/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(s(x),y) -> f(x,s(s(x)))
 f(x,s(s(y))) -> f(y,x)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 1]     [1 0 0]     [0]
   [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                 [0 0 0]     [0 0 0]     [1],
   
             [1 1 0]     [1]
   [s](x0) = [1 1 1]x0 + [0]
             [1 1 1]     [1]
  orientation:
               [3 3 2]    [1 0 0]    [2]    [3 3 2]    [2]               
   f(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0] = f(x,s(s(x)))
               [0 0 0]    [0 0 0]    [1]    [0 0 0]    [1]               
   
                  [1 1 1]    [2 2 1]    [2]    [1 0 0]    [1 1 1]    [0]         
   f(x,s(s(y))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(y,x)
                  [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]         
  problem:
   f(s(x),y) -> f(x,s(s(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 1]     [1 0 0]     [0]
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                  [1 0 0]     [0 0 0]     [1],
    
              [1 0 0]     [0]
    [s](x0) = [0 0 0]x0 + [0]
              [1 0 1]     [1]
   orientation:
                [2 0 1]    [1 0 0]    [1]    [2 0 1]    [0]               
    f(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0] = f(x,s(s(x)))
                [1 0 0]    [0 0 0]    [1]    [1 0 0]    [1]               
   problem:
    
   Qed