MAYBE

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

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