YES

1 decompositions
 #0 -----------
   1: f(a(),b()) -> c()
   2: a() -> a'()
   3: b() -> b'()
   4: c() -> f(a'(),b())
   5: c() -> f(a(),b'())
   6: c() -> f(a(),b())

@Strongly Commuting
--- R
   1: f(a(),b()) -> c()
   2: a() -> a'()
   3: b() -> b'()
   4: c() -> f(a'(),b())
   5: c() -> f(a(),b'())
   6: c() -> f(a(),b())

--- S
   1: f(a(),b()) -> c()
   2: a() -> a'()
   3: b() -> b'()
   4: c() -> f(a'(),b())
   5: c() -> f(a(),b'())
   6: c() -> f(a(),b())