/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [+](x0, x1) = x0 + 4x1,
   
   [0] = 0,
   
   [s](x0) = x0 + 1
  orientation:
   +(0(),y) = 4y >= y = y
   
   +(s(x),0()) = x + 1 >= x + 1 = s(x)
   
   +(s(x),s(y)) = x + 4y + 5 >= x + 4y + 2 = s(+(s(x),+(y,0())))
  problem:
   +(0(),y) -> y
   +(s(x),0()) -> s(x)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]          [1]
    [+](x0, x1) = [0 0 0]x0 + x1 + [0]
                  [0 0 1]          [0],
    
          [0]
    [0] = [0]
          [0],
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 1]  
   orientation:
                   [1]         
    +(0(),y) = y + [0] >= y = y
                   [0]         
    
                  [1 0 0]    [1]    [1 0 0]        
    +(s(x),0()) = [0 0 0]x + [0] >= [0 0 0]x = s(x)
                  [0 0 1]    [0]    [0 0 1]        
   problem:
    
   Qed