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

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 1]  
   [a](x0) = [1 1]x0,
   
             [1 1]     [1]
   [b](x0) = [0 0]x0 + [0],
   
             [1 0]  
   [c](x0) = [0 0]x0
  orientation:
                 [2 2]     [2]    [2 2]     [1]           
   a(a(b(x1))) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b(a(x1))
   
              [1 1]     [1]    [1 1]     [1]              
   c(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(c(a(x1)))
   
           [1 1]      [1 1]                
   a(x1) = [1 1]x1 >= [1 1]x1 = a(c(a(x1)))
  problem:
   strict:
    c(b(x1)) -> b(c(a(x1)))
   weak:
    a(x1) -> a(c(a(x1)))
  String Reversal Processor:
   strict:
    b(c(x1)) -> a(c(b(x1)))
   weak:
    a(x1) -> a(c(a(x1)))
   Bounds Processor:
    bound: 1
    enrichment: match-rt
    automaton:
     final states: {4}
     transitions:
      a1(11) -> 12*
      a1(17) -> 18*
      b1(9) -> 10*
      c1(10) -> 11*
      b0(4) -> 4*
      c0(4) -> 4*
      a0(4) -> 4*
      12 -> 18,10,4
      4 -> 17,9
      18 -> 10*
    problem:
     strict:
      
     weak:
      a(x1) -> a(c(a(x1)))
    Qed