/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]     [1]
   [a](x0) = [0 0]x0 + [1],
   
             [1 1]     [0]
   [b](x0) = [0 0]x0 + [1],
   
             [1 1]  
   [c](x0) = [0 0]x0
  orientation:
                 [1 1]     [2]    [1 1]     [1]              
   a(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(b(c(x1)))
   
                 [1 1]     [1]    [1 1]     [1]              
   b(c(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(b(c(x1)))
   
                 [1 1]     [2]    [1 1]     [2]              
   a(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(a(b(x1)))
   
                 [1 1]     [2]    [1 1]                
   a(c(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 = c(c(c(x1)))
   
                 [1 1]     [2]    [1 1]     [2]              
   c(a(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(b(x1)))
   
                 [1 1]     [2]    [1 1]     [1]              
   b(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(c(b(x1)))
   
                 [1 1]     [1]    [1 1]     [1]              
   c(b(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c(b(x1)))
  problem:
   strict:
    b(c(b(x1))) -> a(b(c(x1)))
    a(a(b(x1))) -> c(a(b(x1)))
   weak:
    c(a(c(x1))) -> c(b(b(x1)))
    c(b(c(x1))) -> c(c(b(x1)))
  RT Transformation Processor:
   b(c(b(x1))) -> a(b(c(x1)))
   a(a(b(x1))) -> c(a(b(x1)))
   c(a(c(x1))) -> c(b(b(x1)))
   c(b(c(x1))) -> c(c(b(x1)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 1 0]     [0]
     [a](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 1 0]     [0]
     [b](x0) = [0 1 1]x0 + [0]
               [0 0 0]     [1],
     
               [1 1 0]     [0]
     [c](x0) = [0 1 1]x0 + [1]
               [0 0 0]     [0]
    orientation:
                   [1 3 2]     [2]    [1 3 2]     [2]              
     b(c(b(x1))) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [2] = a(b(c(x1)))
                   [0 0 0]     [1]    [0 0 0]     [0]              
     
                   [1 3 2]     [1]    [1 3 2]     [1]              
     a(a(b(x1))) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [2] = c(a(b(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
     
                   [1 3 2]     [3]    [1 3 2]     [1]              
     c(a(c(x1))) = [0 1 1]x1 + [3] >= [0 1 1]x1 + [3] = c(b(b(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
     
                   [1 3 2]     [2]    [1 3 2]     [2]              
     c(b(c(x1))) = [0 1 1]x1 + [3] >= [0 1 1]x1 + [3] = c(c(b(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
    problem:
     b(c(b(x1))) -> a(b(c(x1)))
     a(a(b(x1))) -> c(a(b(x1)))
     c(b(c(x1))) -> c(c(b(x1)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [a](x0) = [0 0 0]x0
                [0 0 1]  ,
      
                [1 0 0]     [0]
      [b](x0) = [0 1 0]x0 + [1]
                [0 1 0]     [0],
      
                [1 1 0]  
      [c](x0) = [0 0 0]x0
                [0 0 0]  
     orientation:
                    [1 1 0]     [1]    [1 1 0]                
      b(c(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(b(c(x1)))
                    [0 0 0]     [0]    [0 0 0]                
      
                    [1 0 0]      [1 0 0]                
      a(a(b(x1))) = [0 0 0]x1 >= [0 0 0]x1 = c(a(b(x1)))
                    [0 1 0]      [0 0 0]                
      
                    [1 1 0]     [1]    [1 1 0]     [1]              
      c(b(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c(b(x1)))
                    [0 0 0]     [0]    [0 0 0]     [0]              
     problem:
      a(a(b(x1))) -> c(a(b(x1)))
      c(b(c(x1))) -> c(c(b(x1)))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 1]     [0]
       [a](x0) = [0 0 1]x0 + [0]
                 [0 0 0]     [1],
       
                 [1 1 1]  
       [b](x0) = [0 1 1]x0
                 [0 0 0]  ,
       
                 [1 0 0]     [0]
       [c](x0) = [0 1 1]x0 + [0]
                 [0 0 0]     [1]
      orientation:
                     [1 1 1]     [1]    [1 1 1]     [0]              
       a(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(a(b(x1)))
                     [0 0 0]     [1]    [0 0 0]     [1]              
       
                     [1 1 1]     [1]    [1 1 1]     [0]              
       c(b(c(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = c(c(b(x1)))
                     [0 0 0]     [1]    [0 0 0]     [1]              
      problem:
       
      Qed