MAYBE

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

Proof:
 Complexity Transformation Processor:
  strict:
   f(x,a(b(y))) -> f(a(a(x)),y)
   f(x,b(a(y))) -> f(b(b(x)),y)
   f(a(x),y) -> f(x,a(y))
   f(b(x),y) -> f(x,b(y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [f](x0, x1) = x0 + x1 + 1,
     
     [a](x0) = x0 + 1,
     
     [b](x0) = x0
    orientation:
     f(x,a(b(y))) = x + y + 2 >= x + y + 3 = f(a(a(x)),y)
     
     f(x,b(a(y))) = x + y + 2 >= x + y + 1 = f(b(b(x)),y)
     
     f(a(x),y) = x + y + 2 >= x + y + 2 = f(x,a(y))
     
     f(b(x),y) = x + y + 1 >= x + y + 1 = f(x,b(y))
    problem:
     strict:
      f(x,a(b(y))) -> f(a(a(x)),y)
      f(a(x),y) -> f(x,a(y))
      f(b(x),y) -> f(x,b(y))
     weak:
      f(x,b(a(y))) -> f(b(b(x)),y)
    Open