YES

1 decompositions
 #0 -----------
   1: H(F(x,y)) -> F(H(R(x)),y)
   2: F(x,K(y,z)) -> G(P(y),Q(z,x))
   3: H(Q(x,y)) -> Q(x,H(R(y)))
   4: Q(x,H(R(y))) -> H(Q(x,y))
   5: H(G(x,y)) -> G(x,H(y))

@Strongly Commuting
--- R
   1: H(F(x,y)) -> F(H(R(x)),y)
   2: F(x,K(y,z)) -> G(P(y),Q(z,x))
   3: H(Q(x,y)) -> Q(x,H(R(y)))
   4: Q(x,H(R(y))) -> H(Q(x,y))
   5: H(G(x,y)) -> G(x,H(y))

--- S
   1: H(F(x,y)) -> F(H(R(x)),y)
   2: F(x,K(y,z)) -> G(P(y),Q(z,x))
   3: H(Q(x,y)) -> Q(x,H(R(y)))
   4: Q(x,H(R(y))) -> H(Q(x,y))
   5: H(G(x,y)) -> G(x,H(y))