/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:
 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:
   [s](x0) = 4x0 + 2,
   
   [plus](x0, x1) = x0 + x1,
   
   [times](x0, x1) = 3x0 + 2x1
  orientation:
   plus(plus(X,Y),Z) = X + Y + Z >= X + Y + Z = plus(X,plus(Y,Z))
   
   times(X,s(Y)) = 3X + 8Y + 4 >= 3X + 3Y = plus(X,times(Y,X))
  problem:
   plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 1]     [1 0 0]     [1]
    [plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [1 0 0]     [0 0 1]     [1]
   orientation:
                        [2 0 1]    [1 0 1]    [1 0 0]    [3]    [1 0 1]    [1 0 1]    [1 0 0]    [2]                    
    plus(plus(X,Y),Z) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = plus(X,plus(Y,Z))
                        [1 0 1]    [1 0 0]    [0 0 1]    [2]    [1 0 0]    [1 0 0]    [0 0 1]    [2]                    
   problem:
    
   Qed