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

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