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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> a#(c(x1))
   a#(a(x1)) -> a#(b(a(c(x1))))
   c#(b(b(x1))) -> a#(x1)
  TRS:
   a(x1) -> b(x1)
   a(a(x1)) -> a(b(a(c(x1))))
   c(b(b(x1))) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(c(x1))
    a#(a(x1)) -> a#(b(a(c(x1))))
    c#(b(b(x1))) -> a#(x1)
   TRS:
    a(x1) -> b(x1)
    a(a(x1)) -> a(b(a(c(x1))))
    c(b(b(x1))) -> a(x1)
   graph:
    c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(x1))))
    c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
    c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(c(x1))))
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(a(c(x1)))) -> a#(a(x1)) -> a#(b(a(c(x1))))
    a#(a(x1)) -> a#(b(a(c(x1)))) -> a#(a(x1)) -> a#(c(x1))
    a#(a(x1)) -> a#(b(a(c(x1)))) -> a#(a(x1)) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(c(x1))
     a#(a(x1)) -> a#(b(a(c(x1))))
     c#(b(b(x1))) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     a(a(x1)) -> a(b(a(c(x1))))
     c(b(b(x1))) -> a(x1)
    graph:
     c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
     c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
     c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(x1))))
     a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
     a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
     a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(c(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 7/16
     DPs:
      c#(b(b(x1))) -> a#(x1)
      a#(a(x1)) -> a#(c(x1))
      a#(a(x1)) -> c#(x1)
     TRS:
      a(x1) -> b(x1)
      a(a(x1)) -> a(b(a(c(x1))))
      c(b(b(x1))) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> b(x1)
       a(a(x1)) -> a(b(a(c(x1))))
       c(b(b(x1))) -> a(x1)
      interpretation:
       [c#](x0) = [0 2]x0 + [0],
       
       [a#](x0) = [-& 1 ]x0 + [0],
       
                 [0 0]     [0]
       [c](x0) = [0 1]x0 + [0],
       
                 [-& 0 ]     [0]
       [b](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [a](x0) = [0  1 ]x0 + [0]
      orientation:
       c#(b(b(x1))) = [0 2]x1 + [2] >= [-& 1 ]x1 + [0] = a#(x1)
       
       a#(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = a#(c(x1))
       
       a#(a(x1)) = [1 2]x1 + [1] >= [0 2]x1 + [0] = c#(x1)
       
               [-& 0 ]     [0]    [-& 0 ]     [0]        
       a(x1) = [0  1 ]x1 + [0] >= [0  -&]x1 + [0] = b(x1)
       
                  [0 1]     [0]    [0 1]     [0]                 
       a(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = a(b(a(c(x1))))
       
                     [0 0]     [0]    [-& 0 ]     [0]        
       c(b(b(x1))) = [0 1]x1 + [1] >= [0  1 ]x1 + [0] = a(x1)
      problem:
       DPs:
        a#(a(x1)) -> a#(c(x1))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> b(x1)
        a(a(x1)) -> a(b(a(c(x1))))
        c(b(b(x1))) -> a(x1)
      Restore Modifier:
       DPs:
        a#(a(x1)) -> a#(c(x1))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> b(x1)
        a(a(x1)) -> a(b(a(c(x1))))
        c(b(b(x1))) -> a(x1)
       EDG Processor:
        DPs:
         a#(a(x1)) -> a#(c(x1))
         a#(a(x1)) -> c#(x1)
        TRS:
         a(x1) -> b(x1)
         a(a(x1)) -> a(b(a(c(x1))))
         c(b(b(x1))) -> a(x1)
        graph:
         a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
         a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          a#(a(x1)) -> a#(c(x1))
         TRS:
          a(x1) -> b(x1)
          a(a(x1)) -> a(b(a(c(x1))))
          c(b(b(x1))) -> a(x1)
         Arctic Interpretation Processor:
          dimension: 2
          usable rules:
           a(x1) -> b(x1)
           a(a(x1)) -> a(b(a(c(x1))))
           c(b(b(x1))) -> a(x1)
          interpretation:
           [a#](x0) = [0 0]x0 + [0],
           
                     [0 0]     [0 ]
           [c](x0) = [0 0]x0 + [-&],
           
                     [0 1]     [1 ]
           [b](x0) = [0 0]x0 + [-&],
           
                     [1 1]     [1 ]
           [a](x0) = [0 0]x0 + [-&]
          orientation:
           a#(a(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(c(x1))
           
                   [1 1]     [1 ]    [0 1]     [1 ]        
           a(x1) = [0 0]x1 + [-&] >= [0 0]x1 + [-&] = b(x1)
           
                      [2 2]     [2]    [2 2]     [2]                 
           a(a(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(a(c(x1))))
           
                         [1 1]     [1]    [1 1]     [1 ]        
           c(b(b(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [-&] = a(x1)
          problem:
           DPs:
            
           TRS:
            a(x1) -> b(x1)
            a(a(x1)) -> a(b(a(c(x1))))
            c(b(b(x1))) -> a(x1)
          Qed