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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0) = 2x0 + 1,
   
   [b](x0) = 2x0 + 3,
   
   [c](x0) = 2x0 + 2
  orientation:
   b(b(b(x1))) = 8x1 + 21 >= 8x1 + 17 = b(a(b(x1)))
   
   c(c(c(x1))) = 8x1 + 14 >= 8x1 + 12 = c(b(a(x1)))
   
   c(a(b(x1))) = 8x1 + 16 >= 8x1 + 13 = a(c(c(x1)))
   
   a(b(c(x1))) = 8x1 + 15 >= 8x1 + 15 = b(c(c(x1)))
   
   c(a(c(x1))) = 8x1 + 12 >= 8x1 + 9 = a(c(a(x1)))
   
   b(a(c(x1))) = 8x1 + 13 >= 8x1 + 7 = a(a(a(x1)))
  problem:
   strict:
    
   weak:
    a(b(c(x1))) -> b(c(c(x1)))
  Qed