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

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