YES

1 decompositions
 #1 -----------
   1: a() -> a'()
   2: h(x1,a'(),x2) -> h(x1,x2,x2)
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

@Commutation Lemma

@Development Closedness
--- R
   1: a() -> a'()
   2: h(x1,a'(),x2) -> h(x1,x2,x2)
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

--- S
   2: h(x1,a'(),x2) -> h(x1,x2,x2)

@Commutation Lemma

@Development Closedness
--- R
   2: h(x1,a'(),x2) -> h(x1,x2,x2)

--- S
   1: a() -> a'()
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

@Commutation Lemma

@Development Closedness
--- R
   1: a() -> a'()
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

--- S
   3: h(x1,x2,a'()) -> h(x1,x2,x2)

@Commutation Lemma

@Development Closedness
--- R
   3: h(x1,x2,a'()) -> h(x1,x2,x2)

--- S
   1: a() -> a'()
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

@Rule Labeling
--- R
   1: a() -> a'()
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())

--- S
   1: a() -> a'()
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())


NOTE: input TRS is reduced

original is
   1: a() -> a'()
   2: h(x1,a'(),x2) -> h(x1,x2,x2)
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())
   6: h(g(),a(),a()) -> h(f(),a(),a())

reduced to
   1: a() -> a'()
   2: h(x1,a'(),x2) -> h(x1,x2,x2)
   3: h(x1,x2,a'()) -> h(x1,x2,x2)
   4: g() -> f()
   5: h(f(),a(),a()) -> h(g(),a(),a())