NO Initial ITS Start location: l10 0: l0 -> l1 : tmp1^0'=tmp1^post0, Stored^0'=Stored^post0, tmp___02^0'=tmp___02^post0, (tmp1^0 <= 0 /\ tmp___02^0-tmp___02^post0 == 0 /\ -tmp1^0 <= 0 /\ -1+Stored^post0 == 0 /\ tmp1^0-tmp1^post0 == 0), cost: 1 1: l0 -> l2 : tmp1^0'=tmp1^post1, Stored^0'=Stored^post1, tmp___02^0'=tmp___02^post1, (tmp___02^0-tmp___02^post1 == 0 /\ Stored^0-Stored^post1 == 0 /\ 1-tmp1^0 <= 0 /\ tmp1^0-tmp1^post1 == 0), cost: 1 2: l0 -> l2 : tmp1^0'=tmp1^post2, Stored^0'=Stored^post2, tmp___02^0'=tmp___02^post2, (tmp___02^0-tmp___02^post2 == 0 /\ tmp1^0-tmp1^post2 == 0 /\ 1+tmp1^0 <= 0 /\ -Stored^post2+Stored^0 == 0), cost: 1 9: l1 -> l8 : tmp1^0'=tmp1^post9, Stored^0'=Stored^post9, tmp___02^0'=tmp___02^post9, (tmp1^0-tmp1^post9 == 0 /\ Stored^0-Stored^post9 == 0 /\ -tmp___02^post9+tmp___02^0 == 0), cost: 1 13: l2 -> l7 : tmp1^0'=tmp1^post13, Stored^0'=Stored^post13, tmp___02^0'=tmp___02^post13, (-tmp___02^post13+tmp___02^0 == 0 /\ Stored^0-Stored^post13 == 0 /\ tmp1^0-tmp1^post13 == 0), cost: 1 3: l3 -> l0 : tmp1^0'=tmp1^post3, Stored^0'=Stored^post3, tmp___02^0'=tmp___02^post3, (0 == 0 /\ -Stored^post3+Stored^0 == 0 /\ -tmp___02^post3+tmp___02^0 == 0), cost: 1 4: l4 -> l1 : tmp1^0'=tmp1^post4, Stored^0'=Stored^post4, tmp___02^0'=tmp___02^post4, (-tmp___02^0 <= 0 /\ -Stored^post4+Stored^0 == 0 /\ -tmp___02^post4+tmp___02^0 == 0 /\ -tmp1^post4+tmp1^0 == 0 /\ tmp___02^0 <= 0), cost: 1 5: l4 -> l3 : tmp1^0'=tmp1^post5, Stored^0'=Stored^post5, tmp___02^0'=tmp___02^post5, (-Stored^post5+Stored^0 == 0 /\ -tmp___02^post5+tmp___02^0 == 0 /\ 1-tmp___02^0 <= 0 /\ -tmp1^post5+tmp1^0 == 0), cost: 1 6: l4 -> l3 : tmp1^0'=tmp1^post6, Stored^0'=Stored^post6, tmp___02^0'=tmp___02^post6, (-Stored^post6+Stored^0 == 0 /\ tmp1^0-tmp1^post6 == 0 /\ -tmp___02^post6+tmp___02^0 == 0 /\ 1+tmp___02^0 <= 0), cost: 1 7: l5 -> l6 : tmp1^0'=tmp1^post7, Stored^0'=Stored^post7, tmp___02^0'=tmp___02^post7, (-tmp___02^post7+tmp___02^0 == 0 /\ -Stored^post7+Stored^0 == 0 /\ tmp1^0-tmp1^post7 == 0), cost: 1 8: l7 -> l4 : tmp1^0'=tmp1^post8, Stored^0'=Stored^post8, tmp___02^0'=tmp___02^post8, (0 == 0 /\ Stored^0-Stored^post8 == 0 /\ tmp1^0-tmp1^post8 == 0), cost: 1 10: l8 -> l5 : tmp1^0'=tmp1^post10, Stored^0'=Stored^post10, tmp___02^0'=tmp___02^post10, (Stored^0-Stored^post10 == 0 /\ tmp1^0-tmp1^post10 == 0 /\ -tmp___02^post10+tmp___02^0 == 0 /\ 2-Stored^0 <= 0), cost: 1 11: l8 -> l5 : tmp1^0'=tmp1^post11, Stored^0'=Stored^post11, tmp___02^0'=tmp___02^post11, (tmp1^0-tmp1^post11 == 0 /\ Stored^0-Stored^post11 == 0 /\ Stored^0 <= 0 /\ -tmp___02^post11+tmp___02^0 == 0), cost: 1 12: l8 -> l5 : tmp1^0'=tmp1^post12, Stored^0'=Stored^post12, tmp___02^0'=tmp___02^post12, (-tmp___02^post12+tmp___02^0 == 0 /\ tmp1^0-tmp1^post12 == 0 /\ Stored^post12 == 0 /\ 1-Stored^0 <= 0 /\ -1+Stored^0 <= 0), cost: 1 14: l9 -> l7 : tmp1^0'=tmp1^post14, Stored^0'=Stored^post14, tmp___02^0'=tmp___02^post14, (tmp___02^0-tmp___02^post14 == 0 /\ tmp1^0-tmp1^post14 == 0 /\ Stored^post14 == 0), cost: 1 15: l10 -> l9 : tmp1^0'=tmp1^post15, Stored^0'=Stored^post15, tmp___02^0'=tmp___02^post15, (tmp___02^0-tmp___02^post15 == 0 /\ Stored^0-Stored^post15 == 0 /\ tmp1^0-tmp1^post15 == 0), cost: 1 Removed unreachable rules and leafs Start location: l10 1: l0 -> l2 : tmp1^0'=tmp1^post1, Stored^0'=Stored^post1, tmp___02^0'=tmp___02^post1, (tmp___02^0-tmp___02^post1 == 0 /\ Stored^0-Stored^post1 == 0 /\ 1-tmp1^0 <= 0 /\ tmp1^0-tmp1^post1 == 0), cost: 1 2: l0 -> l2 : tmp1^0'=tmp1^post2, Stored^0'=Stored^post2, tmp___02^0'=tmp___02^post2, (tmp___02^0-tmp___02^post2 == 0 /\ tmp1^0-tmp1^post2 == 0 /\ 1+tmp1^0 <= 0 /\ -Stored^post2+Stored^0 == 0), cost: 1 13: l2 -> l7 : tmp1^0'=tmp1^post13, Stored^0'=Stored^post13, tmp___02^0'=tmp___02^post13, (-tmp___02^post13+tmp___02^0 == 0 /\ Stored^0-Stored^post13 == 0 /\ tmp1^0-tmp1^post13 == 0), cost: 1 3: l3 -> l0 : tmp1^0'=tmp1^post3, Stored^0'=Stored^post3, tmp___02^0'=tmp___02^post3, (0 == 0 /\ -Stored^post3+Stored^0 == 0 /\ -tmp___02^post3+tmp___02^0 == 0), cost: 1 5: l4 -> l3 : tmp1^0'=tmp1^post5, Stored^0'=Stored^post5, tmp___02^0'=tmp___02^post5, (-Stored^post5+Stored^0 == 0 /\ -tmp___02^post5+tmp___02^0 == 0 /\ 1-tmp___02^0 <= 0 /\ -tmp1^post5+tmp1^0 == 0), cost: 1 6: l4 -> l3 : tmp1^0'=tmp1^post6, Stored^0'=Stored^post6, tmp___02^0'=tmp___02^post6, (-Stored^post6+Stored^0 == 0 /\ tmp1^0-tmp1^post6 == 0 /\ -tmp___02^post6+tmp___02^0 == 0 /\ 1+tmp___02^0 <= 0), cost: 1 8: l7 -> l4 : tmp1^0'=tmp1^post8, Stored^0'=Stored^post8, tmp___02^0'=tmp___02^post8, (0 == 0 /\ Stored^0-Stored^post8 == 0 /\ tmp1^0-tmp1^post8 == 0), cost: 1 14: l9 -> l7 : tmp1^0'=tmp1^post14, Stored^0'=Stored^post14, tmp___02^0'=tmp___02^post14, (tmp___02^0-tmp___02^post14 == 0 /\ tmp1^0-tmp1^post14 == 0 /\ Stored^post14 == 0), cost: 1 15: l10 -> l9 : tmp1^0'=tmp1^post15, Stored^0'=Stored^post15, tmp___02^0'=tmp___02^post15, (tmp___02^0-tmp___02^post15 == 0 /\ Stored^0-Stored^post15 == 0 /\ tmp1^0-tmp1^post15 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : tmp1^0'=tmp1^post1, Stored^0'=Stored^post1, tmp___02^0'=tmp___02^post1, (tmp___02^0-tmp___02^post1 == 0 /\ Stored^0-Stored^post1 == 0 /\ 1-tmp1^0 <= 0 /\ tmp1^0-tmp1^post1 == 0), cost: 1 New rule: l0 -> l2 : -1+tmp1^0 >= 0, cost: 1 Applied preprocessing Original rule: l0 -> l2 : tmp1^0'=tmp1^post2, Stored^0'=Stored^post2, tmp___02^0'=tmp___02^post2, (tmp___02^0-tmp___02^post2 == 0 /\ tmp1^0-tmp1^post2 == 0 /\ 1+tmp1^0 <= 0 /\ -Stored^post2+Stored^0 == 0), cost: 1 New rule: l0 -> l2 : 1+tmp1^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : tmp1^0'=tmp1^post3, Stored^0'=Stored^post3, tmp___02^0'=tmp___02^post3, (0 == 0 /\ -Stored^post3+Stored^0 == 0 /\ -tmp___02^post3+tmp___02^0 == 0), cost: 1 New rule: l3 -> l0 : tmp1^0'=tmp1^post3, 0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : tmp1^0'=tmp1^post5, Stored^0'=Stored^post5, tmp___02^0'=tmp___02^post5, (-Stored^post5+Stored^0 == 0 /\ -tmp___02^post5+tmp___02^0 == 0 /\ 1-tmp___02^0 <= 0 /\ -tmp1^post5+tmp1^0 == 0), cost: 1 New rule: l4 -> l3 : -1+tmp___02^0 >= 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : tmp1^0'=tmp1^post6, Stored^0'=Stored^post6, tmp___02^0'=tmp___02^post6, (-Stored^post6+Stored^0 == 0 /\ tmp1^0-tmp1^post6 == 0 /\ -tmp___02^post6+tmp___02^0 == 0 /\ 1+tmp___02^0 <= 0), cost: 1 New rule: l4 -> l3 : 1+tmp___02^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l4 : tmp1^0'=tmp1^post8, Stored^0'=Stored^post8, tmp___02^0'=tmp___02^post8, (0 == 0 /\ Stored^0-Stored^post8 == 0 /\ tmp1^0-tmp1^post8 == 0), cost: 1 New rule: l7 -> l4 : tmp___02^0'=tmp___02^post8, 0 == 0, cost: 1 Applied preprocessing Original rule: l2 -> l7 : tmp1^0'=tmp1^post13, Stored^0'=Stored^post13, tmp___02^0'=tmp___02^post13, (-tmp___02^post13+tmp___02^0 == 0 /\ Stored^0-Stored^post13 == 0 /\ tmp1^0-tmp1^post13 == 0), cost: 1 New rule: l2 -> l7 : TRUE, cost: 1 Applied preprocessing Original rule: l9 -> l7 : tmp1^0'=tmp1^post14, Stored^0'=Stored^post14, tmp___02^0'=tmp___02^post14, (tmp___02^0-tmp___02^post14 == 0 /\ tmp1^0-tmp1^post14 == 0 /\ Stored^post14 == 0), cost: 1 New rule: l9 -> l7 : Stored^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l10 -> l9 : tmp1^0'=tmp1^post15, Stored^0'=Stored^post15, tmp___02^0'=tmp___02^post15, (tmp___02^0-tmp___02^post15 == 0 /\ Stored^0-Stored^post15 == 0 /\ tmp1^0-tmp1^post15 == 0), cost: 1 New rule: l10 -> l9 : TRUE, cost: 1 Simplified rules Start location: l10 16: l0 -> l2 : -1+tmp1^0 >= 0, cost: 1 17: l0 -> l2 : 1+tmp1^0 <= 0, cost: 1 22: l2 -> l7 : TRUE, cost: 1 18: l3 -> l0 : tmp1^0'=tmp1^post3, 0 == 0, cost: 1 19: l4 -> l3 : -1+tmp___02^0 >= 0, cost: 1 20: l4 -> l3 : 1+tmp___02^0 <= 0, cost: 1 21: l7 -> l4 : tmp___02^0'=tmp___02^post8, 0 == 0, cost: 1 23: l9 -> l7 : Stored^0'=0, TRUE, cost: 1 24: l10 -> l9 : TRUE, cost: 1 Eliminating location l9 by chaining: Applied chaining First rule: l10 -> l9 : TRUE, cost: 1 Second rule: l9 -> l7 : Stored^0'=0, TRUE, cost: 1 New rule: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 23 24 Eliminated locations on linear paths Start location: l10 16: l0 -> l2 : -1+tmp1^0 >= 0, cost: 1 17: l0 -> l2 : 1+tmp1^0 <= 0, cost: 1 22: l2 -> l7 : TRUE, cost: 1 18: l3 -> l0 : tmp1^0'=tmp1^post3, 0 == 0, cost: 1 19: l4 -> l3 : -1+tmp___02^0 >= 0, cost: 1 20: l4 -> l3 : 1+tmp___02^0 <= 0, cost: 1 21: l7 -> l4 : tmp___02^0'=tmp___02^post8, 0 == 0, cost: 1 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Eliminating location l4 by chaining: Applied chaining First rule: l7 -> l4 : tmp___02^0'=tmp___02^post8, 0 == 0, cost: 1 Second rule: l4 -> l3 : -1+tmp___02^0 >= 0, cost: 1 New rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, (0 == 0 /\ -1+tmp___02^post8 >= 0), cost: 2 Applied simplification Original rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, (0 == 0 /\ -1+tmp___02^post8 >= 0), cost: 2 New rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, -1+tmp___02^post8 >= 0, cost: 2 Applied chaining First rule: l7 -> l4 : tmp___02^0'=tmp___02^post8, 0 == 0, cost: 1 Second rule: l4 -> l3 : 1+tmp___02^0 <= 0, cost: 1 New rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, (0 == 0 /\ 1+tmp___02^post8 <= 0), cost: 2 Applied simplification Original rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, (0 == 0 /\ 1+tmp___02^post8 <= 0), cost: 2 New rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, 1+tmp___02^post8 <= 0, cost: 2 Applied deletion Removed the following rules: 19 20 21 Eliminating location l0 by chaining: Applied chaining First rule: l3 -> l0 : tmp1^0'=tmp1^post3, 0 == 0, cost: 1 Second rule: l0 -> l2 : -1+tmp1^0 >= 0, cost: 1 New rule: l3 -> l2 : tmp1^0'=tmp1^post3, (0 == 0 /\ -1+tmp1^post3 >= 0), cost: 2 Applied simplification Original rule: l3 -> l2 : tmp1^0'=tmp1^post3, (0 == 0 /\ -1+tmp1^post3 >= 0), cost: 2 New rule: l3 -> l2 : tmp1^0'=tmp1^post3, -1+tmp1^post3 >= 0, cost: 2 Applied chaining First rule: l3 -> l0 : tmp1^0'=tmp1^post3, 0 == 0, cost: 1 Second rule: l0 -> l2 : 1+tmp1^0 <= 0, cost: 1 New rule: l3 -> l2 : tmp1^0'=tmp1^post3, (0 == 0 /\ 1+tmp1^post3 <= 0), cost: 2 Applied simplification Original rule: l3 -> l2 : tmp1^0'=tmp1^post3, (0 == 0 /\ 1+tmp1^post3 <= 0), cost: 2 New rule: l3 -> l2 : tmp1^0'=tmp1^post3, 1+tmp1^post3 <= 0, cost: 2 Applied deletion Removed the following rules: 16 17 18 Eliminated locations on tree-shaped paths Start location: l10 22: l2 -> l7 : TRUE, cost: 1 28: l3 -> l2 : tmp1^0'=tmp1^post3, -1+tmp1^post3 >= 0, cost: 2 29: l3 -> l2 : tmp1^0'=tmp1^post3, 1+tmp1^post3 <= 0, cost: 2 26: l7 -> l3 : tmp___02^0'=tmp___02^post8, -1+tmp___02^post8 >= 0, cost: 2 27: l7 -> l3 : tmp___02^0'=tmp___02^post8, 1+tmp___02^post8 <= 0, cost: 2 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Eliminating location l3 by chaining: Applied chaining First rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, -1+tmp___02^post8 >= 0, cost: 2 Second rule: l3 -> l2 : tmp1^0'=tmp1^post3, -1+tmp1^post3 >= 0, cost: 2 New rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 4 Applied chaining First rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, -1+tmp___02^post8 >= 0, cost: 2 Second rule: l3 -> l2 : tmp1^0'=tmp1^post3, 1+tmp1^post3 <= 0, cost: 2 New rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 4 Applied chaining First rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, 1+tmp___02^post8 <= 0, cost: 2 Second rule: l3 -> l2 : tmp1^0'=tmp1^post3, -1+tmp1^post3 >= 0, cost: 2 New rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 4 Applied chaining First rule: l7 -> l3 : tmp___02^0'=tmp___02^post8, 1+tmp___02^post8 <= 0, cost: 2 Second rule: l3 -> l2 : tmp1^0'=tmp1^post3, 1+tmp1^post3 <= 0, cost: 2 New rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 4 Applied deletion Removed the following rules: 26 27 28 29 Eliminated locations on tree-shaped paths Start location: l10 22: l2 -> l7 : TRUE, cost: 1 30: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 4 31: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 4 32: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 4 33: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 4 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Eliminating location l2 by chaining: Applied chaining First rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 4 Second rule: l2 -> l7 : TRUE, cost: 1 New rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 5 Applied chaining First rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 4 Second rule: l2 -> l7 : TRUE, cost: 1 New rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 5 Applied chaining First rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 4 Second rule: l2 -> l7 : TRUE, cost: 1 New rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 5 Applied chaining First rule: l7 -> l2 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 4 Second rule: l2 -> l7 : TRUE, cost: 1 New rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 5 Applied deletion Removed the following rules: 22 30 31 32 33 Eliminated locations on tree-shaped paths Start location: l10 34: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 5 35: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 5 36: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 5 37: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 5 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Applied nonterm Original rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: 5 New rule: l7 -> [11] : (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_lkkFcC.txt Applied nonterm Original rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (-1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: 5 New rule: l7 -> [11] : (-1+n0 >= 0 /\ -1+tmp___02^post8 >= 0 /\ -1-tmp1^post3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_ADJFDC.txt Applied nonterm Original rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: 5 New rule: l7 -> [11] : (-1+n1 >= 0 /\ -1-tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_JKenap.txt Applied nonterm Original rule: l7 -> l7 : tmp1^0'=tmp1^post3, tmp___02^0'=tmp___02^post8, (1+tmp1^post3 <= 0 /\ 1+tmp___02^post8 <= 0), cost: 5 New rule: l7 -> [11] : (-1-tmp1^post3 >= 0 /\ -1+n2 >= 0 /\ -1-tmp___02^post8 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_pDBCCc.txt Applied simplification Original rule: l7 -> [11] : (-1+n0 >= 0 /\ -1+tmp___02^post8 >= 0 /\ -1-tmp1^post3 >= 0), cost: NONTERM New rule: l7 -> [11] : (-1+n0 >= 0 /\ -1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: NONTERM Applied simplification Original rule: l7 -> [11] : (-1+n1 >= 0 /\ -1-tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0), cost: NONTERM New rule: l7 -> [11] : (-1+n1 >= 0 /\ 1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: NONTERM Applied simplification Original rule: l7 -> [11] : (-1-tmp1^post3 >= 0 /\ -1+n2 >= 0 /\ -1-tmp___02^post8 >= 0), cost: NONTERM New rule: l7 -> [11] : (1+tmp1^post3 <= 0 /\ -1+n2 >= 0 /\ 1+tmp___02^post8 <= 0), cost: NONTERM Applied deletion Removed the following rules: 34 35 36 37 Accelerated simple loops Start location: l10 38: l7 -> [11] : (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0 /\ -1+n >= 0), cost: NONTERM 42: l7 -> [11] : (-1+n0 >= 0 /\ -1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: NONTERM 43: l7 -> [11] : (-1+n1 >= 0 /\ 1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: NONTERM 44: l7 -> [11] : (1+tmp1^post3 <= 0 /\ -1+n2 >= 0 /\ 1+tmp___02^post8 <= 0), cost: NONTERM 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Applied chaining First rule: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Second rule: l7 -> [11] : (-1+tmp___02^post8 >= 0 /\ -1+tmp1^post3 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l10 -> [11] : TRUE, cost: NONTERM Applied chaining First rule: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Second rule: l7 -> [11] : (-1+n0 >= 0 /\ -1+tmp___02^post8 >= 0 /\ 1+tmp1^post3 <= 0), cost: NONTERM New rule: l10 -> [11] : TRUE, cost: NONTERM Applied chaining First rule: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Second rule: l7 -> [11] : (-1+n1 >= 0 /\ 1+tmp___02^post8 <= 0 /\ -1+tmp1^post3 >= 0), cost: NONTERM New rule: l10 -> [11] : TRUE, cost: NONTERM Applied chaining First rule: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 Second rule: l7 -> [11] : (1+tmp1^post3 <= 0 /\ -1+n2 >= 0 /\ 1+tmp___02^post8 <= 0), cost: NONTERM New rule: l10 -> [11] : TRUE, cost: NONTERM Applied deletion Removed the following rules: 38 42 43 44 Chained accelerated rules with incoming rules Start location: l10 25: l10 -> l7 : Stored^0'=0, TRUE, cost: 2 45: l10 -> [11] : TRUE, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l10 45: l10 -> [11] : TRUE, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 45 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: TRUE