NO Initial ITS Start location: l8 0: l0 -> l1 : ___rho_1_^0'=___rho_1_^post0, curr_serv^0'=curr_serv^post0, servers^0'=servers^post0, c^0'=c^post0, resp^0'=resp^post0, (servers^0-servers^post0 == 0 /\ ___rho_1_^0-___rho_1_^post0 == 0 /\ -resp^post0+resp^0 == 0 /\ -c^post0+c^0 == 0 /\ curr_serv^0-curr_serv^post0 == 0), cost: 1 6: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^post6, servers^0'=servers^post6, c^0'=c^post6, resp^0'=resp^post6, (0 == 0 /\ 1-curr_serv^0 <= 0 /\ resp^0-resp^post6 == 0 /\ -servers^post6+servers^0 == 0 /\ curr_serv^0-curr_serv^post6 == 0 /\ -c^post6+c^0 == 0), cost: 1 7: l1 -> l4 : ___rho_1_^0'=___rho_1_^post7, curr_serv^0'=curr_serv^post7, servers^0'=servers^post7, c^0'=c^post7, resp^0'=resp^post7, (-c^post7+c^0 == 0 /\ curr_serv^0-curr_serv^post7 == 0 /\ curr_serv^0 <= 0 /\ ___rho_1_^0-___rho_1_^post7 == 0 /\ servers^0-servers^post7 == 0 /\ -resp^post7+resp^0 == 0), cost: 1 1: l2 -> l3 : ___rho_1_^0'=___rho_1_^post1, curr_serv^0'=curr_serv^post1, servers^0'=servers^post1, c^0'=c^post1, resp^0'=resp^post1, (-servers^post1+servers^0 == 0 /\ ___rho_1_^0-___rho_1_^post1 == 0 /\ c^0-c^post1 == 0 /\ -resp^post1+resp^0 == 0 /\ -curr_serv^post1+curr_serv^0 == 0), cost: 1 2: l4 -> l5 : ___rho_1_^0'=___rho_1_^post2, curr_serv^0'=curr_serv^post2, servers^0'=servers^post2, c^0'=c^post2, resp^0'=resp^post2, (___rho_1_^0-___rho_1_^post2 == 0 /\ -c^post2+c^0 == 0 /\ -servers^post2+servers^0 == 0 /\ curr_serv^0-curr_serv^post2 == 0 /\ -resp^post2+resp^0 == 0), cost: 1 3: l5 -> l4 : ___rho_1_^0'=___rho_1_^post3, curr_serv^0'=curr_serv^post3, servers^0'=servers^post3, c^0'=c^post3, resp^0'=resp^post3, (-resp^post3+resp^0 == 0 /\ servers^0-servers^post3 == 0 /\ c^0-c^post3 == 0 /\ curr_serv^0-curr_serv^post3 == 0 /\ ___rho_1_^0-___rho_1_^post3 == 0), cost: 1 4: l6 -> l0 : ___rho_1_^0'=___rho_1_^post4, curr_serv^0'=curr_serv^post4, servers^0'=servers^post4, c^0'=c^post4, resp^0'=resp^post4, (___rho_1_^0 <= 0 /\ -resp^post4+resp^0 == 0 /\ 1-curr_serv^0+c^0 <= 0 /\ 1-curr_serv^0+curr_serv^post4 == 0 /\ -servers^post4+servers^0 == 0 /\ -c^post4+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post4 == 0), cost: 1 5: l6 -> l0 : ___rho_1_^0'=___rho_1_^post5, curr_serv^0'=curr_serv^post5, servers^0'=servers^post5, c^0'=c^post5, resp^0'=resp^post5, (1-___rho_1_^0 <= 0 /\ servers^0-servers^post5 == 0 /\ ___rho_1_^0-___rho_1_^post5 == 0 /\ 1-curr_serv^0+curr_serv^post5 == 0 /\ -1+resp^post5-resp^0 == 0 /\ 1+c^post5-c^0 == 0), cost: 1 8: l7 -> l0 : ___rho_1_^0'=___rho_1_^post8, curr_serv^0'=curr_serv^post8, servers^0'=servers^post8, c^0'=c^post8, resp^0'=resp^post8, (0 == 0 /\ -8+servers^post8 == 0 /\ ___rho_1_^0-___rho_1_^post8 == 0 /\ 1-c^post8 <= 0 /\ -servers^post8+curr_serv^post8 == 0 /\ resp^post8 == 0), cost: 1 9: l8 -> l7 : ___rho_1_^0'=___rho_1_^post9, curr_serv^0'=curr_serv^post9, servers^0'=servers^post9, c^0'=c^post9, resp^0'=resp^post9, (-resp^post9+resp^0 == 0 /\ servers^0-servers^post9 == 0 /\ -c^post9+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post9 == 0 /\ curr_serv^0-curr_serv^post9 == 0), cost: 1 Removed unreachable rules and leafs Start location: l8 0: l0 -> l1 : ___rho_1_^0'=___rho_1_^post0, curr_serv^0'=curr_serv^post0, servers^0'=servers^post0, c^0'=c^post0, resp^0'=resp^post0, (servers^0-servers^post0 == 0 /\ ___rho_1_^0-___rho_1_^post0 == 0 /\ -resp^post0+resp^0 == 0 /\ -c^post0+c^0 == 0 /\ curr_serv^0-curr_serv^post0 == 0), cost: 1 6: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^post6, servers^0'=servers^post6, c^0'=c^post6, resp^0'=resp^post6, (0 == 0 /\ 1-curr_serv^0 <= 0 /\ resp^0-resp^post6 == 0 /\ -servers^post6+servers^0 == 0 /\ curr_serv^0-curr_serv^post6 == 0 /\ -c^post6+c^0 == 0), cost: 1 7: l1 -> l4 : ___rho_1_^0'=___rho_1_^post7, curr_serv^0'=curr_serv^post7, servers^0'=servers^post7, c^0'=c^post7, resp^0'=resp^post7, (-c^post7+c^0 == 0 /\ curr_serv^0-curr_serv^post7 == 0 /\ curr_serv^0 <= 0 /\ ___rho_1_^0-___rho_1_^post7 == 0 /\ servers^0-servers^post7 == 0 /\ -resp^post7+resp^0 == 0), cost: 1 2: l4 -> l5 : ___rho_1_^0'=___rho_1_^post2, curr_serv^0'=curr_serv^post2, servers^0'=servers^post2, c^0'=c^post2, resp^0'=resp^post2, (___rho_1_^0-___rho_1_^post2 == 0 /\ -c^post2+c^0 == 0 /\ -servers^post2+servers^0 == 0 /\ curr_serv^0-curr_serv^post2 == 0 /\ -resp^post2+resp^0 == 0), cost: 1 3: l5 -> l4 : ___rho_1_^0'=___rho_1_^post3, curr_serv^0'=curr_serv^post3, servers^0'=servers^post3, c^0'=c^post3, resp^0'=resp^post3, (-resp^post3+resp^0 == 0 /\ servers^0-servers^post3 == 0 /\ c^0-c^post3 == 0 /\ curr_serv^0-curr_serv^post3 == 0 /\ ___rho_1_^0-___rho_1_^post3 == 0), cost: 1 4: l6 -> l0 : ___rho_1_^0'=___rho_1_^post4, curr_serv^0'=curr_serv^post4, servers^0'=servers^post4, c^0'=c^post4, resp^0'=resp^post4, (___rho_1_^0 <= 0 /\ -resp^post4+resp^0 == 0 /\ 1-curr_serv^0+c^0 <= 0 /\ 1-curr_serv^0+curr_serv^post4 == 0 /\ -servers^post4+servers^0 == 0 /\ -c^post4+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post4 == 0), cost: 1 5: l6 -> l0 : ___rho_1_^0'=___rho_1_^post5, curr_serv^0'=curr_serv^post5, servers^0'=servers^post5, c^0'=c^post5, resp^0'=resp^post5, (1-___rho_1_^0 <= 0 /\ servers^0-servers^post5 == 0 /\ ___rho_1_^0-___rho_1_^post5 == 0 /\ 1-curr_serv^0+curr_serv^post5 == 0 /\ -1+resp^post5-resp^0 == 0 /\ 1+c^post5-c^0 == 0), cost: 1 8: l7 -> l0 : ___rho_1_^0'=___rho_1_^post8, curr_serv^0'=curr_serv^post8, servers^0'=servers^post8, c^0'=c^post8, resp^0'=resp^post8, (0 == 0 /\ -8+servers^post8 == 0 /\ ___rho_1_^0-___rho_1_^post8 == 0 /\ 1-c^post8 <= 0 /\ -servers^post8+curr_serv^post8 == 0 /\ resp^post8 == 0), cost: 1 9: l8 -> l7 : ___rho_1_^0'=___rho_1_^post9, curr_serv^0'=curr_serv^post9, servers^0'=servers^post9, c^0'=c^post9, resp^0'=resp^post9, (-resp^post9+resp^0 == 0 /\ servers^0-servers^post9 == 0 /\ -c^post9+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post9 == 0 /\ curr_serv^0-curr_serv^post9 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : ___rho_1_^0'=___rho_1_^post0, curr_serv^0'=curr_serv^post0, servers^0'=servers^post0, c^0'=c^post0, resp^0'=resp^post0, (servers^0-servers^post0 == 0 /\ ___rho_1_^0-___rho_1_^post0 == 0 /\ -resp^post0+resp^0 == 0 /\ -c^post0+c^0 == 0 /\ curr_serv^0-curr_serv^post0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l5 : ___rho_1_^0'=___rho_1_^post2, curr_serv^0'=curr_serv^post2, servers^0'=servers^post2, c^0'=c^post2, resp^0'=resp^post2, (___rho_1_^0-___rho_1_^post2 == 0 /\ -c^post2+c^0 == 0 /\ -servers^post2+servers^0 == 0 /\ curr_serv^0-curr_serv^post2 == 0 /\ -resp^post2+resp^0 == 0), cost: 1 New rule: l4 -> l5 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : ___rho_1_^0'=___rho_1_^post3, curr_serv^0'=curr_serv^post3, servers^0'=servers^post3, c^0'=c^post3, resp^0'=resp^post3, (-resp^post3+resp^0 == 0 /\ servers^0-servers^post3 == 0 /\ c^0-c^post3 == 0 /\ curr_serv^0-curr_serv^post3 == 0 /\ ___rho_1_^0-___rho_1_^post3 == 0), cost: 1 New rule: l5 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l0 : ___rho_1_^0'=___rho_1_^post4, curr_serv^0'=curr_serv^post4, servers^0'=servers^post4, c^0'=c^post4, resp^0'=resp^post4, (___rho_1_^0 <= 0 /\ -resp^post4+resp^0 == 0 /\ 1-curr_serv^0+c^0 <= 0 /\ 1-curr_serv^0+curr_serv^post4 == 0 /\ -servers^post4+servers^0 == 0 /\ -c^post4+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post4 == 0), cost: 1 New rule: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 Applied preprocessing Original rule: l6 -> l0 : ___rho_1_^0'=___rho_1_^post5, curr_serv^0'=curr_serv^post5, servers^0'=servers^post5, c^0'=c^post5, resp^0'=resp^post5, (1-___rho_1_^0 <= 0 /\ servers^0-servers^post5 == 0 /\ ___rho_1_^0-___rho_1_^post5 == 0 /\ 1-curr_serv^0+curr_serv^post5 == 0 /\ -1+resp^post5-resp^0 == 0 /\ 1+c^post5-c^0 == 0), cost: 1 New rule: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^post6, servers^0'=servers^post6, c^0'=c^post6, resp^0'=resp^post6, (0 == 0 /\ 1-curr_serv^0 <= 0 /\ resp^0-resp^post6 == 0 /\ -servers^post6+servers^0 == 0 /\ curr_serv^0-curr_serv^post6 == 0 /\ -c^post6+c^0 == 0), cost: 1 New rule: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l4 : ___rho_1_^0'=___rho_1_^post7, curr_serv^0'=curr_serv^post7, servers^0'=servers^post7, c^0'=c^post7, resp^0'=resp^post7, (-c^post7+c^0 == 0 /\ curr_serv^0-curr_serv^post7 == 0 /\ curr_serv^0 <= 0 /\ ___rho_1_^0-___rho_1_^post7 == 0 /\ servers^0-servers^post7 == 0 /\ -resp^post7+resp^0 == 0), cost: 1 New rule: l1 -> l4 : curr_serv^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l0 : ___rho_1_^0'=___rho_1_^post8, curr_serv^0'=curr_serv^post8, servers^0'=servers^post8, c^0'=c^post8, resp^0'=resp^post8, (0 == 0 /\ -8+servers^post8 == 0 /\ ___rho_1_^0-___rho_1_^post8 == 0 /\ 1-c^post8 <= 0 /\ -servers^post8+curr_serv^post8 == 0 /\ resp^post8 == 0), cost: 1 New rule: l7 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 1 Applied preprocessing Original rule: l8 -> l7 : ___rho_1_^0'=___rho_1_^post9, curr_serv^0'=curr_serv^post9, servers^0'=servers^post9, c^0'=c^post9, resp^0'=resp^post9, (-resp^post9+resp^0 == 0 /\ servers^0-servers^post9 == 0 /\ -c^post9+c^0 == 0 /\ ___rho_1_^0-___rho_1_^post9 == 0 /\ curr_serv^0-curr_serv^post9 == 0), cost: 1 New rule: l8 -> l7 : TRUE, cost: 1 Simplified rules Start location: l8 10: l0 -> l1 : TRUE, cost: 1 15: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 16: l1 -> l4 : curr_serv^0 <= 0, cost: 1 11: l4 -> l5 : TRUE, cost: 1 12: l5 -> l4 : TRUE, cost: 1 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 17: l7 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 1 18: l8 -> l7 : TRUE, cost: 1 Eliminating location l7 by chaining: Applied chaining First rule: l8 -> l7 : TRUE, cost: 1 Second rule: l7 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 1 New rule: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Applied deletion Removed the following rules: 17 18 Eliminating location l5 by chaining: Applied chaining First rule: l4 -> l5 : TRUE, cost: 1 Second rule: l5 -> l4 : TRUE, cost: 1 New rule: l4 -> l4 : TRUE, cost: 2 Applied deletion Removed the following rules: 11 12 Eliminated locations on linear paths Start location: l8 10: l0 -> l1 : TRUE, cost: 1 15: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 16: l1 -> l4 : curr_serv^0 <= 0, cost: 1 20: l4 -> l4 : TRUE, cost: 2 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Applied nonterm Original rule: l4 -> l4 : TRUE, cost: 2 New rule: l4 -> [9] : TRUE, cost: NONTERM Applied acceleration Original rule: l4 -> l4 : TRUE, cost: 2 New rule: l4 -> l4 : TRUE, cost: 2*n0 Applied deletion Removed the following rules: 20 Accelerated simple loops Start location: l8 10: l0 -> l1 : TRUE, cost: 1 15: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 16: l1 -> l4 : curr_serv^0 <= 0, cost: 1 21: l4 -> [9] : TRUE, cost: NONTERM 22: l4 -> l4 : TRUE, cost: 2*n0 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Applied chaining First rule: l1 -> l4 : curr_serv^0 <= 0, cost: 1 Second rule: l4 -> [9] : TRUE, cost: NONTERM New rule: l1 -> [9] : curr_serv^0 <= 0, cost: NONTERM Applied chaining First rule: l1 -> l4 : curr_serv^0 <= 0, cost: 1 Second rule: l4 -> l4 : TRUE, cost: 2*n0 New rule: l1 -> l4 : curr_serv^0 <= 0, cost: 1+2*n0 Applied deletion Removed the following rules: 21 22 Chained accelerated rules with incoming rules Start location: l8 10: l0 -> l1 : TRUE, cost: 1 15: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 16: l1 -> l4 : curr_serv^0 <= 0, cost: 1 23: l1 -> [9] : curr_serv^0 <= 0, cost: NONTERM 24: l1 -> l4 : curr_serv^0 <= 0, cost: 1+2*n0 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Removed unreachable locations and irrelevant leafs Start location: l8 10: l0 -> l1 : TRUE, cost: 1 15: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 23: l1 -> [9] : curr_serv^0 <= 0, cost: NONTERM 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : TRUE, cost: 1 Second rule: l1 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 1 New rule: l0 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 2 Applied chaining First rule: l0 -> l1 : TRUE, cost: 1 Second rule: l1 -> [9] : curr_serv^0 <= 0, cost: NONTERM New rule: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM Applied deletion Removed the following rules: 10 15 23 Eliminated locations on tree-shaped paths Start location: l8 25: l0 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 2 26: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM 13: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 14: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Eliminating location l6 by chaining: Applied chaining First rule: l0 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 2 Second rule: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, (___rho_1_^0 <= 0 /\ 1-curr_serv^0+c^0 <= 0), cost: 1 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, (-1+curr_serv^0 >= 0 /\ 1-curr_serv^0+c^0 <= 0 /\ ___rho_1_^post6 <= 0), cost: 3 Applied chaining First rule: l0 -> l6 : ___rho_1_^0'=___rho_1_^post6, -1+curr_serv^0 >= 0, cost: 2 Second rule: l6 -> l0 : curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, -1+___rho_1_^0 >= 0, cost: 1 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3 Applied deletion Removed the following rules: 13 14 25 Eliminated locations on tree-shaped paths Start location: l8 26: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM 27: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, (-1+curr_serv^0 >= 0 /\ 1-curr_serv^0+c^0 <= 0 /\ ___rho_1_^post6 <= 0), cost: 3 28: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Applied acceleration Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, (-1+curr_serv^0 >= 0 /\ 1-curr_serv^0+c^0 <= 0 /\ ___rho_1_^post6 <= 0), cost: 3 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^0-n4, (-___rho_1_^post6 >= 0 /\ curr_serv^0-n4-c^0 >= 0 /\ -1+n4 >= 0 /\ curr_serv^0-n4 >= 0), cost: 3*n4 Applied instantiation Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^0-n4, (-___rho_1_^post6 >= 0 /\ curr_serv^0-n4-c^0 >= 0 /\ -1+n4 >= 0 /\ curr_serv^0-n4 >= 0), cost: 3*n4 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^0, (0 >= 0 /\ -___rho_1_^post6 >= 0 /\ c^0 >= 0 /\ -1+curr_serv^0-c^0 >= 0), cost: 3*curr_serv^0-3*c^0 Applied instantiation Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=curr_serv^0-n4, (-___rho_1_^post6 >= 0 /\ curr_serv^0-n4-c^0 >= 0 /\ -1+n4 >= 0 /\ curr_serv^0-n4 >= 0), cost: 3*n4 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, (0 >= 0 /\ -___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0 /\ -c^0 >= 0), cost: 3*curr_serv^0 Applied acceleration Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-1+curr_serv^0, c^0'=-1+c^0, resp^0'=1+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-n7+curr_serv^0, c^0'=-n7+c^0, resp^0'=n7+resp^0, (-n7+curr_serv^0 >= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+n7 >= 0), cost: 3*n7 Applied instantiation Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=-n7+curr_serv^0, c^0'=-n7+c^0, resp^0'=n7+resp^0, (-n7+curr_serv^0 >= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+n7 >= 0), cost: 3*n7 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, c^0'=-curr_serv^0+c^0, resp^0'=curr_serv^0+resp^0, (0 >= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3*curr_serv^0 Applied simplification Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^0, (0 >= 0 /\ -___rho_1_^post6 >= 0 /\ c^0 >= 0 /\ -1+curr_serv^0-c^0 >= 0), cost: 3*curr_serv^0-3*c^0 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^0, (c^0 >= 0 /\ ___rho_1_^post6 <= 0 /\ -1+curr_serv^0-c^0 >= 0), cost: 3*curr_serv^0-3*c^0 Applied simplification Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, (0 >= 0 /\ -___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0 /\ -c^0 >= 0), cost: 3*curr_serv^0 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, (-1+curr_serv^0 >= 0 /\ c^0 <= 0 /\ ___rho_1_^post6 <= 0), cost: 3*curr_serv^0 Applied simplification Original rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, c^0'=-curr_serv^0+c^0, resp^0'=curr_serv^0+resp^0, (0 >= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3*curr_serv^0 New rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, c^0'=-curr_serv^0+c^0, resp^0'=curr_serv^0+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3*curr_serv^0 Applied deletion Removed the following rules: 27 28 Accelerated simple loops Start location: l8 26: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM 32: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^0, (c^0 >= 0 /\ ___rho_1_^post6 <= 0 /\ -1+curr_serv^0-c^0 >= 0), cost: 3*curr_serv^0-3*c^0 33: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, (-1+curr_serv^0 >= 0 /\ c^0 <= 0 /\ ___rho_1_^post6 <= 0), cost: 3*curr_serv^0 34: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, c^0'=-curr_serv^0+c^0, resp^0'=curr_serv^0+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3*curr_serv^0 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Applied chaining First rule: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Second rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^0, (c^0 >= 0 /\ ___rho_1_^post6 <= 0 /\ -1+curr_serv^0-c^0 >= 0), cost: 3*curr_serv^0-3*c^0 New rule: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^post8, servers^0'=8, c^0'=c^post8, resp^0'=0, (-7+c^post8 <= 0 /\ ___rho_1_^post6 <= 0 /\ -1+c^post8 >= 0), cost: 26-3*c^post8 Applied chaining First rule: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 Second rule: l0 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, c^0'=-curr_serv^0+c^0, resp^0'=curr_serv^0+resp^0, (-1+___rho_1_^post6 >= 0 /\ -1+curr_serv^0 >= 0), cost: 3*curr_serv^0 New rule: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, servers^0'=8, c^0'=-8+c^post8, resp^0'=8, (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: 26 Applied deletion Removed the following rules: 32 33 34 Chained accelerated rules with incoming rules Start location: l8 26: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM 19: l8 -> l0 : curr_serv^0'=8, servers^0'=8, c^0'=c^post8, resp^0'=0, -1+c^post8 >= 0, cost: 2 35: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^post8, servers^0'=8, c^0'=c^post8, resp^0'=0, (-7+c^post8 <= 0 /\ ___rho_1_^post6 <= 0 /\ -1+c^post8 >= 0), cost: 26-3*c^post8 36: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, servers^0'=8, c^0'=-8+c^post8, resp^0'=8, (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: 26 Eliminating location l0 by chaining: Applied chaining First rule: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=0, servers^0'=8, c^0'=-8+c^post8, resp^0'=8, (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: 26 Second rule: l0 -> [9] : curr_serv^0 <= 0, cost: NONTERM New rule: l8 -> [9] : (0 <= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: NONTERM Applied simplification Original rule: l8 -> [9] : (0 <= 0 /\ -1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: NONTERM New rule: l8 -> [9] : (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: NONTERM Applied partial deletion Original rule: l8 -> l0 : ___rho_1_^0'=___rho_1_^post6, curr_serv^0'=c^post8, servers^0'=8, c^0'=c^post8, resp^0'=0, (-7+c^post8 <= 0 /\ ___rho_1_^post6 <= 0 /\ -1+c^post8 >= 0), cost: 26-3*c^post8 New rule: l8 -> [11] : (-7+c^post8 <= 0 /\ ___rho_1_^post6 <= 0 /\ -1+c^post8 >= 0), cost: 26-3*c^post8 Applied deletion Removed the following rules: 19 26 35 36 Eliminated locations on tree-shaped paths Start location: l8 37: l8 -> [9] : (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0), cost: NONTERM 38: l8 -> [11] : (-7+c^post8 <= 0 /\ ___rho_1_^post6 <= 0 /\ -1+c^post8 >= 0), cost: 26-3*c^post8 Computing asymptotic complexity Proved nontermination of rule 37 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+___rho_1_^post6 >= 0 /\ -1+c^post8 >= 0)