with(DifferentialAlgebra):
ring_diff := DifferentialRing(blocks = [[EGF_EGFR, EGFR, pEGFR, pAkt_S6, pEGFR_Akt, pAkt, S6, pS6, Akt], [y1, y2, y3] , [pro_EGFR]], derivations = [t]):
sys := [
diff(EGF_EGFR(t), t) - (reaction_1_k1*EGF_EGFR(t) - reaction_9_k1*EGF_EGFR(t) - reaction_1_k2*EGF_EGFR(t)),
diff(EGFR(t), t) - (-reaction_1_k1*EGF_EGFR(t) + reaction_1_k2*EGF_EGFR(t) - EGFR(t)*EGFR_turnover + EGFR_turnover*pro_EGFR(t)),
diff(pEGFR(t), t) - (-reaction_4_k1*pEGFR(t) + reaction_9_k1*EGF_EGFR(t) - pEGFR(t)*Akt(t)*reaction_2_k1 + reaction_3_k1*pEGFR_Akt(t) + pEGFR_Akt(t)*reaction_2_k2),
diff(pAkt_S6(t), t) - (pAkt(t)*reaction_5_k1*S6(t) - reaction_6_k1*pAkt_S6(t) - pAkt_S6(t)*reaction_5_k2),
diff(pEGFR_Akt(t), t) - (pEGFR(t)*Akt(t)*reaction_2_k1 - reaction_3_k1*pEGFR_Akt(t) - pEGFR_Akt(t)*reaction_2_k2),
diff(pAkt(t), t) - (-pAkt(t)*reaction_7_k1 - pAkt(t)*reaction_5_k1*S6(t) + reaction_6_k1*pAkt_S6(t) + reaction_3_k1*pEGFR_Akt(t) + pAkt_S6(t)*reaction_5_k2),
diff(S6(t), t) - (pS6(t)*reaction_8_k1 - pAkt(t)*reaction_5_k1*S6(t) + pAkt_S6(t)*reaction_5_k2),
diff(pS6(t), t) - (-pS6(t)*reaction_8_k1 + reaction_6_k1*pAkt_S6(t)),
diff(Akt(t), t) - (pAkt(t)*reaction_7_k1 - pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2),
y1(t) - (pEGFR(t)*a1 + a1*pEGFR_Akt(t)),
y2(t) - (a2*pAkt(t) + a2*pAkt_S6(t)),
y3(t) - (pS6(t)*a3)
];
res := CodeTools[CPUTime](RosenfeldGroebner(sys, ring_diff, singsol=none));