YES
Input TRS:
    1: f(a(),x) -> a()
    2: f(b(),x) -> b()
    3: g(a(),x) -> c() | f(x,a()) --> a()
    4: g(x,a()) -> d() | f(x,b()) --> b()
    5: c() -> c()
Infeasibility test:
    f(a(),b()) --> b()
    f(a(),a()) --> a()
Symbol transition graph:
    c	--> c
    g	--> c d
    f	--> a b
  Collapsable symbols: { }