/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 strict:
  a(c(a(x1))) -> a(c(b(x1)))
  b(b(c(x1))) -> b(c(c(x1)))
  c(c(b(x1))) -> c(a(b(x1)))
  b(a(a(x1))) -> a(b(a(x1)))
  b(a(c(x1))) -> a(b(a(x1)))
  a(c(a(x1))) -> b(c(c(x1)))
 weak:
  b(c(a(x1))) -> b(a(a(x1)))

Proof:
 String Reversal Processor:
  strict:
   a(c(a(x1))) -> b(c(a(x1)))
   c(b(b(x1))) -> c(c(b(x1)))
   b(c(c(x1))) -> b(a(c(x1)))
   a(a(b(x1))) -> a(b(a(x1)))
   c(a(b(x1))) -> a(b(a(x1)))
   a(c(a(x1))) -> c(c(b(x1)))
  weak:
   a(c(b(x1))) -> a(a(b(x1)))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 1]  
    [c](x0) = [0 1]x0,
    
              [1 0]     [0]
    [a](x0) = [0 0]x0 + [2],
    
              [1 0]  
    [b](x0) = [0 0]x0
   orientation:
                  [1 0]     [2]    [1 0]     [2]              
    a(c(a(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [0] = b(c(a(x1)))
    
                  [1 0]      [1 0]                
    c(b(b(x1))) = [0 0]x1 >= [0 0]x1 = c(c(b(x1)))
    
                  [1 2]      [1 1]                
    b(c(c(x1))) = [0 0]x1 >= [0 0]x1 = b(a(c(x1)))
    
                  [1 0]     [0]    [1 0]     [0]              
    a(a(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(b(a(x1)))
    
                  [1 0]     [2]    [1 0]     [0]              
    c(a(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(b(a(x1)))
    
                  [1 0]     [2]    [1 0]                
    a(c(a(x1))) = [0 0]x1 + [2] >= [0 0]x1 = c(c(b(x1)))
    
                  [1 0]     [0]    [1 0]     [0]              
    a(c(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(a(b(x1)))
   problem:
    strict:
     a(c(a(x1))) -> b(c(a(x1)))
     c(b(b(x1))) -> c(c(b(x1)))
     b(c(c(x1))) -> b(a(c(x1)))
     a(a(b(x1))) -> a(b(a(x1)))
    weak:
     a(c(b(x1))) -> a(a(b(x1)))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [1 1]  
     [c](x0) = [0 0]x0,
     
               [1 0]     [0]
     [a](x0) = [0 0]x0 + [2],
     
               [1 0]     [0]
     [b](x0) = [0 0]x0 + [1]
    orientation:
                   [1 0]     [2]    [1 0]     [2]              
     a(c(a(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [1] = b(c(a(x1)))
     
                   [1 0]     [1]    [1 0]     [1]              
     c(b(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c(b(x1)))
     
                   [1 1]     [0]    [1 1]     [0]              
     b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
     
                   [1 0]     [0]    [1 0]     [0]              
     a(a(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(b(a(x1)))
     
                   [1 0]     [1]    [1 0]     [0]              
     a(c(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(a(b(x1)))
    problem:
     strict:
      a(c(a(x1))) -> b(c(a(x1)))
      c(b(b(x1))) -> c(c(b(x1)))
      b(c(c(x1))) -> b(a(c(x1)))
      a(a(b(x1))) -> a(b(a(x1)))
     weak:
      
    Matrix Interpretation Processor: dim=2
     
     interpretation:
                [1 0]     [1]
      [c](x0) = [1 0]x0 + [0],
      
                [1 1]     [0]
      [a](x0) = [0 0]x0 + [1],
      
                [1 1]     [0]
      [b](x0) = [0 0]x0 + [1]
     orientation:
                    [2 2]     [1]    [2 2]     [1]              
      a(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(a(x1)))
      
                    [1 1]     [2]    [1 1]     [2]              
      c(b(b(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = c(c(b(x1)))
      
                    [2 0]     [3]    [2 0]     [2]              
      b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
      
                    [1 1]     [2]    [1 1]     [2]              
      a(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(b(a(x1)))
     problem:
      strict:
       a(c(a(x1))) -> b(c(a(x1)))
       c(b(b(x1))) -> c(c(b(x1)))
       a(a(b(x1))) -> a(b(a(x1)))
      weak:
       
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [c](x0) = x0,
       
       [a](x0) = 8x0,
       
       [b](x0) = x0
      orientation:
       a(c(a(x1))) = 16x1 >= 8x1 = b(c(a(x1)))
       
       c(b(b(x1))) = x1 >= x1 = c(c(b(x1)))
       
       a(a(b(x1))) = 16x1 >= 16x1 = a(b(a(x1)))
      problem:
       strict:
        c(b(b(x1))) -> c(c(b(x1)))
        a(a(b(x1))) -> a(b(a(x1)))
       weak:
        
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [c](x0) = 3x0,
        
        [a](x0) = x0,
        
        [b](x0) = 4x0
       orientation:
        c(b(b(x1))) = 11x1 >= 10x1 = c(c(b(x1)))
        
        a(a(b(x1))) = 4x1 >= 4x1 = a(b(a(x1)))
       problem:
        strict:
         a(a(b(x1))) -> a(b(a(x1)))
        weak:
         
       LPO Processor:
        precedence:
         a > b
        problem:
         strict:
          
         weak:
          
        Qed