MAYBE

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

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