WORST_CASE(Omega(0),?) Initial ITS Start location: l11 0: l0 -> l1 : a^0'=a^post0, i^0'=i^post0, tmp^0'=tmp^post0, b^0'=b^post0, n^0'=n^post0, (a^0 <= 0 /\ tmp^0-tmp^post0 == 0 /\ a^0-a^post0 == 0 /\ -n^post0+n^0 == 0 /\ -b^post0+b^0 == 0 /\ i^0-i^post0 == 0), cost: 1 1: l0 -> l2 : a^0'=a^post1, i^0'=i^post1, tmp^0'=tmp^post1, b^0'=b^post1, n^0'=n^post1, (-tmp^post1+tmp^0 == 0 /\ 1-a^0 <= 0 /\ -1-b^0+b^post1 == 0 /\ 1-a^0+a^post1 == 0 /\ -n^post1+n^0 == 0 /\ -i^post1+i^0 == 0), cost: 1 3: l2 -> l4 : a^0'=a^post3, i^0'=i^post3, tmp^0'=tmp^post3, b^0'=b^post3, n^0'=n^post3, (-n^post3+n^0 == 0 /\ tmp^0-tmp^post3 == 0 /\ b^0-b^post3 == 0 /\ i^0-i^post3 == 0 /\ a^0-a^post3 == 0), cost: 1 2: l3 -> l0 : a^0'=a^post2, i^0'=i^post2, tmp^0'=tmp^post2, b^0'=b^post2, n^0'=n^post2, (a^0-a^post2 == 0 /\ -b^post2+b^0 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i^0-i^post2 == 0 /\ -n^post2+n^0 == 0), cost: 1 12: l4 -> l3 : a^0'=a^post12, i^0'=i^post12, tmp^0'=tmp^post12, b^0'=b^post12, n^0'=n^post12, (-tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0 /\ a^0-a^post12 == 0 /\ b^0 <= 0 /\ b^0-b^post12 == 0 /\ -i^post12+i^0 == 0), cost: 1 13: l4 -> l6 : a^0'=a^post13, i^0'=i^post13, tmp^0'=tmp^post13, b^0'=b^post13, n^0'=n^post13, (1+b^post13-b^0 == 0 /\ -n^post13+n^0 == 0 /\ a^0-a^post13 == 0 /\ 1-b^0 <= 0 /\ 1-a^0+i^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1 4: l5 -> l6 : a^0'=a^post4, i^0'=i^post4, tmp^0'=tmp^post4, b^0'=b^post4, n^0'=n^post4, (-n^post4+n^0 == 0 /\ 1-i^0+i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -b^post4+b^0 == 0 /\ a^0-a^post4 == 0), cost: 1 5: l6 -> l7 : a^0'=a^post5, i^0'=i^post5, tmp^0'=tmp^post5, b^0'=b^post5, n^0'=n^post5, (-n^post5+n^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ a^0-a^post5 == 0 /\ -b^post5+b^0 == 0 /\ i^0-i^post5 == 0), cost: 1 10: l7 -> l2 : a^0'=a^post10, i^0'=i^post10, tmp^0'=tmp^post10, b^0'=b^post10, n^0'=n^post10, (i^0 <= 0 /\ n^0-n^post10 == 0 /\ -tmp^post10+tmp^0 == 0 /\ -b^post10+b^0 == 0 /\ a^0-a^post10 == 0 /\ i^0-i^post10 == 0), cost: 1 11: l7 -> l9 : a^0'=a^post11, i^0'=i^post11, tmp^0'=tmp^post11, b^0'=b^post11, n^0'=n^post11, (0 == 0 /\ 1-i^0 <= 0 /\ -n^post11+n^0 == 0 /\ a^0-a^post11 == 0 /\ i^0-i^post11 == 0 /\ -b^post11+b^0 == 0), cost: 1 6: l8 -> l5 : a^0'=a^post6, i^0'=i^post6, tmp^0'=tmp^post6, b^0'=b^post6, n^0'=n^post6, (n^0-n^post6 == 0 /\ -1+b^post6-b^0 == 0 /\ -tmp^post6+tmp^0 == 0 /\ i^0-i^post6 == 0 /\ 1-a^0+a^post6 == 0), cost: 1 7: l9 -> l5 : a^0'=a^post7, i^0'=i^post7, tmp^0'=tmp^post7, b^0'=b^post7, n^0'=n^post7, (-b^post7+b^0 == 0 /\ i^0-i^post7 == 0 /\ tmp^0 <= 0 /\ a^0-a^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -tmp^0 <= 0 /\ -n^post7+n^0 == 0), cost: 1 8: l9 -> l8 : a^0'=a^post8, i^0'=i^post8, tmp^0'=tmp^post8, b^0'=b^post8, n^0'=n^post8, (-n^post8+n^0 == 0 /\ a^0-a^post8 == 0 /\ -b^post8+b^0 == 0 /\ i^0-i^post8 == 0 /\ 1-tmp^0 <= 0 /\ -tmp^post8+tmp^0 == 0), cost: 1 9: l9 -> l8 : a^0'=a^post9, i^0'=i^post9, tmp^0'=tmp^post9, b^0'=b^post9, n^0'=n^post9, (-n^post9+n^0 == 0 /\ tmp^0-tmp^post9 == 0 /\ 1+tmp^0 <= 0 /\ -b^post9+b^0 == 0 /\ a^0-a^post9 == 0 /\ i^0-i^post9 == 0), cost: 1 14: l10 -> l3 : a^0'=a^post14, i^0'=i^post14, tmp^0'=tmp^post14, b^0'=b^post14, n^0'=n^post14, (-n^post14+n^0 == 0 /\ a^post14-n^0 == 0 /\ -i^post14+i^0 == 0 /\ -tmp^post14+tmp^0 == 0 /\ b^post14 == 0), cost: 1 15: l11 -> l10 : a^0'=a^post15, i^0'=i^post15, tmp^0'=tmp^post15, b^0'=b^post15, n^0'=n^post15, (-n^post15+n^0 == 0 /\ -tmp^post15+tmp^0 == 0 /\ -b^post15+b^0 == 0 /\ a^0-a^post15 == 0 /\ i^0-i^post15 == 0), cost: 1 Removed unreachable rules and leafs Start location: l11 1: l0 -> l2 : a^0'=a^post1, i^0'=i^post1, tmp^0'=tmp^post1, b^0'=b^post1, n^0'=n^post1, (-tmp^post1+tmp^0 == 0 /\ 1-a^0 <= 0 /\ -1-b^0+b^post1 == 0 /\ 1-a^0+a^post1 == 0 /\ -n^post1+n^0 == 0 /\ -i^post1+i^0 == 0), cost: 1 3: l2 -> l4 : a^0'=a^post3, i^0'=i^post3, tmp^0'=tmp^post3, b^0'=b^post3, n^0'=n^post3, (-n^post3+n^0 == 0 /\ tmp^0-tmp^post3 == 0 /\ b^0-b^post3 == 0 /\ i^0-i^post3 == 0 /\ a^0-a^post3 == 0), cost: 1 2: l3 -> l0 : a^0'=a^post2, i^0'=i^post2, tmp^0'=tmp^post2, b^0'=b^post2, n^0'=n^post2, (a^0-a^post2 == 0 /\ -b^post2+b^0 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i^0-i^post2 == 0 /\ -n^post2+n^0 == 0), cost: 1 12: l4 -> l3 : a^0'=a^post12, i^0'=i^post12, tmp^0'=tmp^post12, b^0'=b^post12, n^0'=n^post12, (-tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0 /\ a^0-a^post12 == 0 /\ b^0 <= 0 /\ b^0-b^post12 == 0 /\ -i^post12+i^0 == 0), cost: 1 13: l4 -> l6 : a^0'=a^post13, i^0'=i^post13, tmp^0'=tmp^post13, b^0'=b^post13, n^0'=n^post13, (1+b^post13-b^0 == 0 /\ -n^post13+n^0 == 0 /\ a^0-a^post13 == 0 /\ 1-b^0 <= 0 /\ 1-a^0+i^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1 4: l5 -> l6 : a^0'=a^post4, i^0'=i^post4, tmp^0'=tmp^post4, b^0'=b^post4, n^0'=n^post4, (-n^post4+n^0 == 0 /\ 1-i^0+i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -b^post4+b^0 == 0 /\ a^0-a^post4 == 0), cost: 1 5: l6 -> l7 : a^0'=a^post5, i^0'=i^post5, tmp^0'=tmp^post5, b^0'=b^post5, n^0'=n^post5, (-n^post5+n^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ a^0-a^post5 == 0 /\ -b^post5+b^0 == 0 /\ i^0-i^post5 == 0), cost: 1 10: l7 -> l2 : a^0'=a^post10, i^0'=i^post10, tmp^0'=tmp^post10, b^0'=b^post10, n^0'=n^post10, (i^0 <= 0 /\ n^0-n^post10 == 0 /\ -tmp^post10+tmp^0 == 0 /\ -b^post10+b^0 == 0 /\ a^0-a^post10 == 0 /\ i^0-i^post10 == 0), cost: 1 11: l7 -> l9 : a^0'=a^post11, i^0'=i^post11, tmp^0'=tmp^post11, b^0'=b^post11, n^0'=n^post11, (0 == 0 /\ 1-i^0 <= 0 /\ -n^post11+n^0 == 0 /\ a^0-a^post11 == 0 /\ i^0-i^post11 == 0 /\ -b^post11+b^0 == 0), cost: 1 6: l8 -> l5 : a^0'=a^post6, i^0'=i^post6, tmp^0'=tmp^post6, b^0'=b^post6, n^0'=n^post6, (n^0-n^post6 == 0 /\ -1+b^post6-b^0 == 0 /\ -tmp^post6+tmp^0 == 0 /\ i^0-i^post6 == 0 /\ 1-a^0+a^post6 == 0), cost: 1 7: l9 -> l5 : a^0'=a^post7, i^0'=i^post7, tmp^0'=tmp^post7, b^0'=b^post7, n^0'=n^post7, (-b^post7+b^0 == 0 /\ i^0-i^post7 == 0 /\ tmp^0 <= 0 /\ a^0-a^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -tmp^0 <= 0 /\ -n^post7+n^0 == 0), cost: 1 8: l9 -> l8 : a^0'=a^post8, i^0'=i^post8, tmp^0'=tmp^post8, b^0'=b^post8, n^0'=n^post8, (-n^post8+n^0 == 0 /\ a^0-a^post8 == 0 /\ -b^post8+b^0 == 0 /\ i^0-i^post8 == 0 /\ 1-tmp^0 <= 0 /\ -tmp^post8+tmp^0 == 0), cost: 1 9: l9 -> l8 : a^0'=a^post9, i^0'=i^post9, tmp^0'=tmp^post9, b^0'=b^post9, n^0'=n^post9, (-n^post9+n^0 == 0 /\ tmp^0-tmp^post9 == 0 /\ 1+tmp^0 <= 0 /\ -b^post9+b^0 == 0 /\ a^0-a^post9 == 0 /\ i^0-i^post9 == 0), cost: 1 14: l10 -> l3 : a^0'=a^post14, i^0'=i^post14, tmp^0'=tmp^post14, b^0'=b^post14, n^0'=n^post14, (-n^post14+n^0 == 0 /\ a^post14-n^0 == 0 /\ -i^post14+i^0 == 0 /\ -tmp^post14+tmp^0 == 0 /\ b^post14 == 0), cost: 1 15: l11 -> l10 : a^0'=a^post15, i^0'=i^post15, tmp^0'=tmp^post15, b^0'=b^post15, n^0'=n^post15, (-n^post15+n^0 == 0 /\ -tmp^post15+tmp^0 == 0 /\ -b^post15+b^0 == 0 /\ a^0-a^post15 == 0 /\ i^0-i^post15 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : a^0'=a^post1, i^0'=i^post1, tmp^0'=tmp^post1, b^0'=b^post1, n^0'=n^post1, (-tmp^post1+tmp^0 == 0 /\ 1-a^0 <= 0 /\ -1-b^0+b^post1 == 0 /\ 1-a^0+a^post1 == 0 /\ -n^post1+n^0 == 0 /\ -i^post1+i^0 == 0), cost: 1 New rule: l0 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : a^0'=a^post2, i^0'=i^post2, tmp^0'=tmp^post2, b^0'=b^post2, n^0'=n^post2, (a^0-a^post2 == 0 /\ -b^post2+b^0 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i^0-i^post2 == 0 /\ -n^post2+n^0 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l4 : a^0'=a^post3, i^0'=i^post3, tmp^0'=tmp^post3, b^0'=b^post3, n^0'=n^post3, (-n^post3+n^0 == 0 /\ tmp^0-tmp^post3 == 0 /\ b^0-b^post3 == 0 /\ i^0-i^post3 == 0 /\ a^0-a^post3 == 0), cost: 1 New rule: l2 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l6 : a^0'=a^post4, i^0'=i^post4, tmp^0'=tmp^post4, b^0'=b^post4, n^0'=n^post4, (-n^post4+n^0 == 0 /\ 1-i^0+i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -b^post4+b^0 == 0 /\ a^0-a^post4 == 0), cost: 1 New rule: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l7 : a^0'=a^post5, i^0'=i^post5, tmp^0'=tmp^post5, b^0'=b^post5, n^0'=n^post5, (-n^post5+n^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ a^0-a^post5 == 0 /\ -b^post5+b^0 == 0 /\ i^0-i^post5 == 0), cost: 1 New rule: l6 -> l7 : TRUE, cost: 1 Applied preprocessing Original rule: l8 -> l5 : a^0'=a^post6, i^0'=i^post6, tmp^0'=tmp^post6, b^0'=b^post6, n^0'=n^post6, (n^0-n^post6 == 0 /\ -1+b^post6-b^0 == 0 /\ -tmp^post6+tmp^0 == 0 /\ i^0-i^post6 == 0 /\ 1-a^0+a^post6 == 0), cost: 1 New rule: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, TRUE, cost: 1 Applied preprocessing Original rule: l9 -> l5 : a^0'=a^post7, i^0'=i^post7, tmp^0'=tmp^post7, b^0'=b^post7, n^0'=n^post7, (-b^post7+b^0 == 0 /\ i^0-i^post7 == 0 /\ tmp^0 <= 0 /\ a^0-a^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -tmp^0 <= 0 /\ -n^post7+n^0 == 0), cost: 1 New rule: l9 -> l5 : tmp^0 == 0, cost: 1 Applied preprocessing Original rule: l9 -> l8 : a^0'=a^post8, i^0'=i^post8, tmp^0'=tmp^post8, b^0'=b^post8, n^0'=n^post8, (-n^post8+n^0 == 0 /\ a^0-a^post8 == 0 /\ -b^post8+b^0 == 0 /\ i^0-i^post8 == 0 /\ 1-tmp^0 <= 0 /\ -tmp^post8+tmp^0 == 0), cost: 1 New rule: l9 -> l8 : -1+tmp^0 >= 0, cost: 1 Applied preprocessing Original rule: l9 -> l8 : a^0'=a^post9, i^0'=i^post9, tmp^0'=tmp^post9, b^0'=b^post9, n^0'=n^post9, (-n^post9+n^0 == 0 /\ tmp^0-tmp^post9 == 0 /\ 1+tmp^0 <= 0 /\ -b^post9+b^0 == 0 /\ a^0-a^post9 == 0 /\ i^0-i^post9 == 0), cost: 1 New rule: l9 -> l8 : 1+tmp^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l2 : a^0'=a^post10, i^0'=i^post10, tmp^0'=tmp^post10, b^0'=b^post10, n^0'=n^post10, (i^0 <= 0 /\ n^0-n^post10 == 0 /\ -tmp^post10+tmp^0 == 0 /\ -b^post10+b^0 == 0 /\ a^0-a^post10 == 0 /\ i^0-i^post10 == 0), cost: 1 New rule: l7 -> l2 : i^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l9 : a^0'=a^post11, i^0'=i^post11, tmp^0'=tmp^post11, b^0'=b^post11, n^0'=n^post11, (0 == 0 /\ 1-i^0 <= 0 /\ -n^post11+n^0 == 0 /\ a^0-a^post11 == 0 /\ i^0-i^post11 == 0 /\ -b^post11+b^0 == 0), cost: 1 New rule: l7 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : a^0'=a^post12, i^0'=i^post12, tmp^0'=tmp^post12, b^0'=b^post12, n^0'=n^post12, (-tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0 /\ a^0-a^post12 == 0 /\ b^0 <= 0 /\ b^0-b^post12 == 0 /\ -i^post12+i^0 == 0), cost: 1 New rule: l4 -> l3 : b^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l6 : a^0'=a^post13, i^0'=i^post13, tmp^0'=tmp^post13, b^0'=b^post13, n^0'=n^post13, (1+b^post13-b^0 == 0 /\ -n^post13+n^0 == 0 /\ a^0-a^post13 == 0 /\ 1-b^0 <= 0 /\ 1-a^0+i^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1 New rule: l4 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 1 Applied preprocessing Original rule: l10 -> l3 : a^0'=a^post14, i^0'=i^post14, tmp^0'=tmp^post14, b^0'=b^post14, n^0'=n^post14, (-n^post14+n^0 == 0 /\ a^post14-n^0 == 0 /\ -i^post14+i^0 == 0 /\ -tmp^post14+tmp^0 == 0 /\ b^post14 == 0), cost: 1 New rule: l10 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l11 -> l10 : a^0'=a^post15, i^0'=i^post15, tmp^0'=tmp^post15, b^0'=b^post15, n^0'=n^post15, (-n^post15+n^0 == 0 /\ -tmp^post15+tmp^0 == 0 /\ -b^post15+b^0 == 0 /\ a^0-a^post15 == 0 /\ i^0-i^post15 == 0), cost: 1 New rule: l11 -> l10 : TRUE, cost: 1 Simplified rules Start location: l11 16: l0 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 1 18: l2 -> l4 : TRUE, cost: 1 17: l3 -> l0 : TRUE, cost: 1 27: l4 -> l3 : b^0 <= 0, cost: 1 28: l4 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 1 19: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 20: l6 -> l7 : TRUE, cost: 1 25: l7 -> l2 : i^0 <= 0, cost: 1 26: l7 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 1 21: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, TRUE, cost: 1 22: l9 -> l5 : tmp^0 == 0, cost: 1 23: l9 -> l8 : -1+tmp^0 >= 0, cost: 1 24: l9 -> l8 : 1+tmp^0 <= 0, cost: 1 29: l10 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 1 30: l11 -> l10 : TRUE, cost: 1 Eliminating location l10 by chaining: Applied chaining First rule: l11 -> l10 : TRUE, cost: 1 Second rule: l10 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 1 New rule: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 29 30 Eliminating location l0 by chaining: Applied chaining First rule: l3 -> l0 : TRUE, cost: 1 Second rule: l0 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 1 New rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Applied deletion Removed the following rules: 16 17 Eliminated locations on linear paths Start location: l11 18: l2 -> l4 : TRUE, cost: 1 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 27: l4 -> l3 : b^0 <= 0, cost: 1 28: l4 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 1 19: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 20: l6 -> l7 : TRUE, cost: 1 25: l7 -> l2 : i^0 <= 0, cost: 1 26: l7 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 1 21: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, TRUE, cost: 1 22: l9 -> l5 : tmp^0 == 0, cost: 1 23: l9 -> l8 : -1+tmp^0 >= 0, cost: 1 24: l9 -> l8 : 1+tmp^0 <= 0, cost: 1 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Eliminating location l4 by chaining: Applied chaining First rule: l2 -> l4 : TRUE, cost: 1 Second rule: l4 -> l3 : b^0 <= 0, cost: 1 New rule: l2 -> l3 : b^0 <= 0, cost: 2 Applied chaining First rule: l2 -> l4 : TRUE, cost: 1 Second rule: l4 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 1 New rule: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 Applied deletion Removed the following rules: 18 27 28 Eliminating location l7 by chaining: Applied chaining First rule: l6 -> l7 : TRUE, cost: 1 Second rule: l7 -> l2 : i^0 <= 0, cost: 1 New rule: l6 -> l2 : i^0 <= 0, cost: 2 Applied chaining First rule: l6 -> l7 : TRUE, cost: 1 Second rule: l7 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 1 New rule: l6 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 2 Applied deletion Removed the following rules: 20 25 26 Eliminating location l8 by chaining: Applied chaining First rule: l9 -> l8 : -1+tmp^0 >= 0, cost: 1 Second rule: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, TRUE, cost: 1 New rule: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, -1+tmp^0 >= 0, cost: 2 Applied chaining First rule: l9 -> l8 : 1+tmp^0 <= 0, cost: 1 Second rule: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, TRUE, cost: 1 New rule: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, 1+tmp^0 <= 0, cost: 2 Applied deletion Removed the following rules: 21 23 24 Eliminated locations on tree-shaped paths Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 19: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 35: l6 -> l2 : i^0 <= 0, cost: 2 36: l6 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 2 22: l9 -> l5 : tmp^0 == 0, cost: 1 37: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, -1+tmp^0 >= 0, cost: 2 38: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, 1+tmp^0 <= 0, cost: 2 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Eliminating location l9 by chaining: Applied chaining First rule: l6 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 2 Second rule: l9 -> l5 : tmp^0 == 0, cost: 1 New rule: l6 -> l5 : tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 3 Applied chaining First rule: l6 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 2 Second rule: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, -1+tmp^0 >= 0, cost: 2 New rule: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 4 Applied chaining First rule: l6 -> l9 : tmp^0'=tmp^post11, -1+i^0 >= 0, cost: 2 Second rule: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, 1+tmp^0 <= 0, cost: 2 New rule: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 4 Applied deletion Removed the following rules: 22 36 37 38 Eliminated locations on tree-shaped paths Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 19: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 35: l6 -> l2 : i^0 <= 0, cost: 2 39: l6 -> l5 : tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 3 40: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 4 41: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 4 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 3 Second rule: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 New rule: l6 -> l6 : i^0'=-1+i^0, tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 4 Applied chaining First rule: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 4 Second rule: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 New rule: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5 Applied chaining First rule: l6 -> l5 : a^0'=-1+a^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 4 Second rule: l5 -> l6 : i^0'=-1+i^0, TRUE, cost: 1 New rule: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5 Applied deletion Removed the following rules: 19 39 40 41 Eliminated locations on tree-shaped paths Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 35: l6 -> l2 : i^0 <= 0, cost: 2 42: l6 -> l6 : i^0'=-1+i^0, tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 4 43: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5 44: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied simplification Original rule: l6 -> l6 : i^0'=-1+i^0, tmp^0'=tmp^post11, (-1+i^0 >= 0 /\ tmp^post11 == 0), cost: 4 New rule: l6 -> l6 : i^0'=-1+i^0, tmp^0'=0, -1+i^0 >= 0, cost: 4 Simplified simple loops Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 35: l6 -> l2 : i^0 <= 0, cost: 2 43: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5 44: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5 45: l6 -> l6 : i^0'=-1+i^0, tmp^0'=0, -1+i^0 >= 0, cost: 4 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied acceleration Original rule: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5 New rule: l6 -> l6 : a^0'=a^0-n2, i^0'=-n2+i^0, tmp^0'=tmp^post11, b^0'=n2+b^0, (-1+n2 >= 0 /\ -n2+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*n2 Applied instantiation Original rule: l6 -> l6 : a^0'=a^0-n2, i^0'=-n2+i^0, tmp^0'=tmp^post11, b^0'=n2+b^0, (-1+n2 >= 0 /\ -n2+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*n2 New rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (0 >= 0 /\ -1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*i^0 Applied acceleration Original rule: l6 -> l6 : a^0'=-1+a^0, i^0'=-1+i^0, tmp^0'=tmp^post11, b^0'=1+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5 New rule: l6 -> l6 : a^0'=a^0-n4, i^0'=i^0-n4, tmp^0'=tmp^post11, b^0'=b^0+n4, (-1-tmp^post11 >= 0 /\ -1+n4 >= 0 /\ i^0-n4 >= 0), cost: 5*n4 Applied instantiation Original rule: l6 -> l6 : a^0'=a^0-n4, i^0'=i^0-n4, tmp^0'=tmp^post11, b^0'=b^0+n4, (-1-tmp^post11 >= 0 /\ -1+n4 >= 0 /\ i^0-n4 >= 0), cost: 5*n4 New rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (0 >= 0 /\ -1-tmp^post11 >= 0 /\ -1+i^0 >= 0), cost: 5*i^0 Applied acceleration Original rule: l6 -> l6 : i^0'=-1+i^0, tmp^0'=0, -1+i^0 >= 0, cost: 4 New rule: l6 -> l6 : i^0'=-n6+i^0, tmp^0'=0, (-1+n6 >= 0 /\ -n6+i^0 >= 0), cost: 4*n6 Applied instantiation Original rule: l6 -> l6 : i^0'=-n6+i^0, tmp^0'=0, (-1+n6 >= 0 /\ -n6+i^0 >= 0), cost: 4*n6 New rule: l6 -> l6 : i^0'=0, tmp^0'=0, (0 >= 0 /\ -1+i^0 >= 0), cost: 4*i^0 Applied simplification Original rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (0 >= 0 /\ -1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*i^0 New rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*i^0 Applied simplification Original rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (0 >= 0 /\ -1-tmp^post11 >= 0 /\ -1+i^0 >= 0), cost: 5*i^0 New rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5*i^0 Applied simplification Original rule: l6 -> l6 : i^0'=0, tmp^0'=0, (0 >= 0 /\ -1+i^0 >= 0), cost: 4*i^0 New rule: l6 -> l6 : i^0'=0, tmp^0'=0, -1+i^0 >= 0, cost: 4*i^0 Applied deletion Removed the following rules: 43 44 45 Accelerated simple loops Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 35: l6 -> l2 : i^0 <= 0, cost: 2 49: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*i^0 50: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5*i^0 51: l6 -> l6 : i^0'=0, tmp^0'=0, -1+i^0 >= 0, cost: 4*i^0 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied chaining First rule: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 Second rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (-1+i^0 >= 0 /\ -1+tmp^post11 >= 0), cost: 5*i^0 New rule: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -3+5*a^0 Applied chaining First rule: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 Second rule: l6 -> l6 : a^0'=a^0-i^0, i^0'=0, tmp^0'=tmp^post11, b^0'=i^0+b^0, (1+tmp^post11 <= 0 /\ -1+i^0 >= 0), cost: 5*i^0 New rule: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -3+5*a^0 Applied chaining First rule: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 Second rule: l6 -> l6 : i^0'=0, tmp^0'=0, -1+i^0 >= 0, cost: 4*i^0 New rule: l2 -> l6 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -2+4*a^0 Applied deletion Removed the following rules: 49 50 51 Chained accelerated rules with incoming rules Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 34: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 52: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -3+5*a^0 53: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -3+5*a^0 54: l2 -> l6 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -2+4*a^0 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 35: l6 -> l2 : i^0 <= 0, cost: 2 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Eliminating location l6 by chaining: Applied chaining First rule: l2 -> l6 : i^0'=-1+a^0, b^0'=-1+b^0, -1+b^0 >= 0, cost: 2 Second rule: l6 -> l2 : i^0 <= 0, cost: 2 New rule: l2 -> l2 : i^0'=-1+a^0, b^0'=-1+b^0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4 Applied chaining First rule: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -3+5*a^0 Second rule: l6 -> l2 : i^0 <= 0, cost: 2 New rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (0 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 Applied simplification Original rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (0 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 New rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 Applied chaining First rule: l2 -> l6 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -3+5*a^0 Second rule: l6 -> l2 : i^0 <= 0, cost: 2 New rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (0 <= 0 /\ 1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 Applied simplification Original rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (0 <= 0 /\ 1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 New rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 Applied chaining First rule: l2 -> l6 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -2+4*a^0 Second rule: l6 -> l2 : i^0 <= 0, cost: 2 New rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (0 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0 Applied simplification Original rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (0 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0 New rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0 Applied deletion Removed the following rules: 34 35 52 53 54 Eliminated locations on tree-shaped paths Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 55: l2 -> l2 : i^0'=-1+a^0, b^0'=-1+b^0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4 56: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 57: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 58: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied acceleration Original rule: l2 -> l2 : i^0'=-1+a^0, b^0'=-1+b^0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4 New rule: l2 -> l2 : i^0'=-1+a^0, b^0'=-n24+b^0, (1-a^0 >= 0 /\ -1+n24 >= 0 /\ -n24+b^0 >= 0), cost: 4*n24 Applied instantiation Original rule: l2 -> l2 : i^0'=-1+a^0, b^0'=-n24+b^0, (1-a^0 >= 0 /\ -1+n24 >= 0 /\ -n24+b^0 >= 0), cost: 4*n24 New rule: l2 -> l2 : i^0'=-1+a^0, b^0'=0, (0 >= 0 /\ 1-a^0 >= 0 /\ -1+b^0 >= 0), cost: 4*b^0 Applied acceleration Original rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=-1+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0 New rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=b^0-n28, (b^0-n28 >= 0 /\ -1+n28 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*n28 Applied instantiation Original rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=b^0-n28, (b^0-n28 >= 0 /\ -1+n28 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*n28 New rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=0, (0 >= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*b^0 Applied simplification Original rule: l2 -> l2 : i^0'=-1+a^0, b^0'=0, (0 >= 0 /\ 1-a^0 >= 0 /\ -1+b^0 >= 0), cost: 4*b^0 New rule: l2 -> l2 : i^0'=-1+a^0, b^0'=0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4*b^0 Applied simplification Original rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=0, (0 >= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*b^0 New rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*b^0 Applied deletion Removed the following rules: 55 58 Accelerated simple loops Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 56: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 57: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 61: l2 -> l2 : i^0'=-1+a^0, b^0'=0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4*b^0 62: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*b^0 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Second rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-1+b^0 >= 0 /\ -2+a^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -1+5*a^0 New rule: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Second rule: l2 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -1+b^0 >= 0 /\ -2+a^0 >= 0), cost: -1+5*a^0 New rule: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Second rule: l2 -> l2 : i^0'=-1+a^0, b^0'=0, (-1+a^0 <= 0 /\ -1+b^0 >= 0), cost: 4*b^0 New rule: l3 -> l2 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 6+4*b^0 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Second rule: l2 -> l2 : i^0'=0, tmp^0'=0, b^0'=0, (-1+b^0 >= 0 /\ -2+a^0 >= 0), cost: 4*a^0*b^0 New rule: l3 -> l2 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 2+4*(-1+a^0)*(1+b^0) Applied deletion Removed the following rules: 56 57 61 62 Chained accelerated rules with incoming rules Start location: l11 33: l2 -> l3 : b^0 <= 0, cost: 2 32: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 63: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 64: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 65: l3 -> l2 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 6+4*b^0 66: l3 -> l2 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 2+4*(-1+a^0)*(1+b^0) 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Eliminating location l2 by chaining: Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, -1+a^0 >= 0, cost: 2 Second rule: l2 -> l3 : b^0 <= 0, cost: 2 New rule: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, (-1+a^0 >= 0 /\ 1+b^0 <= 0), cost: 4 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 6+4*b^0 Second rule: l2 -> l3 : b^0 <= 0, cost: 2 New rule: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (0 <= 0 /\ -1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 Applied simplification Original rule: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (0 <= 0 /\ -1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 New rule: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 Applied chaining First rule: l3 -> l2 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 2+4*(-1+a^0)*(1+b^0) Second rule: l2 -> l3 : b^0 <= 0, cost: 2 New rule: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (0 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) Applied simplification Original rule: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (0 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) New rule: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) Applied partial deletion Original rule: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 New rule: l3 -> [14] : (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 Applied partial deletion Original rule: l3 -> l2 : a^0'=1, i^0'=0, tmp^0'=tmp^post11, b^0'=-2+a^0+b^0, (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 New rule: l3 -> [14] : (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 Applied deletion Removed the following rules: 32 33 63 64 65 66 Eliminated locations on tree-shaped paths Start location: l11 67: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, (-1+a^0 >= 0 /\ 1+b^0 <= 0), cost: 4 68: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 69: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) 70: l3 -> [14] : (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 71: l3 -> [14] : (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied merging first rule: l3 -> [14] : (-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0), cost: -4+5*a^0 second rule: l3 -> [14] : (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+5*a^0 new rule: l3 -> [14] : ((-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0) \/ (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0)), cost: -4+5*a^0 Merged rules Start location: l11 67: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, (-1+a^0 >= 0 /\ 1+b^0 <= 0), cost: 4 68: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 69: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) 72: l3 -> [14] : ((-3+a^0 >= 0 /\ b^0 >= 0 /\ -1+tmp^post11 >= 0) \/ (1+tmp^post11 <= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0)), cost: -4+5*a^0 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied pruning (of leafs and parallel rules): Start location: l11 67: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, (-1+a^0 >= 0 /\ 1+b^0 <= 0), cost: 4 68: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 69: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied acceleration Original rule: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, (-1+a^0 >= 0 /\ 1+b^0 <= 0), cost: 4 New rule: l3 -> l3 : a^0'=a^0-n39, b^0'=n39+b^0, (-n39-b^0 >= 0 /\ a^0-n39 >= 0 /\ n39 >= 0), cost: 4*n39 Applied instantiation Original rule: l3 -> l3 : a^0'=a^0-n39, b^0'=n39+b^0, (-n39-b^0 >= 0 /\ a^0-n39 >= 0 /\ n39 >= 0), cost: 4*n39 New rule: l3 -> l3 : a^0'=0, b^0'=a^0+b^0, (0 >= 0 /\ a^0 >= 0 /\ -a^0-b^0 >= 0), cost: 4*a^0 Applied instantiation Original rule: l3 -> l3 : a^0'=a^0-n39, b^0'=n39+b^0, (-n39-b^0 >= 0 /\ a^0-n39 >= 0 /\ n39 >= 0), cost: 4*n39 New rule: l3 -> l3 : a^0'=a^0+b^0, b^0'=0, (0 >= 0 /\ a^0+b^0 >= 0 /\ -b^0 >= 0), cost: -4*b^0 Applied acceleration Original rule: l3 -> l3 : a^0'=-1+a^0, i^0'=-2+a^0, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8+4*b^0 New rule: l3 -> l3 : a^0'=a^0-n42, i^0'=-1+a^0-n42, b^0'=0, (2-a^0 >= 0 /\ -1+n42 >= 0 /\ b^0 >= 0 /\ a^0-n42 >= 0), cost: 8*n42 Applied instantiation Original rule: l3 -> l3 : a^0'=a^0-n42, i^0'=-1+a^0-n42, b^0'=0, (2-a^0 >= 0 /\ -1+n42 >= 0 /\ b^0 >= 0 /\ a^0-n42 >= 0), cost: 8*n42 New rule: l3 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (0 >= 0 /\ 2-a^0 >= 0 /\ -1+a^0 >= 0 /\ b^0 >= 0), cost: 8*a^0 Applied acceleration Original rule: l3 -> l3 : a^0'=-1+a^0, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: 4+4*(-1+a^0)*(1+b^0) New rule: l3 -> l3 : a^0'=a^0-n44, i^0'=0, tmp^0'=0, b^0'=0, (-2+a^0-n44 >= 0 /\ b^0 >= 0 /\ -1+n44 >= 0), cost: -2*n44^2+2*n44+4*a^0*n44 Applied instantiation Original rule: l3 -> l3 : a^0'=a^0-n44, i^0'=0, tmp^0'=0, b^0'=0, (-2+a^0-n44 >= 0 /\ b^0 >= 0 /\ -1+n44 >= 0), cost: -2*n44^2+2*n44+4*a^0*n44 New rule: l3 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, (0 >= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+2*a^0+4*a^0*(-2+a^0)-2*(-2+a^0)^2 Applied simplification Original rule: l3 -> l3 : a^0'=0, b^0'=a^0+b^0, (0 >= 0 /\ a^0 >= 0 /\ -a^0-b^0 >= 0), cost: 4*a^0 New rule: l3 -> l3 : a^0'=0, b^0'=a^0+b^0, (a^0 >= 0 /\ -a^0-b^0 >= 0), cost: 4*a^0 Applied simplification Original rule: l3 -> l3 : a^0'=a^0+b^0, b^0'=0, (0 >= 0 /\ a^0+b^0 >= 0 /\ -b^0 >= 0), cost: -4*b^0 New rule: l3 -> l3 : a^0'=a^0+b^0, b^0'=0, (a^0+b^0 >= 0 /\ b^0 <= 0), cost: -4*b^0 Applied simplification Original rule: l3 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (0 >= 0 /\ 2-a^0 >= 0 /\ -1+a^0 >= 0 /\ b^0 >= 0), cost: 8*a^0 New rule: l3 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8*a^0 Applied simplification Original rule: l3 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, (0 >= 0 /\ -3+a^0 >= 0 /\ b^0 >= 0), cost: -4+2*a^0+4*a^0*(-2+a^0)-2*(-2+a^0)^2 New rule: l3 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: -4+2*a^0+4*a^0*(-2+a^0)-2*(-2+a^0)^2 Applied deletion Removed the following rules: 67 68 69 Accelerated simple loops Start location: l11 77: l3 -> l3 : a^0'=0, b^0'=a^0+b^0, (a^0 >= 0 /\ -a^0-b^0 >= 0), cost: 4*a^0 78: l3 -> l3 : a^0'=a^0+b^0, b^0'=0, (a^0+b^0 >= 0 /\ b^0 <= 0), cost: -4*b^0 79: l3 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8*a^0 80: l3 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: -4+2*a^0+4*a^0*(-2+a^0)-2*(-2+a^0)^2 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Applied chaining First rule: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Second rule: l3 -> l3 : a^0'=0, b^0'=a^0+b^0, (a^0 >= 0 /\ -a^0-b^0 >= 0), cost: 4*a^0 New rule: l11 -> l3 : a^0'=0, b^0'=n^0, n^0 == 0, cost: 2+4*n^0 Applied chaining First rule: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Second rule: l3 -> l3 : a^0'=a^0+b^0, b^0'=0, (a^0+b^0 >= 0 /\ b^0 <= 0), cost: -4*b^0 New rule: l11 -> l3 : a^0'=n^0, b^0'=0, n^0 >= 0, cost: 2 Applied chaining First rule: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Second rule: l3 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (-1+a^0 >= 0 /\ b^0 >= 0 /\ -2+a^0 <= 0), cost: 8*a^0 New rule: l11 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (-2+n^0 <= 0 /\ -1+n^0 >= 0), cost: 2+8*n^0 Applied chaining First rule: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 Second rule: l3 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, (-3+a^0 >= 0 /\ b^0 >= 0), cost: -4+2*a^0+4*a^0*(-2+a^0)-2*(-2+a^0)^2 New rule: l11 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, -3+n^0 >= 0, cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0 Applied deletion Removed the following rules: 77 78 79 80 Chained accelerated rules with incoming rules Start location: l11 31: l11 -> l3 : a^0'=n^0, b^0'=0, TRUE, cost: 2 81: l11 -> l3 : a^0'=0, b^0'=n^0, n^0 == 0, cost: 2+4*n^0 82: l11 -> l3 : a^0'=n^0, b^0'=0, n^0 >= 0, cost: 2 83: l11 -> l3 : a^0'=0, i^0'=-1, b^0'=0, (-2+n^0 <= 0 /\ -1+n^0 >= 0), cost: 2+8*n^0 84: l11 -> l3 : a^0'=2, i^0'=0, tmp^0'=0, b^0'=0, -3+n^0 >= 0, cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0 Removed unreachable locations and irrelevant leafs Start location: l11 Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0