NO

Problem:
 H(F(x,y)) -> F(H(R(x)),y)
 F(x,K(y,z)) -> G(P(y),Q(z,x))
 H(Q(x,y)) -> Q(x,H(R(y)))
 Q(x,H(R(y))) -> H(Q(x,y))
 H(G(x,y)) -> G(x,H(y))

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [G](x0, x1) = 3x0 + 4x1 + 1,
   
   [Q](x0, x1) = 2x0 + x1,
   
   [P](x0) = 2x0,
   
   [K](x0, x1) = 4x0 + 2x1 + 4,
   
   [R](x0) = x0,
   
   [H](x0) = x0,
   
   [F](x0, x1) = 4x0 + 4x1 + 1
  orientation:
   H(F(x,y)) = 4x + 4y + 1 >= 4x + 4y + 1 = F(H(R(x)),y)
   
   F(x,K(y,z)) = 4x + 16y + 8z + 17 >= 4x + 6y + 8z + 1 = G(P(y),Q(z,x))
   
   H(Q(x,y)) = 2x + y >= 2x + y = Q(x,H(R(y)))
   
   Q(x,H(R(y))) = 2x + y >= 2x + y = H(Q(x,y))
   
   H(G(x,y)) = 3x + 4y + 1 >= 3x + 4y + 1 = G(x,H(y))
  problem:
   H(F(x,y)) -> F(H(R(x)),y)
   H(Q(x,y)) -> Q(x,H(R(y)))
   Q(x,H(R(y))) -> H(Q(x,y))
   H(G(x,y)) -> G(x,H(y))
  Unfolding Processor:
   loop length: 2
   terms:
    H(Q(x31,x32))
    Q(x31,H(R(x32)))
   context: []
   substitution:
    x31 -> x31
    x32 -> x32
   Qed