NO Initial ITS Start location: l5 0: l0 -> l1 : __const_99^0'=__const_99^post0, lo^0'=lo^post0, hi^0'=hi^post0, (0 == 0 /\ __const_99^0-__const_99^post0 == 0 /\ lo^0-lo^post0 == 0), cost: 1 1: l0 -> l1 : __const_99^0'=__const_99^post1, lo^0'=lo^post1, hi^0'=hi^post1, (0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ hi^0-hi^post1 == 0), cost: 1 4: l1 -> l2 : __const_99^0'=__const_99^post4, lo^0'=lo^post4, hi^0'=hi^post4, (lo^0-lo^post4 == 0 /\ hi^0-hi^post4 == 0 /\ __const_99^0-__const_99^post4 == 0), cost: 1 2: l2 -> l3 : __const_99^0'=__const_99^post2, lo^0'=lo^post2, hi^0'=hi^post2, (lo^0-hi^0 <= 0 /\ lo^0-lo^post2 == 0 /\ hi^0-hi^post2 == 0 /\ __const_99^0-__const_99^post2 == 0), cost: 1 3: l2 -> l0 : __const_99^0'=__const_99^post3, lo^0'=lo^post3, hi^0'=hi^post3, (hi^0-hi^post3 == 0 /\ 1-lo^0+hi^0 <= 0 /\ __const_99^0-__const_99^post3 == 0 /\ lo^0-lo^post3 == 0), cost: 1 5: l4 -> l1 : __const_99^0'=__const_99^post5, lo^0'=lo^post5, hi^0'=hi^post5, (-__const_99^0+lo^post5 == 0 /\ __const_99^0-__const_99^post5 == 0 /\ hi^post5 == 0), cost: 1 6: l5 -> l4 : __const_99^0'=__const_99^post6, lo^0'=lo^post6, hi^0'=hi^post6, (hi^0-hi^post6 == 0 /\ __const_99^0-__const_99^post6 == 0 /\ lo^0-lo^post6 == 0), cost: 1 Removed unreachable rules and leafs Start location: l5 0: l0 -> l1 : __const_99^0'=__const_99^post0, lo^0'=lo^post0, hi^0'=hi^post0, (0 == 0 /\ __const_99^0-__const_99^post0 == 0 /\ lo^0-lo^post0 == 0), cost: 1 1: l0 -> l1 : __const_99^0'=__const_99^post1, lo^0'=lo^post1, hi^0'=hi^post1, (0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ hi^0-hi^post1 == 0), cost: 1 4: l1 -> l2 : __const_99^0'=__const_99^post4, lo^0'=lo^post4, hi^0'=hi^post4, (lo^0-lo^post4 == 0 /\ hi^0-hi^post4 == 0 /\ __const_99^0-__const_99^post4 == 0), cost: 1 3: l2 -> l0 : __const_99^0'=__const_99^post3, lo^0'=lo^post3, hi^0'=hi^post3, (hi^0-hi^post3 == 0 /\ 1-lo^0+hi^0 <= 0 /\ __const_99^0-__const_99^post3 == 0 /\ lo^0-lo^post3 == 0), cost: 1 5: l4 -> l1 : __const_99^0'=__const_99^post5, lo^0'=lo^post5, hi^0'=hi^post5, (-__const_99^0+lo^post5 == 0 /\ __const_99^0-__const_99^post5 == 0 /\ hi^post5 == 0), cost: 1 6: l5 -> l4 : __const_99^0'=__const_99^post6, lo^0'=lo^post6, hi^0'=hi^post6, (hi^0-hi^post6 == 0 /\ __const_99^0-__const_99^post6 == 0 /\ lo^0-lo^post6 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : __const_99^0'=__const_99^post0, lo^0'=lo^post0, hi^0'=hi^post0, (0 == 0 /\ __const_99^0-__const_99^post0 == 0 /\ lo^0-lo^post0 == 0), cost: 1 New rule: l0 -> l1 : hi^0'=hi^post0, 0 == 0, cost: 1 Applied preprocessing Original rule: l0 -> l1 : __const_99^0'=__const_99^post1, lo^0'=lo^post1, hi^0'=hi^post1, (0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ hi^0-hi^post1 == 0), cost: 1 New rule: l0 -> l1 : lo^0'=lo^post1, 0 == 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : __const_99^0'=__const_99^post3, lo^0'=lo^post3, hi^0'=hi^post3, (hi^0-hi^post3 == 0 /\ 1-lo^0+hi^0 <= 0 /\ __const_99^0-__const_99^post3 == 0 /\ lo^0-lo^post3 == 0), cost: 1 New rule: l2 -> l0 : 1-lo^0+hi^0 <= 0, cost: 1 Applied preprocessing Original rule: l1 -> l2 : __const_99^0'=__const_99^post4, lo^0'=lo^post4, hi^0'=hi^post4, (lo^0-lo^post4 == 0 /\ hi^0-hi^post4 == 0 /\ __const_99^0-__const_99^post4 == 0), cost: 1 New rule: l1 -> l2 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l1 : __const_99^0'=__const_99^post5, lo^0'=lo^post5, hi^0'=hi^post5, (-__const_99^0+lo^post5 == 0 /\ __const_99^0-__const_99^post5 == 0 /\ hi^post5 == 0), cost: 1 New rule: l4 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : __const_99^0'=__const_99^post6, lo^0'=lo^post6, hi^0'=hi^post6, (hi^0-hi^post6 == 0 /\ __const_99^0-__const_99^post6 == 0 /\ lo^0-lo^post6 == 0), cost: 1 New rule: l5 -> l4 : TRUE, cost: 1 Simplified rules Start location: l5 7: l0 -> l1 : hi^0'=hi^post0, 0 == 0, cost: 1 8: l0 -> l1 : lo^0'=lo^post1, 0 == 0, cost: 1 10: l1 -> l2 : TRUE, cost: 1 9: l2 -> l0 : 1-lo^0+hi^0 <= 0, cost: 1 11: l4 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 1 12: l5 -> l4 : TRUE, cost: 1 Eliminating location l4 by chaining: Applied chaining First rule: l5 -> l4 : TRUE, cost: 1 Second rule: l4 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 1 New rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 11 12 Eliminating location l2 by chaining: Applied chaining First rule: l1 -> l2 : TRUE, cost: 1 Second rule: l2 -> l0 : 1-lo^0+hi^0 <= 0, cost: 1 New rule: l1 -> l0 : 1-lo^0+hi^0 <= 0, cost: 2 Applied deletion Removed the following rules: 9 10 Eliminated locations on linear paths Start location: l5 7: l0 -> l1 : hi^0'=hi^post0, 0 == 0, cost: 1 8: l0 -> l1 : lo^0'=lo^post1, 0 == 0, cost: 1 14: l1 -> l0 : 1-lo^0+hi^0 <= 0, cost: 2 13: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Eliminating location l0 by chaining: Applied chaining First rule: l1 -> l0 : 1-lo^0+hi^0 <= 0, cost: 2 Second rule: l0 -> l1 : hi^0'=hi^post0, 0 == 0, cost: 1 New rule: l1 -> l1 : hi^0'=hi^post0, (0 == 0 /\ 1-lo^0+hi^0 <= 0), cost: 3 Applied simplification Original rule: l1 -> l1 : hi^0'=hi^post0, (0 == 0 /\ 1-lo^0+hi^0 <= 0), cost: 3 New rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 Applied chaining First rule: l1 -> l0 : 1-lo^0+hi^0 <= 0, cost: 2 Second rule: l0 -> l1 : lo^0'=lo^post1, 0 == 0, cost: 1 New rule: l1 -> l1 : lo^0'=lo^post1, (0 == 0 /\ 1-lo^0+hi^0 <= 0), cost: 3 Applied simplification Original rule: l1 -> l1 : lo^0'=lo^post1, (0 == 0 /\ 1-lo^0+hi^0 <= 0), cost: 3 New rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 Applied deletion Removed the following rules: 7 8 14 Eliminated locations on tree-shaped paths Start location: l5 15: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 16: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 13: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Applied acceleration Original rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n1 Applied unrolling Original rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: 6 Applied non-termination processor Original rule: l1 -> l1 : hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: 6 New rule: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: NONTERM Applied acceleration Original rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : lo^0'=lo^post1, (-1+n3 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n3 Applied unrolling Original rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : lo^0'=lo^post1, (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: 6 Applied non-termination processor Original rule: l1 -> l1 : lo^0'=lo^post1, (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: 6 New rule: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: NONTERM Applied chaining First rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: 6 Applied acceleration Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: 6 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n5 Applied chaining First rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n5 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+6*n5 Applied chaining First rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: 6 Applied acceleration Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: 6 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n7 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n7 Applied chaining First rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n7 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n7 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0 /\ -1+n7 >= 0), cost: 3+6*n7 Applied chaining First rule: l1 -> l1 : hi^0'=hi^post0, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : lo^0'=lo^post1, (-1+n3 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n3 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n3 Applied nonterm Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n3 New rule: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM Applied acceleration Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n3 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+n3 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n9 >= 0 /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0)) /\ ((-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0) \/ (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0))), cost: 3*n3*n9+3*n9 Applied chaining First rule: l1 -> l1 : lo^0'=lo^post1, (-1+n3 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n3 Second rule: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM Heuristically decided not to add the following rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+n3 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n9 >= 0 /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0)) /\ ((-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0) \/ (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0))), cost: 3*n3*n9+3*n9 Applied chaining First rule: l1 -> l1 : lo^0'=lo^post1, 1-lo^0+hi^0 <= 0, cost: 3 Second rule: l1 -> l1 : hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n1 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n1 Applied nonterm Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n1 New rule: l1 -> [6] : (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM Applied acceleration Original rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+3*n1 New rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+n13 >= 0 /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0)) /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0))), cost: 3*n1*n13+3*n13 Applied chaining First rule: l1 -> l1 : hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n1 Second rule: l1 -> [6] : (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l1 -> [6] : (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM Heuristically decided not to add the following rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+n13 >= 0 /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0)) /\ ((-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0) \/ (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0))), cost: 3*n1*n13+3*n13 Applied deletion Removed the following rules: 15 16 Accelerated simple loops Start location: l5 17: l1 -> l1 : hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n1 18: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: NONTERM 19: l1 -> l1 : lo^0'=lo^post1, (-1+n3 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n3 20: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: NONTERM 21: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n5 22: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+6*n5 23: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n7 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n7 24: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0 /\ -1+n7 >= 0), cost: 3+6*n7 25: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM 26: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM 27: l1 -> [6] : (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM 28: l1 -> [6] : (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM 13: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n1 New rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=hi^post0, (-1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n1 >= 0), cost: 2+3*n1 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^post0-lo^0 <= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : lo^0'=lo^post1, (-1+n3 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 3*n3 New rule: l5 -> l1 : lo^0'=lo^post1, hi^0'=0, (-1+n3 >= 0 /\ -1+lo^post1 >= 0 /\ -1+__const_99^0 >= 0), cost: 2+3*n3 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (1-lo^0+hi^0 <= 0 /\ 1+hi^0-lo^post1 <= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n5 New rule: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n5 >= 0), cost: 2+6*n5 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n5 >= 0 /\ 1-lo^0+hi^0 <= 0), cost: 3+6*n5 New rule: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+lo^post1 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n5 >= 0), cost: 5+6*n5 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n7 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: 6*n7 New rule: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+lo^post1 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n7 >= 0), cost: 2+6*n7 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ 1-lo^0+hi^0 <= 0 /\ -1+n7 >= 0), cost: 3+6*n7 New rule: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n7 >= 0), cost: 5+6*n7 Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (-1+n3 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (-1-hi^post0+lo^post1 >= 0 /\ -1-hi^0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : (-1-hi^post0+lo^0 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+n1 >= 0 /\ -1+lo^0-hi^0 >= 0), cost: NONTERM New rule: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 17 18 19 20 21 22 23 24 25 26 27 28 Chained accelerated rules with incoming rules Start location: l5 13: l5 -> l1 : lo^0'=__const_99^0, hi^0'=0, TRUE, cost: 2 29: l5 -> l1 : lo^0'=__const_99^0, hi^0'=hi^post0, (-1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n1 >= 0), cost: 2+3*n1 30: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 31: l5 -> l1 : lo^0'=lo^post1, hi^0'=0, (-1+n3 >= 0 /\ -1+lo^post1 >= 0 /\ -1+__const_99^0 >= 0), cost: 2+3*n3 32: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 33: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n5 >= 0), cost: 2+6*n5 34: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+lo^post1 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n5 >= 0), cost: 5+6*n5 35: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1+lo^post1 >= 0 /\ -1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n7 >= 0), cost: 2+6*n7 36: l5 -> l1 : lo^0'=lo^post1, hi^0'=hi^post0, (-1-hi^post0+lo^post1 >= 0 /\ -1+__const_99^0-hi^post0 >= 0 /\ -1+__const_99^0 >= 0 /\ -1+n7 >= 0), cost: 5+6*n7 37: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 38: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 39: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 40: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l5 30: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 32: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 37: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 38: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 39: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM 40: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Removed duplicate rules (ignoring updates) Start location: l5 40: l5 -> [6] : -1+__const_99^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 40 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1+__const_99^0 >= 0