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

Proof:
 String Reversal Processor:
  strict:
   a(a(c(x1))) -> a(c(a(x1)))
   c(c(a(x1))) -> b(c(a(x1)))
   b(b(a(x1))) -> b(a(a(x1)))
  weak:
   c(c(a(x1))) -> b(a(c(x1)))
   b(a(a(x1))) -> b(a(c(x1)))
   b(b(a(x1))) -> c(b(a(x1)))
   a(a(a(x1))) -> a(b(c(x1)))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 0]     [1]
    [c](x0) = [0 0]x0 + [1],
    
              [1 0]     [1]
    [a](x0) = [0 0]x0 + [0],
    
              [1 1]     [0]
    [b](x0) = [0 0]x0 + [1]
   orientation:
                  [1 0]     [3]    [1 0]     [3]              
    a(a(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c(a(x1)))
    
                  [1 0]     [3]    [1 0]     [3]              
    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(a(x1)))
    
                  [1 0]     [2]    [1 0]     [2]              
    b(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(a(x1)))
    
                  [1 0]     [3]    [1 0]     [2]              
    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
    
                  [1 0]     [2]    [1 0]     [2]              
    b(a(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
    
                  [1 0]     [2]    [1 0]     [2]              
    b(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(b(a(x1)))
    
                  [1 0]     [3]    [1 0]     [3]              
    a(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b(c(x1)))
   problem:
    strict:
     a(a(c(x1))) -> a(c(a(x1)))
     c(c(a(x1))) -> b(c(a(x1)))
     b(b(a(x1))) -> b(a(a(x1)))
    weak:
     b(a(a(x1))) -> b(a(c(x1)))
     b(b(a(x1))) -> c(b(a(x1)))
     a(a(a(x1))) -> a(b(c(x1)))
   String Reversal Processor:
    strict:
     c(a(a(x1))) -> a(c(a(x1)))
     a(c(c(x1))) -> a(c(b(x1)))
     a(b(b(x1))) -> a(a(b(x1)))
    weak:
     a(a(b(x1))) -> c(a(b(x1)))
     a(b(b(x1))) -> a(b(c(x1)))
     a(a(a(x1))) -> c(b(a(x1)))
    Bounds Processor:
     bound: 1
     enrichment: match-rt
     automaton:
      final states: {4}
      transitions:
       a1(19) -> 20*
       b1(53) -> 54*
       b1(17) -> 18*
       b1(67) -> 68*
       c1(31) -> 32*
       c1(18) -> 19*
       c0(4) -> 4*
       b0(4) -> 4*
       a0(4) -> 4*
       19 -> 4*
       68 -> 18*
       4 -> 17*
       54 -> 18*
       31 -> 53*
       20 -> 31,4
       18 -> 67*
       32 -> 19*
     problem:
      strict:
       c(a(a(x1))) -> a(c(a(x1)))
       a(b(b(x1))) -> a(a(b(x1)))
      weak:
       a(a(b(x1))) -> c(a(b(x1)))
       a(b(b(x1))) -> a(b(c(x1)))
       a(a(a(x1))) -> c(b(a(x1)))
     String Reversal Processor:
      strict:
       a(a(c(x1))) -> a(c(a(x1)))
       b(b(a(x1))) -> b(a(a(x1)))
      weak:
       b(a(a(x1))) -> b(a(c(x1)))
       b(b(a(x1))) -> c(b(a(x1)))
       a(a(a(x1))) -> a(b(c(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [c](x0) = 3x0,
        
        [a](x0) = 9x0,
        
        [b](x0) = 9x0
       orientation:
        a(a(c(x1))) = 21x1 >= 21x1 = a(c(a(x1)))
        
        b(b(a(x1))) = 27x1 >= 27x1 = b(a(a(x1)))
        
        b(a(a(x1))) = 27x1 >= 21x1 = b(a(c(x1)))
        
        b(b(a(x1))) = 27x1 >= 21x1 = c(b(a(x1)))
        
        a(a(a(x1))) = 27x1 >= 21x1 = a(b(c(x1)))
       problem:
        strict:
         a(a(c(x1))) -> a(c(a(x1)))
         b(b(a(x1))) -> b(a(a(x1)))
        weak:
         
       String Reversal Processor:
        strict:
         c(a(a(x1))) -> a(c(a(x1)))
         a(b(b(x1))) -> a(a(b(x1)))
        weak:
         
        Arctic Interpretation Processor:
         dimension: 1
         interpretation:
          [c](x0) = 3x0,
          
          [a](x0) = 1x0,
          
          [b](x0) = 2x0
         orientation:
          c(a(a(x1))) = 5x1 >= 5x1 = a(c(a(x1)))
          
          a(b(b(x1))) = 5x1 >= 4x1 = a(a(b(x1)))
         problem:
          strict:
           c(a(a(x1))) -> a(c(a(x1)))
          weak:
           
         LPO Processor:
          precedence:
           c > a
          problem:
           strict:
            
           weak:
            
          Qed