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

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