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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> a#(b(c(x1)))
   a#(a(x1)) -> b#(a(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(a(b(c(x1))))
   b(x1) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(a(b(c(x1))))
    b(x1) -> x1
    c(b(x1)) -> a(c(x1))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(b(c(x1))))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(c(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(a(b(c(x1))))
     b(x1) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> x1
      a(a(x1)) -> b(a(b(c(x1))))
      b(x1) -> x1
      c(b(x1)) -> a(c(x1))
     interpretation:
      [c#](x0) = [-& -& 0 ]x0 + [1],
      
      [a#](x0) = [1 0 0]x0 + [0],
      
                [0  -& 0 ]     [0]
      [b](x0) = [-& 0  0 ]x0 + [1]
                [0  0  1 ]     [1],
      
                [-& -& 0 ]     [0]
      [c](x0) = [0  -& 0 ]x0 + [0]
                [-& -& 0 ]     [0],
      
                [1  -& 1 ]     [1]
      [a](x0) = [0  0  0 ]x0 + [0]
                [1  -& 0 ]     [0]
     orientation:
      c#(b(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [1] = c#(x1)
      
      c#(b(x1)) = [0 0 1]x1 + [1] >= [0  -& 1 ]x1 + [1] = a#(c(x1))
      
      a#(a(x1)) = [2 0 2]x1 + [2] >= [-& -& 0 ]x1 + [1] = c#(x1)
      
      a#(a(x1)) = [2 0 2]x1 + [2] >= [0  -& 1 ]x1 + [1] = a#(b(c(x1)))
      
              [1  -& 1 ]     [1]           
      a(x1) = [0  0  0 ]x1 + [0] >= x1 = x1
              [1  -& 0 ]     [0]           
      
                 [2  -& 2 ]     [2]    [1  -& 2 ]     [2]                 
      a(a(x1)) = [1  0  1 ]x1 + [1] >= [0  -& 1 ]x1 + [1] = b(a(b(c(x1))))
                 [2  -& 2 ]     [2]    [1  -& 2 ]     [2]                 
      
              [0  -& 0 ]     [0]           
      b(x1) = [-& 0  0 ]x1 + [1] >= x1 = x1
              [0  0  1 ]     [1]           
      
                 [0 0 1]     [1]    [-& -& 1 ]     [1]           
      c(b(x1)) = [0 0 1]x1 + [1] >= [0  -& 0 ]x1 + [0] = a(c(x1))
                 [0 0 1]     [1]    [-& -& 1 ]     [1]           
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(x1) -> x1
       c(b(x1)) -> a(c(x1))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(x1) -> x1
       c(b(x1)) -> a(c(x1))
      EDG Processor:
       DPs:
        c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(a(b(c(x1))))
        b(x1) -> x1
        c(b(x1)) -> a(c(x1))
       graph:
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/4
        DPs:
         c#(b(x1)) -> c#(x1)
        TRS:
         a(x1) -> x1
         a(a(x1)) -> b(a(b(c(x1))))
         b(x1) -> x1
         c(b(x1)) -> a(c(x1))
        Usable Rule Processor:
         DPs:
          c#(b(x1)) -> c#(x1)
         TRS:
          
         Arctic Interpretation Processor:
          dimension: 4
          usable rules:
           
          interpretation:
           [c#](x0) = [0  -& -& -&]x0,
           
                     [1 0 0 0]     [0]
                     [0 0 0 0]     [0]
           [b](x0) = [1 0 0 0]x0 + [0]
                     [0 0 0 0]     [0]
          orientation:
           c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = c#(x1)
          problem:
           DPs:
            
           TRS:
            
          Qed