MAYBE

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

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