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

Proof:
 String Reversal Processor:
  strict:
   a(b(a(x1))) -> c(c(b(x1)))
   c(a(b(x1))) -> c(a(a(x1)))
   a(b(a(x1))) -> c(c(a(x1)))
   a(b(b(x1))) -> a(b(a(x1)))
  weak:
   c(a(a(x1))) -> c(b(a(x1)))
   c(c(a(x1))) -> a(b(c(x1)))
   c(c(b(x1))) -> a(c(c(x1)))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 1]     [0]
    [b](x0) = [1 0]x0 + [1],
    
              [1 1]     [0]
    [a](x0) = [1 0]x0 + [1],
    
              [1 1]  
    [c](x0) = [1 0]x0
   orientation:
                  [3 2]     [2]    [3 2]     [1]              
    a(b(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [1] = c(c(b(x1)))
    
                  [3 2]     [2]    [3 2]     [2]              
    c(a(b(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = c(a(a(x1)))
    
                  [3 2]     [2]    [3 2]     [1]              
    a(b(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [1] = c(c(a(x1)))
    
                  [3 2]     [2]    [3 2]     [2]              
    a(b(b(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [2] = a(b(a(x1)))
    
                  [3 2]     [2]    [3 2]     [2]              
    c(a(a(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = c(b(a(x1)))
    
                  [3 2]     [1]    [3 2]     [1]              
    c(c(a(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(b(c(x1)))
    
                  [3 2]     [1]    [3 2]     [0]              
    c(c(b(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(c(c(x1)))
   problem:
    strict:
     c(a(b(x1))) -> c(a(a(x1)))
     a(b(b(x1))) -> a(b(a(x1)))
    weak:
     c(a(a(x1))) -> c(b(a(x1)))
     c(c(a(x1))) -> a(b(c(x1)))
   String Reversal Processor:
    strict:
     b(a(c(x1))) -> a(a(c(x1)))
     b(b(a(x1))) -> a(b(a(x1)))
    weak:
     a(a(c(x1))) -> a(b(c(x1)))
     a(c(c(x1))) -> c(b(a(x1)))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b](x0) = 1x0,
      
      [a](x0) = 1x0,
      
      [c](x0) = 14x0
     orientation:
      b(a(c(x1))) = 16x1 >= 16x1 = a(a(c(x1)))
      
      b(b(a(x1))) = 3x1 >= 3x1 = a(b(a(x1)))
      
      a(a(c(x1))) = 16x1 >= 16x1 = a(b(c(x1)))
      
      a(c(c(x1))) = 29x1 >= 16x1 = c(b(a(x1)))
     problem:
      strict:
       b(a(c(x1))) -> a(a(c(x1)))
       b(b(a(x1))) -> a(b(a(x1)))
      weak:
       a(a(c(x1))) -> a(b(c(x1)))
     Bounds Processor:
      bound: 1
      enrichment: match-rt
      automaton:
       final states: {4}
       transitions:
        a1(11) -> 12*
        a1(10) -> 11*
        b1(31) -> 32*
        b1(25) -> 26*
        c1(9) -> 10*
        b0(4) -> 4*
        c0(4) -> 4*
        a0(4) -> 4*
        12 -> 25,4
        4 -> 9*
        26 -> 11*
        10 -> 31*
        32 -> 11*
      problem:
       strict:
        b(b(a(x1))) -> a(b(a(x1)))
       weak:
        a(a(c(x1))) -> a(b(c(x1)))
      Bounds Processor:
       bound: 1
       enrichment: match-rt
       automaton:
        final states: {4}
        transitions:
         a1(11) -> 12*
         a1(9) -> 10*
         b1(13) -> 14*
         b1(20) -> 21*
         b1(10) -> 11*
         c1(19) -> 20*
         b0(4) -> 4*
         a0(4) -> 4*
         c0(4) -> 4*
         12 -> 13,4
         14 -> 11*
         4 -> 19,9
         21 -> 9*
       problem:
        strict:
         
        weak:
         a(a(c(x1))) -> a(b(c(x1)))
       Qed