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

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