/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES

Problem:
 strict:
  l(m(x)) -> m(l(x))
  m(r(x)) -> r(m(x))
  f(m(x),y) -> f(x,m(y))
 weak:
  b() -> l(b())
  f(x,y) -> f(x,r(y))

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