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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = 2x0 + 4,
   
   [c](x0) = 2x0,
   
   [a](x0) = 2x0 + 2
  orientation:
   b(b(c(x1))) = 8x1 + 12 >= 8x1 + 4 = c(a(c(x1)))
   
   a(c(b(x1))) = 8x1 + 18 >= 8x1 + 4 = b(c(c(x1)))
   
   b(b(b(x1))) = 8x1 + 28 >= 8x1 + 12 = b(c(a(x1)))
   
   b(a(a(x1))) = 8x1 + 16 >= 8x1 = c(c(c(x1)))
   
   a(a(b(x1))) = 8x1 + 22 >= 8x1 + 16 = b(a(a(x1)))
   
   c(a(b(x1))) = 8x1 + 20 >= 8x1 + 20 = b(b(a(x1)))
   
   b(a(a(x1))) = 8x1 + 16 >= 8x1 + 16 = c(c(b(x1)))
  problem:
   strict:
    
   weak:
    c(a(b(x1))) -> b(b(a(x1)))
    b(a(a(x1))) -> c(c(b(x1)))
  Qed