YES

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

@Rule Labeling
--- R
   1: f(a(),b()) -> c()
   2: a() -> a'()
   3: b() -> b'()
   6: c() -> f(a(),b())

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


NOTE: input TRS is reduced

original is
   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())

reduced to
   1: f(a(),b()) -> c()
   2: a() -> a'()
   3: b() -> b'()
   6: c() -> f(a(),b())