/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:
 f(c(X,s(Y))) -> f(c(s(X),Y))
 g(c(s(X),Y)) -> f(c(X,s(Y)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0, x1) = x0 + x1 + 2,
   
   [g](x0) = x0 + 7,
   
   [s](x0) = x0,
   
   [f](x0) = x0 + 6
  orientation:
   f(c(X,s(Y))) = X + Y + 8 >= X + Y + 8 = f(c(s(X),Y))
   
   g(c(s(X),Y)) = X + Y + 9 >= X + Y + 8 = f(c(X,s(Y)))
  problem:
   f(c(X,s(Y))) -> f(c(s(X),Y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]       
    [c](x0, x1) = [0 0 0]x0 + x1
                  [0 0 0]       ,
    
                   [0]
    [s](x0) = x0 + [0]
                   [1],
    
              [1 0 1]  
    [f](x0) = [0 1 0]x0
              [0 0 0]  
   orientation:
                   [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]                
    f(c(X,s(Y))) = [0 0 0]X + [0 1 0]Y + [0] >= [0 0 0]X + [0 1 0]Y = f(c(s(X),Y))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
   problem:
    
   Qed