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

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