WORST_CASE(Omega(0),?) Initial ITS Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, x_5^0'=x_5^post0, (0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -x_5^post0+x_5^0 == 0 /\ x_5^0 <= 0), cost: 1 1: l0 -> l1 : Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, x_5^0'=x_5^post1, (0 == 0 /\ y_6^0 <= 0 /\ y_6^0-y_6^post1 == 0 /\ 1-x_5^0 <= 0 /\ x_5^0-x_5^post1 == 0), cost: 1 2: l0 -> l1 : Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, x_5^0'=x_5^post2, (0 == 0 /\ 1-y_6^0 <= 0 /\ y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ 1-x_5^0 <= 0 /\ y_6^0+x_5^0 <= 0), cost: 1 3: l0 -> l2 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (1-y_6^0 <= 0 /\ -1+y_6^post3-x_5^post3 == 0 /\ 1-x_5^0 <= 0 /\ 2-y_6^0+x_5^post3 == 0 /\ 1-y_6^0-x_5^0 <= 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1 4: l2 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 5: l3 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, (Result_4^0-Result_4^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0), cost: 1 6: l4 -> l3 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 3: l0 -> l2 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (1-y_6^0 <= 0 /\ -1+y_6^post3-x_5^post3 == 0 /\ 1-x_5^0 <= 0 /\ 2-y_6^0+x_5^post3 == 0 /\ 1-y_6^0-x_5^0 <= 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1 4: l2 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 5: l3 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, (Result_4^0-Result_4^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0), cost: 1 6: l4 -> l3 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (1-y_6^0 <= 0 /\ -1+y_6^post3-x_5^post3 == 0 /\ 1-x_5^0 <= 0 /\ 2-y_6^0+x_5^post3 == 0 /\ 1-y_6^0-x_5^0 <= 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1 New rule: l0 -> l2 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 1 Applied preprocessing Original rule: l2 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, (Result_4^0-Result_4^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l3 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0), cost: 1 New rule: l4 -> l3 : TRUE, cost: 1 Simplified rules Start location: l4 7: l0 -> l2 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 1 8: l2 -> l0 : TRUE, cost: 1 9: l3 -> l0 : TRUE, cost: 1 10: l4 -> l3 : TRUE, cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l4 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 9 10 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 2 Applied deletion Removed the following rules: 7 8 Eliminated locations on linear paths Start location: l4 12: l0 -> l0 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 2 11: l4 -> l0 : TRUE, cost: 2 Applied acceleration Original rule: l0 -> l0 : y_6^0'=-1+y_6^0, x_5^0'=-2+y_6^0, (-1+y_6^0 >= 0 /\ -1+x_5^0 >= 0), cost: 2 New rule: l0 -> l0 : y_6^0'=y_6^0-n0, x_5^0'=-1+y_6^0-n0, (-1+y_6^0-n0 >= 0 /\ -1+x_5^0 >= 0 /\ -1+n0 >= 0 /\ y_6^0-n0 >= 0), cost: 2*n0 Applied instantiation Original rule: l0 -> l0 : y_6^0'=y_6^0-n0, x_5^0'=-1+y_6^0-n0, (-1+y_6^0-n0 >= 0 /\ -1+x_5^0 >= 0 /\ -1+n0 >= 0 /\ y_6^0-n0 >= 0), cost: 2*n0 New rule: l0 -> l0 : y_6^0'=1, x_5^0'=0, (0 >= 0 /\ 1 >= 0 /\ -1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: -2+2*y_6^0 Applied instantiation Original rule: l0 -> l0 : y_6^0'=y_6^0-n0, x_5^0'=-1+y_6^0-n0, (-1+y_6^0-n0 >= 0 /\ -1+x_5^0 >= 0 /\ -1+n0 >= 0 /\ y_6^0-n0 >= 0), cost: 2*n0 New rule: l0 -> l0 : y_6^0'=0, x_5^0'=-1, (0 >= 0 /\ -1+y_6^0 >= 0 /\ -1+x_5^0 >= 0 /\ -1 >= 0), cost: 2*y_6^0 Applied simplification Original rule: l0 -> l0 : y_6^0'=1, x_5^0'=0, (0 >= 0 /\ 1 >= 0 /\ -1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: -2+2*y_6^0 New rule: l0 -> l0 : y_6^0'=1, x_5^0'=0, (-1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: -2+2*y_6^0 Applied deletion Removed the following rules: 12 Accelerated simple loops Start location: l4 14: l0 -> l0 : y_6^0'=0, x_5^0'=-1, (0 >= 0 /\ -1+y_6^0 >= 0 /\ -1+x_5^0 >= 0 /\ -1 >= 0), cost: 2*y_6^0 15: l0 -> l0 : y_6^0'=1, x_5^0'=0, (-1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: -2+2*y_6^0 11: l4 -> l0 : TRUE, cost: 2 Applied chaining First rule: l4 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : y_6^0'=1, x_5^0'=0, (-1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: -2+2*y_6^0 New rule: l4 -> l0 : y_6^0'=1, x_5^0'=0, (-1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: 2*y_6^0 Applied deletion Removed the following rules: 14 15 Chained accelerated rules with incoming rules Start location: l4 11: l4 -> l0 : TRUE, cost: 2 16: l4 -> l0 : y_6^0'=1, x_5^0'=0, (-1+x_5^0 >= 0 /\ -2+y_6^0 >= 0), cost: 2*y_6^0 Removed unreachable locations and irrelevant leafs Start location: l4 Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0