(c(a(x1))) -> a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> c#(a(x1))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(c(a(x1)))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(c(a(x1)))))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 8/16
     DPs:
      a#(a(b(x1))) -> a#(c(a(x1)))
      a#(a(b(x1))) -> a#(x1)
     TRS:
      a(x1) -> x1
      a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
      c(b(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
       c(b(x1)) -> x1
      interpretation:
       [a#](x0) = [0 0 0]x0 + [0],
       
                 [-& 0  -&]     [0]
       [c](x0) = [-& 0  -&]x0 + [0]
                 [-& 0  -&]     [0],
       
                 [0  1  1 ]     [1 ]
       [b](x0) = [0  0  0 ]x0 + [-&]
                 [-& 0  0 ]     [0 ],
       
                 [0  0  1 ]     [0]
       [a](x0) = [-& 0  0 ]x0 + [0]
                 [0  0  0 ]     [0]
      orientation:
       a#(a(b(x1))) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = a#(c(a(x1)))
       
       a#(a(b(x1))) = [0 1 1]x1 + [1] >= [0 0 0]x1 + [0] = a#(x1)
       
               [0  0  1 ]     [0]           
       a(x1) = [-& 0  0 ]x1 + [0] >= x1 = x1
               [0  0  0 ]     [0]           
       
                     [1 2 2]     [2]    [-& 2  2 ]     [2]                       
       a(a(b(x1))) = [0 1 1]x1 + [1] >= [-& 1  1 ]x1 + [1] = b(a(b(a(c(a(x1))))))
                     [0 1 1]     [1]    [-& 1  1 ]     [1]                       
       
                  [0 0 0]     [0]           
       c(b(x1)) = [0 0 0]x1 + [0] >= x1 = x1
                  [0 0 0]     [0]           
      problem:
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
        c(b(x1)) -> x1
      Restore Modifier:
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
        c(b(x1)) -> x1
       EDG Processor:
        DPs:
         a#(a(b(x1))) -> a#(x1)
        TRS:
         a(x1) -> x1
         a(a(b(x1))) -> b(a(b(a(c(a(x1))))))
         c(b(x1)) -> x1
        graph:
         a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
        Usable Rule Processor:
         DPs:
          a#(a(b(x1))) -> a#(x1)
         TRS:
          
         Arctic Interpretation Processor:
          dimension: 1
          usable rules:
           
          interpretation:
           [a#](x0) = x0,
           
           [b](x0) = 14x0 + 6,
           
           [a](x0) = 2x0 + -16
          orientation:
           a#(a(b(x1))) = 16x1 + 8 >= x1 = a#(x1)
          problem:
           DPs:
            
           TRS:
            
          Qed