NO Initial ITS Start location: l10 0: l0 -> l1 : i5^0'=i5^post0, s^0'=s^post0, tmp___08^0'=tmp___08^post0, length4^0'=length4^post0, tmp^0'=tmp^post0, (tmp___08^0-tmp___08^post0 == 0 /\ -i5^0+length4^0 <= 0 /\ i5^0-i5^post0 == 0 /\ -tmp^post0+tmp^0 == 0 /\ -length4^post0+length4^0 == 0 /\ s^0-s^post0 == 0), cost: 1 1: l0 -> l2 : i5^0'=i5^post1, s^0'=s^post1, tmp___08^0'=tmp___08^post1, length4^0'=length4^post1, tmp^0'=tmp^post1, (0 == 0 /\ -1-i5^0+i5^post1 == 0 /\ length4^0-length4^post1 == 0 /\ 1+i5^0-length4^0 <= 0 /\ -tmp^post1+tmp^0 == 0 /\ -s^post1+s^0 == 0), cost: 1 7: l1 -> l7 : i5^0'=i5^post7, s^0'=s^post7, tmp___08^0'=tmp___08^post7, length4^0'=length4^post7, tmp^0'=tmp^post7, (-length4^post7+length4^0 == 0 /\ s^0-s^post7 == 0 /\ i5^0-i5^post7 == 0 /\ tmp___08^0-tmp___08^post7 == 0 /\ -tmp^post7+tmp^0 == 0), cost: 1 2: l2 -> l0 : i5^0'=i5^post2, s^0'=s^post2, tmp___08^0'=tmp___08^post2, length4^0'=length4^post2, tmp^0'=tmp^post2, (i5^0-i5^post2 == 0 /\ -length4^post2+length4^0 == 0 /\ -tmp___08^post2+tmp___08^0 == 0 /\ s^0-s^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1 3: l3 -> l4 : i5^0'=i5^post3, s^0'=s^post3, tmp___08^0'=tmp___08^post3, length4^0'=length4^post3, tmp^0'=tmp^post3, (-tmp^post3+tmp^0 == 0 /\ tmp___08^0-tmp___08^post3 == 0 /\ length4^0-length4^post3 == 0 /\ s^0-s^post3 == 0 /\ i5^0-i5^post3 == 0), cost: 1 12: l4 -> l5 : i5^0'=i5^post12, s^0'=s^post12, tmp___08^0'=tmp___08^post12, length4^0'=length4^post12, tmp^0'=tmp^post12, (-tmp___08^post12+tmp___08^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i5^0-i5^post12 == 0 /\ length4^0-length4^post12 == 0 /\ -s^post12+s^0 == 0), cost: 1 4: l5 -> l3 : i5^0'=i5^post4, s^0'=s^post4, tmp___08^0'=tmp___08^post4, length4^0'=length4^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___08^post4+tmp___08^0 == 0 /\ -length4^post4+length4^0 == 0 /\ i5^0-i5^post4 == 0 /\ s^0-s^post4 == 0), cost: 1 5: l5 -> l6 : i5^0'=i5^post5, s^0'=s^post5, tmp___08^0'=tmp___08^post5, length4^0'=length4^post5, tmp^0'=tmp^post5, (-tmp^post5+tmp^0 == 0 /\ tmp___08^0-tmp___08^post5 == 0 /\ i5^0-i5^post5 == 0 /\ -length4^post5+length4^0 == 0 /\ s^0-s^post5 == 0), cost: 1 6: l5 -> l3 : i5^0'=i5^post6, s^0'=s^post6, tmp___08^0'=tmp___08^post6, length4^0'=length4^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -tmp___08^post6+tmp___08^0 == 0 /\ i5^0-i5^post6 == 0 /\ s^0-s^post6 == 0 /\ -length4^post6+length4^0 == 0), cost: 1 9: l7 -> l8 : i5^0'=i5^post9, s^0'=s^post9, tmp___08^0'=tmp___08^post9, length4^0'=length4^post9, tmp^0'=tmp^post9, (-tmp^post9+tmp^0 == 0 /\ tmp___08^0-tmp___08^post9 == 0 /\ -length4^post9+length4^0 == 0 /\ i5^0-i5^post9 == 0 /\ s^0-s^post9 == 0), cost: 1 10: l7 -> l8 : i5^0'=i5^post10, s^0'=s^post10, tmp___08^0'=tmp___08^post10, length4^0'=length4^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___08^post10+tmp___08^0 == 0 /\ -length4^post10+length4^0 == 0 /\ i5^0-i5^post10 == 0 /\ s^0-s^post10 == 0), cost: 1 11: l7 -> l4 : i5^0'=i5^post11, s^0'=s^post11, tmp___08^0'=tmp___08^post11, length4^0'=length4^post11, tmp^0'=tmp^post11, (tmp___08^0-tmp___08^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i5^0-i5^post11 == 0 /\ s^0-s^post11 == 0 /\ -length4^post11+length4^0 == 0), cost: 1 8: l8 -> l1 : i5^0'=i5^post8, s^0'=s^post8, tmp___08^0'=tmp___08^post8, length4^0'=length4^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i5^0-i5^post8 == 0 /\ -length4^post8+length4^0 == 0 /\ s^0-s^post8 == 0 /\ -tmp___08^post8+tmp___08^0 == 0), cost: 1 13: l9 -> l2 : i5^0'=i5^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post13, length4^0'=length4^post13, tmp^0'=tmp^post13, (0 == 0 /\ length4^post13-s^post13 == 0 /\ i5^post13 == 0 /\ -tmp^post13+s^post13 == 0 /\ tmp___08^0-tmp___08^post13 == 0), cost: 1 14: l10 -> l9 : i5^0'=i5^post14, s^0'=s^post14, tmp___08^0'=tmp___08^post14, length4^0'=length4^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i5^0-i5^post14 == 0 /\ length4^0-length4^post14 == 0 /\ -s^post14+s^0 == 0 /\ -tmp___08^post14+tmp___08^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l10 0: l0 -> l1 : i5^0'=i5^post0, s^0'=s^post0, tmp___08^0'=tmp___08^post0, length4^0'=length4^post0, tmp^0'=tmp^post0, (tmp___08^0-tmp___08^post0 == 0 /\ -i5^0+length4^0 <= 0 /\ i5^0-i5^post0 == 0 /\ -tmp^post0+tmp^0 == 0 /\ -length4^post0+length4^0 == 0 /\ s^0-s^post0 == 0), cost: 1 1: l0 -> l2 : i5^0'=i5^post1, s^0'=s^post1, tmp___08^0'=tmp___08^post1, length4^0'=length4^post1, tmp^0'=tmp^post1, (0 == 0 /\ -1-i5^0+i5^post1 == 0 /\ length4^0-length4^post1 == 0 /\ 1+i5^0-length4^0 <= 0 /\ -tmp^post1+tmp^0 == 0 /\ -s^post1+s^0 == 0), cost: 1 7: l1 -> l7 : i5^0'=i5^post7, s^0'=s^post7, tmp___08^0'=tmp___08^post7, length4^0'=length4^post7, tmp^0'=tmp^post7, (-length4^post7+length4^0 == 0 /\ s^0-s^post7 == 0 /\ i5^0-i5^post7 == 0 /\ tmp___08^0-tmp___08^post7 == 0 /\ -tmp^post7+tmp^0 == 0), cost: 1 2: l2 -> l0 : i5^0'=i5^post2, s^0'=s^post2, tmp___08^0'=tmp___08^post2, length4^0'=length4^post2, tmp^0'=tmp^post2, (i5^0-i5^post2 == 0 /\ -length4^post2+length4^0 == 0 /\ -tmp___08^post2+tmp___08^0 == 0 /\ s^0-s^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1 3: l3 -> l4 : i5^0'=i5^post3, s^0'=s^post3, tmp___08^0'=tmp___08^post3, length4^0'=length4^post3, tmp^0'=tmp^post3, (-tmp^post3+tmp^0 == 0 /\ tmp___08^0-tmp___08^post3 == 0 /\ length4^0-length4^post3 == 0 /\ s^0-s^post3 == 0 /\ i5^0-i5^post3 == 0), cost: 1 12: l4 -> l5 : i5^0'=i5^post12, s^0'=s^post12, tmp___08^0'=tmp___08^post12, length4^0'=length4^post12, tmp^0'=tmp^post12, (-tmp___08^post12+tmp___08^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i5^0-i5^post12 == 0 /\ length4^0-length4^post12 == 0 /\ -s^post12+s^0 == 0), cost: 1 4: l5 -> l3 : i5^0'=i5^post4, s^0'=s^post4, tmp___08^0'=tmp___08^post4, length4^0'=length4^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___08^post4+tmp___08^0 == 0 /\ -length4^post4+length4^0 == 0 /\ i5^0-i5^post4 == 0 /\ s^0-s^post4 == 0), cost: 1 6: l5 -> l3 : i5^0'=i5^post6, s^0'=s^post6, tmp___08^0'=tmp___08^post6, length4^0'=length4^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -tmp___08^post6+tmp___08^0 == 0 /\ i5^0-i5^post6 == 0 /\ s^0-s^post6 == 0 /\ -length4^post6+length4^0 == 0), cost: 1 9: l7 -> l8 : i5^0'=i5^post9, s^0'=s^post9, tmp___08^0'=tmp___08^post9, length4^0'=length4^post9, tmp^0'=tmp^post9, (-tmp^post9+tmp^0 == 0 /\ tmp___08^0-tmp___08^post9 == 0 /\ -length4^post9+length4^0 == 0 /\ i5^0-i5^post9 == 0 /\ s^0-s^post9 == 0), cost: 1 10: l7 -> l8 : i5^0'=i5^post10, s^0'=s^post10, tmp___08^0'=tmp___08^post10, length4^0'=length4^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___08^post10+tmp___08^0 == 0 /\ -length4^post10+length4^0 == 0 /\ i5^0-i5^post10 == 0 /\ s^0-s^post10 == 0), cost: 1 11: l7 -> l4 : i5^0'=i5^post11, s^0'=s^post11, tmp___08^0'=tmp___08^post11, length4^0'=length4^post11, tmp^0'=tmp^post11, (tmp___08^0-tmp___08^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i5^0-i5^post11 == 0 /\ s^0-s^post11 == 0 /\ -length4^post11+length4^0 == 0), cost: 1 8: l8 -> l1 : i5^0'=i5^post8, s^0'=s^post8, tmp___08^0'=tmp___08^post8, length4^0'=length4^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i5^0-i5^post8 == 0 /\ -length4^post8+length4^0 == 0 /\ s^0-s^post8 == 0 /\ -tmp___08^post8+tmp___08^0 == 0), cost: 1 13: l9 -> l2 : i5^0'=i5^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post13, length4^0'=length4^post13, tmp^0'=tmp^post13, (0 == 0 /\ length4^post13-s^post13 == 0 /\ i5^post13 == 0 /\ -tmp^post13+s^post13 == 0 /\ tmp___08^0-tmp___08^post13 == 0), cost: 1 14: l10 -> l9 : i5^0'=i5^post14, s^0'=s^post14, tmp___08^0'=tmp___08^post14, length4^0'=length4^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i5^0-i5^post14 == 0 /\ length4^0-length4^post14 == 0 /\ -s^post14+s^0 == 0 /\ -tmp___08^post14+tmp___08^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : i5^0'=i5^post0, s^0'=s^post0, tmp___08^0'=tmp___08^post0, length4^0'=length4^post0, tmp^0'=tmp^post0, (tmp___08^0-tmp___08^post0 == 0 /\ -i5^0+length4^0 <= 0 /\ i5^0-i5^post0 == 0 /\ -tmp^post0+tmp^0 == 0 /\ -length4^post0+length4^0 == 0 /\ s^0-s^post0 == 0), cost: 1 New rule: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 Applied preprocessing Original rule: l0 -> l2 : i5^0'=i5^post1, s^0'=s^post1, tmp___08^0'=tmp___08^post1, length4^0'=length4^post1, tmp^0'=tmp^post1, (0 == 0 /\ -1-i5^0+i5^post1 == 0 /\ length4^0-length4^post1 == 0 /\ 1+i5^0-length4^0 <= 0 /\ -tmp^post1+tmp^0 == 0 /\ -s^post1+s^0 == 0), cost: 1 New rule: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : i5^0'=i5^post2, s^0'=s^post2, tmp___08^0'=tmp___08^post2, length4^0'=length4^post2, tmp^0'=tmp^post2, (i5^0-i5^post2 == 0 /\ -length4^post2+length4^0 == 0 /\ -tmp___08^post2+tmp___08^0 == 0 /\ s^0-s^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l4 : i5^0'=i5^post3, s^0'=s^post3, tmp___08^0'=tmp___08^post3, length4^0'=length4^post3, tmp^0'=tmp^post3, (-tmp^post3+tmp^0 == 0 /\ tmp___08^0-tmp___08^post3 == 0 /\ length4^0-length4^post3 == 0 /\ s^0-s^post3 == 0 /\ i5^0-i5^post3 == 0), cost: 1 New rule: l3 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l3 : i5^0'=i5^post4, s^0'=s^post4, tmp___08^0'=tmp___08^post4, length4^0'=length4^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___08^post4+tmp___08^0 == 0 /\ -length4^post4+length4^0 == 0 /\ i5^0-i5^post4 == 0 /\ s^0-s^post4 == 0), cost: 1 New rule: l5 -> l3 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l3 : i5^0'=i5^post6, s^0'=s^post6, tmp___08^0'=tmp___08^post6, length4^0'=length4^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -tmp___08^post6+tmp___08^0 == 0 /\ i5^0-i5^post6 == 0 /\ s^0-s^post6 == 0 /\ -length4^post6+length4^0 == 0), cost: 1 New rule: l5 -> l3 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l7 : i5^0'=i5^post7, s^0'=s^post7, tmp___08^0'=tmp___08^post7, length4^0'=length4^post7, tmp^0'=tmp^post7, (-length4^post7+length4^0 == 0 /\ s^0-s^post7 == 0 /\ i5^0-i5^post7 == 0 /\ tmp___08^0-tmp___08^post7 == 0 /\ -tmp^post7+tmp^0 == 0), cost: 1 New rule: l1 -> l7 : TRUE, cost: 1 Applied preprocessing Original rule: l8 -> l1 : i5^0'=i5^post8, s^0'=s^post8, tmp___08^0'=tmp___08^post8, length4^0'=length4^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i5^0-i5^post8 == 0 /\ -length4^post8+length4^0 == 0 /\ s^0-s^post8 == 0 /\ -tmp___08^post8+tmp___08^0 == 0), cost: 1 New rule: l8 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l8 : i5^0'=i5^post9, s^0'=s^post9, tmp___08^0'=tmp___08^post9, length4^0'=length4^post9, tmp^0'=tmp^post9, (-tmp^post9+tmp^0 == 0 /\ tmp___08^0-tmp___08^post9 == 0 /\ -length4^post9+length4^0 == 0 /\ i5^0-i5^post9 == 0 /\ s^0-s^post9 == 0), cost: 1 New rule: l7 -> l8 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l8 : i5^0'=i5^post10, s^0'=s^post10, tmp___08^0'=tmp___08^post10, length4^0'=length4^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___08^post10+tmp___08^0 == 0 /\ -length4^post10+length4^0 == 0 /\ i5^0-i5^post10 == 0 /\ s^0-s^post10 == 0), cost: 1 New rule: l7 -> l8 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l4 : i5^0'=i5^post11, s^0'=s^post11, tmp___08^0'=tmp___08^post11, length4^0'=length4^post11, tmp^0'=tmp^post11, (tmp___08^0-tmp___08^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i5^0-i5^post11 == 0 /\ s^0-s^post11 == 0 /\ -length4^post11+length4^0 == 0), cost: 1 New rule: l7 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l5 : i5^0'=i5^post12, s^0'=s^post12, tmp___08^0'=tmp___08^post12, length4^0'=length4^post12, tmp^0'=tmp^post12, (-tmp___08^post12+tmp___08^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i5^0-i5^post12 == 0 /\ length4^0-length4^post12 == 0 /\ -s^post12+s^0 == 0), cost: 1 New rule: l4 -> l5 : TRUE, cost: 1 Applied preprocessing Original rule: l9 -> l2 : i5^0'=i5^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post13, length4^0'=length4^post13, tmp^0'=tmp^post13, (0 == 0 /\ length4^post13-s^post13 == 0 /\ i5^post13 == 0 /\ -tmp^post13+s^post13 == 0 /\ tmp___08^0-tmp___08^post13 == 0), cost: 1 New rule: l9 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 1 Applied preprocessing Original rule: l10 -> l9 : i5^0'=i5^post14, s^0'=s^post14, tmp___08^0'=tmp___08^post14, length4^0'=length4^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i5^0-i5^post14 == 0 /\ length4^0-length4^post14 == 0 /\ -s^post14+s^0 == 0 /\ -tmp___08^post14+tmp___08^0 == 0), cost: 1 New rule: l10 -> l9 : TRUE, cost: 1 Applied deletion Removed the following rules: 19 23 Simplified rules Start location: l10 15: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 16: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 21: l1 -> l7 : TRUE, cost: 1 17: l2 -> l0 : TRUE, cost: 1 18: l3 -> l4 : TRUE, cost: 1 26: l4 -> l5 : TRUE, cost: 1 20: l5 -> l3 : TRUE, cost: 1 24: l7 -> l8 : TRUE, cost: 1 25: l7 -> l4 : TRUE, cost: 1 22: l8 -> l1 : TRUE, cost: 1 27: l9 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 1 28: l10 -> l9 : TRUE, cost: 1 Eliminating location l9 by chaining: Applied chaining First rule: l10 -> l9 : TRUE, cost: 1 Second rule: l9 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 1 New rule: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Applied deletion Removed the following rules: 27 28 Eliminating location l8 by chaining: Applied chaining First rule: l7 -> l8 : TRUE, cost: 1 Second rule: l8 -> l1 : TRUE, cost: 1 New rule: l7 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 22 24 Eliminating location l5 by chaining: Applied chaining First rule: l4 -> l5 : TRUE, cost: 1 Second rule: l5 -> l3 : TRUE, cost: 1 New rule: l4 -> l3 : TRUE, cost: 2 Applied deletion Removed the following rules: 20 26 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : TRUE, cost: 2 Second rule: l3 -> l4 : TRUE, cost: 1 New rule: l4 -> l4 : TRUE, cost: 3 Applied deletion Removed the following rules: 18 31 Eliminated locations on linear paths Start location: l10 15: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 16: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 21: l1 -> l7 : TRUE, cost: 1 17: l2 -> l0 : TRUE, cost: 1 32: l4 -> l4 : TRUE, cost: 3 25: l7 -> l4 : TRUE, cost: 1 30: l7 -> l1 : TRUE, cost: 2 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Applied nonterm Original rule: l4 -> l4 : TRUE, cost: 3 New rule: l4 -> [11] : TRUE, cost: NONTERM Applied acceleration Original rule: l4 -> l4 : TRUE, cost: 3 New rule: l4 -> l4 : TRUE, cost: 3*n0 Applied deletion Removed the following rules: 32 Accelerated simple loops Start location: l10 15: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 16: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 21: l1 -> l7 : TRUE, cost: 1 17: l2 -> l0 : TRUE, cost: 1 33: l4 -> [11] : TRUE, cost: NONTERM 34: l4 -> l4 : TRUE, cost: 3*n0 25: l7 -> l4 : TRUE, cost: 1 30: l7 -> l1 : TRUE, cost: 2 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Applied chaining First rule: l7 -> l4 : TRUE, cost: 1 Second rule: l4 -> [11] : TRUE, cost: NONTERM New rule: l7 -> [11] : TRUE, cost: NONTERM Applied chaining First rule: l7 -> l4 : TRUE, cost: 1 Second rule: l4 -> l4 : TRUE, cost: 3*n0 New rule: l7 -> l4 : TRUE, cost: 1+3*n0 Applied deletion Removed the following rules: 33 34 Chained accelerated rules with incoming rules Start location: l10 15: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 16: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 21: l1 -> l7 : TRUE, cost: 1 17: l2 -> l0 : TRUE, cost: 1 25: l7 -> l4 : TRUE, cost: 1 30: l7 -> l1 : TRUE, cost: 2 35: l7 -> [11] : TRUE, cost: NONTERM 36: l7 -> l4 : TRUE, cost: 1+3*n0 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Removed unreachable locations and irrelevant leafs Start location: l10 15: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 16: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 21: l1 -> l7 : TRUE, cost: 1 17: l2 -> l0 : TRUE, cost: 1 30: l7 -> l1 : TRUE, cost: 2 35: l7 -> [11] : TRUE, cost: NONTERM 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Eliminating location l0 by chaining: Applied chaining First rule: l2 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : -i5^0+length4^0 <= 0, cost: 1 New rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 Applied chaining First rule: l2 -> l0 : TRUE, cost: 1 Second rule: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 1 New rule: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 2 Applied deletion Removed the following rules: 15 16 17 Eliminating location l7 by chaining: Applied chaining First rule: l1 -> l7 : TRUE, cost: 1 Second rule: l7 -> l1 : TRUE, cost: 2 New rule: l1 -> l1 : TRUE, cost: 3 Applied chaining First rule: l1 -> l7 : TRUE, cost: 1 Second rule: l7 -> [11] : TRUE, cost: NONTERM New rule: l1 -> [11] : TRUE, cost: NONTERM Applied deletion Removed the following rules: 21 30 35 Eliminated locations on tree-shaped paths Start location: l10 39: l1 -> l1 : TRUE, cost: 3 40: l1 -> [11] : TRUE, cost: NONTERM 37: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 38: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 2 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Applied nonterm Original rule: l1 -> l1 : TRUE, cost: 3 New rule: l1 -> [12] : TRUE, cost: NONTERM Applied acceleration Original rule: l1 -> l1 : TRUE, cost: 3 New rule: l1 -> l1 : TRUE, cost: 3*n3 Applied deletion Removed the following rules: 39 Applied acceleration Original rule: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post1, 1+i5^0-length4^0 <= 0, cost: 2 New rule: l2 -> l2 : i5^0'=i5^0+n6, tmp___08^0'=tmp___08^post1, (-i5^0-n6+length4^0 >= 0 /\ -1+n6 >= 0), cost: 2*n6 Applied instantiation Original rule: l2 -> l2 : i5^0'=i5^0+n6, tmp___08^0'=tmp___08^post1, (-i5^0-n6+length4^0 >= 0 /\ -1+n6 >= 0), cost: 2*n6 New rule: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post1, (0 >= 0 /\ -1-i5^0+length4^0 >= 0), cost: -2*i5^0+2*length4^0 Applied simplification Original rule: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post1, (0 >= 0 /\ -1-i5^0+length4^0 >= 0), cost: -2*i5^0+2*length4^0 New rule: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post1, -1-i5^0+length4^0 >= 0, cost: -2*i5^0+2*length4^0 Applied deletion Removed the following rules: 38 Accelerated simple loops Start location: l10 40: l1 -> [11] : TRUE, cost: NONTERM 41: l1 -> [12] : TRUE, cost: NONTERM 42: l1 -> l1 : TRUE, cost: 3*n3 37: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 44: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post1, -1-i5^0+length4^0 >= 0, cost: -2*i5^0+2*length4^0 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Applied chaining First rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 Second rule: l1 -> [12] : TRUE, cost: NONTERM New rule: l2 -> [12] : -i5^0+length4^0 <= 0, cost: NONTERM Applied chaining First rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 Second rule: l1 -> l1 : TRUE, cost: 3*n3 New rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2+3*n3 Applied deletion Removed the following rules: 41 42 Applied chaining First rule: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Second rule: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post1, -1-i5^0+length4^0 >= 0, cost: -2*i5^0+2*length4^0 New rule: l10 -> l2 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 2+2*s^post13 Applied deletion Removed the following rules: 44 Chained accelerated rules with incoming rules Start location: l10 40: l1 -> [11] : TRUE, cost: NONTERM 37: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 45: l2 -> [12] : -i5^0+length4^0 <= 0, cost: NONTERM 46: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2+3*n3 29: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 47: l10 -> l2 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 2+2*s^post13 Eliminating location l2 by chaining: Applied chaining First rule: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Second rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 New rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, (0 == 0 /\ s^post13 <= 0), cost: 4 Applied simplification Original rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, (0 == 0 /\ s^post13 <= 0), cost: 4 New rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4 Applied chaining First rule: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Second rule: l2 -> [12] : -i5^0+length4^0 <= 0, cost: NONTERM New rule: l10 -> [12] : (0 == 0 /\ s^post13 <= 0), cost: NONTERM Applied simplification Original rule: l10 -> [12] : (0 == 0 /\ s^post13 <= 0), cost: NONTERM New rule: l10 -> [12] : s^post13 <= 0, cost: NONTERM Applied chaining First rule: l10 -> l2 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, 0 == 0, cost: 2 Second rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2+3*n3 New rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, (0 == 0 /\ s^post13 <= 0), cost: 4+3*n3 Applied simplification Original rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, (0 == 0 /\ s^post13 <= 0), cost: 4+3*n3 New rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4+3*n3 Applied chaining First rule: l10 -> l2 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 2+2*s^post13 Second rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2 New rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, (0 <= 0 /\ -1+s^post13 >= 0), cost: 4+2*s^post13 Applied simplification Original rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, (0 <= 0 /\ -1+s^post13 >= 0), cost: 4+2*s^post13 New rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13 Applied chaining First rule: l10 -> l2 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 2+2*s^post13 Second rule: l2 -> [12] : -i5^0+length4^0 <= 0, cost: NONTERM New rule: l10 -> [12] : (0 <= 0 /\ -1+s^post13 >= 0), cost: NONTERM Applied simplification Original rule: l10 -> [12] : (0 <= 0 /\ -1+s^post13 >= 0), cost: NONTERM New rule: l10 -> [12] : -1+s^post13 >= 0, cost: NONTERM Applied chaining First rule: l10 -> l2 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 2+2*s^post13 Second rule: l2 -> l1 : -i5^0+length4^0 <= 0, cost: 2+3*n3 New rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, (0 <= 0 /\ -1+s^post13 >= 0), cost: 4+2*s^post13+3*n3 Applied simplification Original rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, (0 <= 0 /\ -1+s^post13 >= 0), cost: 4+2*s^post13+3*n3 New rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13+3*n3 Applied deletion Removed the following rules: 29 37 45 46 47 Eliminated locations on tree-shaped paths Start location: l10 40: l1 -> [11] : TRUE, cost: NONTERM 48: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4 49: l10 -> [12] : s^post13 <= 0, cost: NONTERM 50: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4+3*n3 51: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13 52: l10 -> [12] : -1+s^post13 >= 0, cost: NONTERM 53: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13+3*n3 Applied merging first rule: l10 -> [12] : s^post13 <= 0, cost: NONTERM second rule: l10 -> [12] : -1+s^post13 >= 0, cost: NONTERM new rule: l10 -> [12] : (-1+s^post13 >= 0 \/ s^post13 <= 0), cost: NONTERM Merged rules Start location: l10 40: l1 -> [11] : TRUE, cost: NONTERM 48: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4 50: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4+3*n3 51: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13 53: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13+3*n3 54: l10 -> [12] : (-1+s^post13 >= 0 \/ s^post13 <= 0), cost: NONTERM Eliminating location l1 by chaining: Applied chaining First rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4 Second rule: l1 -> [11] : TRUE, cost: NONTERM New rule: l10 -> [11] : s^post13 <= 0, cost: NONTERM Applied chaining First rule: l10 -> l1 : i5^0'=0, s^0'=s^post13, length4^0'=s^post13, tmp^0'=s^post13, s^post13 <= 0, cost: 4+3*n3 Second rule: l1 -> [11] : TRUE, cost: NONTERM New rule: l10 -> [11] : s^post13 <= 0, cost: NONTERM Applied chaining First rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13 Second rule: l1 -> [11] : TRUE, cost: NONTERM New rule: l10 -> [11] : -1+s^post13 >= 0, cost: NONTERM Applied chaining First rule: l10 -> l1 : i5^0'=s^post13, s^0'=s^post13, tmp___08^0'=tmp___08^post1, length4^0'=s^post13, tmp^0'=s^post13, -1+s^post13 >= 0, cost: 4+2*s^post13+3*n3 Second rule: l1 -> [11] : TRUE, cost: NONTERM New rule: l10 -> [11] : -1+s^post13 >= 0, cost: NONTERM Applied deletion Removed the following rules: 40 48 50 51 53 Eliminated locations on tree-shaped paths Start location: l10 54: l10 -> [12] : (-1+s^post13 >= 0 \/ s^post13 <= 0), cost: NONTERM 55: l10 -> [11] : s^post13 <= 0, cost: NONTERM 56: l10 -> [11] : s^post13 <= 0, cost: NONTERM 57: l10 -> [11] : -1+s^post13 >= 0, cost: NONTERM 58: l10 -> [11] : -1+s^post13 >= 0, cost: NONTERM Removed duplicate rules (ignoring updates) Start location: l10 54: l10 -> [12] : (-1+s^post13 >= 0 \/ s^post13 <= 0), cost: NONTERM 56: l10 -> [11] : s^post13 <= 0, cost: NONTERM 58: l10 -> [11] : -1+s^post13 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 54 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+s^post13 >= 0 \/ s^post13 <= 0)