/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:
 a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
 f(a(x),a(y)) -> a(f(x,y))
 f(b(x),b(y)) -> b(f(x,y))

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