/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:
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 +(s(x),y) -> +(x,s(y))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [+](x0, x1) = x0 + x1 + 6,
   
   [0] = 1,
   
   [s](x0) = x0
  orientation:
   +(0(),y) = y + 7 >= y = y
   
   +(s(x),y) = x + y + 6 >= x + y + 6 = s(+(x,y))
   
   +(s(x),y) = x + y + 6 >= x + y + 6 = +(x,s(y))
  problem:
   +(s(x),y) -> s(+(x,y))
   +(s(x),y) -> +(x,s(y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 1]     [1 0 0]  
    [+](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                  [0 0 1]     [0 0 0]  ,
    
              [1 0 0]     [0]
    [s](x0) = [0 0 0]x0 + [0]
              [0 0 1]     [1]
   orientation:
                [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]    [0]            
    +(s(x),y) = [0 0 1]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [0] = s(+(x,y))
                [0 0 1]    [0 0 0]    [1]    [0 0 1]    [0 0 0]    [1]            
    
                [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]             
    +(s(x),y) = [0 0 1]x + [0 0 0]y + [1] >= [0 0 1]x + [0 0 0]y = +(x,s(y))
                [0 0 1]    [0 0 0]    [1]    [0 0 1]    [0 0 0]             
   problem:
    
   Qed