/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:
 strict:
  f(el(x),y) -> f(x,el(y))
 weak:
  f(x,y) -> f(l(x),y)
  f(x,y) -> f(x,r(y))
  l(el(x)) -> el(l(x))
  el(r(x)) -> r(el(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
               
   [r](x0) = x0,
   
               
   [l](x0) = x0,
   
                 [2 2]     [1 0]  
   [f](x0, x1) = [2 0]x0 + [2 0]x1,
   
                   [0]
   [el](x0) = x0 + [1]
  orientation:
                [2 2]    [1 0]    [2]    [2 2]    [1 0]              
   f(el(x),y) = [2 0]x + [2 0]y + [0] >= [2 0]x + [2 0]y = f(x,el(y))
   
            [2 2]    [1 0]     [2 2]    [1 0]             
   f(x,y) = [2 0]x + [2 0]y >= [2 0]x + [2 0]y = f(l(x),y)
   
            [2 2]    [1 0]     [2 2]    [1 0]             
   f(x,y) = [2 0]x + [2 0]y >= [2 0]x + [2 0]y = f(x,r(y))
   
                  [0]        [0]           
   l(el(x)) = x + [1] >= x + [1] = el(l(x))
   
                  [0]        [0]           
   el(r(x)) = x + [1] >= x + [1] = r(el(x))
  problem:
   strict:
    
   weak:
    f(x,y) -> f(l(x),y)
    f(x,y) -> f(x,r(y))
    l(el(x)) -> el(l(x))
    el(r(x)) -> r(el(x))
  Qed