/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f(s(x),y) -> f(x,s(x))
 f(x,s(y)) -> f(y,x)
 f(c(x),y) -> f(x,s(x))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0) = 3x0 + 3,
   
   [f](x0, x1) = 4x0 + 2x1 + 3,
   
   [s](x0) = 4x0 + 6
  orientation:
   f(s(x),y) = 16x + 2y + 27 >= 12x + 15 = f(x,s(x))
   
   f(x,s(y)) = 4x + 8y + 15 >= 2x + 4y + 3 = f(y,x)
   
   f(c(x),y) = 12x + 2y + 15 >= 12x + 15 = f(x,s(x))
  problem:
   f(c(x),y) -> f(x,s(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c](x0) = 4x0 + 4,
    
    [f](x0, x1) = 4x0 + 2x1 + 4,
    
    [s](x0) = 2x0 + 1
   orientation:
    f(c(x),y) = 16x + 2y + 20 >= 8x + 6 = f(x,s(x))
   problem:
    
   Qed