MAYBE

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:
 Complexity Transformation Processor:
  strict:
   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))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 2
   max_matrix:
    [1 1]
    [0 1]
    interpretation:
               [1 0]  
     [b](x0) = [0 0]x0,
     
               [1 1]     [0]
     [a](x0) = [0 1]x0 + [1],
     
                          
     [f](x0, x1) = x0 + x1
    orientation:
                    [1 2]    [1 2]    [1]    [1 1]    [1 1]    [0]                                       
     a(a(f(x,y))) = [0 1]x + [0 1]y + [2] >= [0 0]x + [0 0]y + [2] = f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
     
                    [1 1]    [1 1]    [0]    [1 1]    [1 1]    [0]            
     f(a(x),a(y)) = [0 1]x + [0 1]y + [2] >= [0 1]x + [0 1]y + [1] = a(f(x,y))
     
                    [1 0]    [1 0]     [1 0]    [1 0]             
     f(b(x),b(y)) = [0 0]x + [0 0]y >= [0 0]x + [0 0]y = b(f(x,y))
    problem:
     strict:
      f(a(x),a(y)) -> a(f(x,y))
      f(b(x),b(y)) -> b(f(x,y))
     weak:
      a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
    Open