/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:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [times](x0, x1) = 2x0 + x1 + 2,
   
   [s](x0) = 2x0 + 1,
   
   [plus](x0, x1) = x0 + x1
  orientation:
   plus(plus(X,Y),Z) = X + Y + Z >= X + Y + Z = plus(X,plus(Y,Z))
   
   times(X,s(Y)) = 2X + 2Y + 3 >= 2X + 2Y + 2 = plus(X,times(Y,X))
  problem:
   plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [plus](x0, x1) = 2x0 + x1 + 1
   orientation:
    plus(plus(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = plus(X,plus(Y,Z))
   problem:
    
   Qed