YES
Time: 0.417

Problem:
 Equations:
  
 TRS:
  +AC(f(a()),g(b())) -> +AC(f(b()),g(a()))
  k(a(),g(g(a()))) -> k(g(a()),f(a()))
  +AC(g(x),y) -> g(+AC(x,y))
  f(+AC(x,y)) -> +AC(f(x),y)
  k(a(),b()) -> k(b(),a())
  k(g(a()),a()) -> k(a(),g(b()))
  k(g(a()),b()) -> k(a(),g(a()))

Proof:
 AC-KBO Processor:
  precedence:
   f > a > +AC > k > g > b
   weight function:
    [k](x0, x1) = x0 + x1,
    
    [g](x0) = x0 + 12,
    
    [b] = 1,
    
    [f](x0) = 8x0,
    
    [a] = 1,
    
    [+AC](x0, x1) = x0 + x1
   problem:
    Equations:
     
    TRS:
     
   Qed