YES

Problem:
 f(g(f(x))) -> x
 f(g(x)) -> g(f(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [g](x0) = 8x0,
   
   [f](x0) = 8x0
  orientation:
   f(g(f(x))) = 24x >= x = x
   
   f(g(x)) = 16x >= 16x = g(f(x))
  problem:
   f(g(x)) -> g(f(x))
  KBO Processor:
   weight function:
    w0 = 1
    w(g) = w(f) = 1
   precedence:
    f > g
   problem:
    
   Qed