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:
 RT 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
   interpretation:
    [b] = 1,
    
    [c] = 12,
    
    [f](x0, x1) = x0 + x1 + 4,
    
    [a] = 4
   orientation:
    f(a(),f(a(),x)) = x + 16 >= x + 21 = f(c(),f(b(),x))
    
    f(b(),f(b(),x)) = x + 10 >= x + 24 = f(a(),f(c(),x))
    
    f(c(),f(c(),x)) = x + 32 >= x + 13 = 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
    interpretation:
     [b] = 4,
     
     [c] = 17,
     
     [f](x0, x1) = x0 + x1 + 5,
     
     [a] = 18
    orientation:
     f(a(),f(a(),x)) = x + 46 >= x + 31 = f(c(),f(b(),x))
     
     f(b(),f(b(),x)) = x + 18 >= x + 45 = f(a(),f(c(),x))
     
     f(c(),f(c(),x)) = x + 44 >= x + 32 = f(b(),f(a(),x))
    problem:
     strict:
      f(b(),f(b(),x)) -> f(a(),f(c(),x))
     weak:
      f(a(),f(a(),x)) -> f(c(),f(b(),x))
      f(c(),f(c(),x)) -> f(b(),f(a(),x))
    Open