YES

1 decompositions
 #0 -----------
   1: p(x) -> q(x)
   2: p(x) -> r(x)
   3: q(x) -> s(p(x))
   4: r(x) -> s(p(x))
   5: s(x) -> f(p(x))

@Strongly Commuting
--- R
   1: p(x) -> q(x)
   2: p(x) -> r(x)
   3: q(x) -> s(p(x))
   4: r(x) -> s(p(x))
   5: s(x) -> f(p(x))

--- S
   1: p(x) -> q(x)
   2: p(x) -> r(x)
   3: q(x) -> s(p(x))
   4: r(x) -> s(p(x))
   5: s(x) -> f(p(x))