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

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