NO Initial ITS Start location: l9 0: l0 -> l1 : tmp_6^0'=tmp_6^post0, Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, (x_5^0-x_5^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0), cost: 1 1: l1 -> l2 : tmp_6^0'=tmp_6^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, (0 == 0 /\ -tmp_6^post1 <= 0 /\ tmp_6^post1 <= 0 /\ x_5^0-x_5^post1 == 0 /\ x_5^0 <= 0), cost: 1 2: l1 -> l3 : tmp_6^0'=tmp_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (0 == 0 /\ x_5^0-x_5^post2 == 0 /\ tmp_6^post2 <= 0 /\ 1-x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l1 -> l4 : tmp_6^0'=tmp_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (0 == 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 8: l1 -> l7 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0), cost: 1 3: l3 -> l1 : tmp_6^0'=tmp_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0), cost: 1 5: l4 -> l5 : tmp_6^0'=tmp_6^post5, Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, (-Result_4^post5+Result_4^0 == 0 /\ -x_5^post5+x_5^0 == 0 /\ 1+tmp_6^0 <= 0 /\ -tmp_6^post5+tmp_6^0 == 0), cost: 1 6: l4 -> l5 : tmp_6^0'=tmp_6^post6, Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, (-Result_4^post6+Result_4^0 == 0 /\ tmp_6^0-tmp_6^post6 == 0 /\ -x_5^post6+x_5^0 == 0 /\ 1-tmp_6^0 <= 0), cost: 1 7: l5 -> l2 : tmp_6^0'=tmp_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (0 == 0 /\ x_5^post7 <= 0 /\ 1+x_5^post7-x_5^0 == 0 /\ tmp_6^0-tmp_6^post7 == 0), cost: 1 9: l7 -> l8 : tmp_6^0'=tmp_6^post9, Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, (tmp_6^0-tmp_6^post9 == 0 /\ 1+tmp_6^0 <= 0 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 0), cost: 1 10: l7 -> l8 : tmp_6^0'=tmp_6^post10, Result_4^0'=Result_4^post10, x_5^0'=x_5^post10, (Result_4^0-Result_4^post10 == 0 /\ tmp_6^0-tmp_6^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ 1-tmp_6^0 <= 0), cost: 1 11: l8 -> l6 : tmp_6^0'=tmp_6^post11, Result_4^0'=Result_4^post11, x_5^0'=x_5^post11, (tmp_6^0-tmp_6^post11 == 0 /\ Result_4^0-Result_4^post11 == 0 /\ 1-x_5^post11 <= 0 /\ 1+x_5^post11-x_5^0 == 0), cost: 1 12: l6 -> l1 : tmp_6^0'=tmp_6^post12, Result_4^0'=Result_4^post12, x_5^0'=x_5^post12, (Result_4^0-Result_4^post12 == 0 /\ -x_5^post12+x_5^0 == 0 /\ tmp_6^0-tmp_6^post12 == 0), cost: 1 13: l9 -> l0 : tmp_6^0'=tmp_6^post13, Result_4^0'=Result_4^post13, x_5^0'=x_5^post13, (-x_5^post13+x_5^0 == 0 /\ Result_4^0-Result_4^post13 == 0 /\ tmp_6^0-tmp_6^post13 == 0), cost: 1 Removed unreachable rules and leafs Start location: l9 0: l0 -> l1 : tmp_6^0'=tmp_6^post0, Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, (x_5^0-x_5^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0), cost: 1 2: l1 -> l3 : tmp_6^0'=tmp_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (0 == 0 /\ x_5^0-x_5^post2 == 0 /\ tmp_6^post2 <= 0 /\ 1-x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 8: l1 -> l7 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0), cost: 1 3: l3 -> l1 : tmp_6^0'=tmp_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0), cost: 1 9: l7 -> l8 : tmp_6^0'=tmp_6^post9, Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, (tmp_6^0-tmp_6^post9 == 0 /\ 1+tmp_6^0 <= 0 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 0), cost: 1 10: l7 -> l8 : tmp_6^0'=tmp_6^post10, Result_4^0'=Result_4^post10, x_5^0'=x_5^post10, (Result_4^0-Result_4^post10 == 0 /\ tmp_6^0-tmp_6^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ 1-tmp_6^0 <= 0), cost: 1 11: l8 -> l6 : tmp_6^0'=tmp_6^post11, Result_4^0'=Result_4^post11, x_5^0'=x_5^post11, (tmp_6^0-tmp_6^post11 == 0 /\ Result_4^0-Result_4^post11 == 0 /\ 1-x_5^post11 <= 0 /\ 1+x_5^post11-x_5^0 == 0), cost: 1 12: l6 -> l1 : tmp_6^0'=tmp_6^post12, Result_4^0'=Result_4^post12, x_5^0'=x_5^post12, (Result_4^0-Result_4^post12 == 0 /\ -x_5^post12+x_5^0 == 0 /\ tmp_6^0-tmp_6^post12 == 0), cost: 1 13: l9 -> l0 : tmp_6^0'=tmp_6^post13, Result_4^0'=Result_4^post13, x_5^0'=x_5^post13, (-x_5^post13+x_5^0 == 0 /\ Result_4^0-Result_4^post13 == 0 /\ tmp_6^0-tmp_6^post13 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : tmp_6^0'=tmp_6^post0, Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, (x_5^0-x_5^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l3 : tmp_6^0'=tmp_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (0 == 0 /\ x_5^0-x_5^post2 == 0 /\ tmp_6^post2 <= 0 /\ 1-x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 New rule: l1 -> l3 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : tmp_6^0'=tmp_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0), cost: 1 New rule: l3 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l7 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0), cost: 1 New rule: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 Applied preprocessing Original rule: l7 -> l8 : tmp_6^0'=tmp_6^post9, Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, (tmp_6^0-tmp_6^post9 == 0 /\ 1+tmp_6^0 <= 0 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 0), cost: 1 New rule: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l7 -> l8 : tmp_6^0'=tmp_6^post10, Result_4^0'=Result_4^post10, x_5^0'=x_5^post10, (Result_4^0-Result_4^post10 == 0 /\ tmp_6^0-tmp_6^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ 1-tmp_6^0 <= 0), cost: 1 New rule: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 Applied preprocessing Original rule: l8 -> l6 : tmp_6^0'=tmp_6^post11, Result_4^0'=Result_4^post11, x_5^0'=x_5^post11, (tmp_6^0-tmp_6^post11 == 0 /\ Result_4^0-Result_4^post11 == 0 /\ 1-x_5^post11 <= 0 /\ 1+x_5^post11-x_5^0 == 0), cost: 1 New rule: l8 -> l6 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l6 -> l1 : tmp_6^0'=tmp_6^post12, Result_4^0'=Result_4^post12, x_5^0'=x_5^post12, (Result_4^0-Result_4^post12 == 0 /\ -x_5^post12+x_5^0 == 0 /\ tmp_6^0-tmp_6^post12 == 0), cost: 1 New rule: l6 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l9 -> l0 : tmp_6^0'=tmp_6^post13, Result_4^0'=Result_4^post13, x_5^0'=x_5^post13, (-x_5^post13+x_5^0 == 0 /\ Result_4^0-Result_4^post13 == 0 /\ tmp_6^0-tmp_6^post13 == 0), cost: 1 New rule: l9 -> l0 : TRUE, cost: 1 Simplified rules Start location: l9 14: l0 -> l1 : TRUE, cost: 1 15: l1 -> l3 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 1 17: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 16: l3 -> l1 : TRUE, cost: 1 18: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 19: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 20: l8 -> l6 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 1 21: l6 -> l1 : TRUE, cost: 1 22: l9 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l9 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l9 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 14 22 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 1 Second rule: l3 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 15 16 Eliminating location l6 by chaining: Applied chaining First rule: l8 -> l6 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 1 Second rule: l6 -> l1 : TRUE, cost: 1 New rule: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 20 21 Eliminated locations on linear paths Start location: l9 17: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 24: l1 -> l1 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 2 18: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 19: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 25: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 23: l9 -> l1 : TRUE, cost: 2 Applied nonterm Original rule: l1 -> l1 : tmp_6^0'=0, -1+x_5^0 >= 0, cost: 2 New rule: l1 -> [10] : (-1+n >= 0 /\ -1+x_5^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_aICbmh.txt Applied deletion Removed the following rules: 24 Accelerated simple loops Start location: l9 17: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 26: l1 -> [10] : (-1+n >= 0 /\ -1+x_5^0 >= 0), cost: NONTERM 18: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 19: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 25: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 23: l9 -> l1 : TRUE, cost: 2 Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> [10] : (-1+n >= 0 /\ -1+x_5^0 >= 0), cost: NONTERM New rule: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 Second rule: l1 -> [10] : (-1+n >= 0 /\ -1+x_5^0 >= 0), cost: NONTERM New rule: l8 -> [10] : -2+x_5^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 26 Chained accelerated rules with incoming rules Start location: l9 17: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 18: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 19: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 25: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 28: l8 -> [10] : -2+x_5^0 >= 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM Eliminating location l7 by chaining: Applied chaining First rule: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 Second rule: l7 -> l8 : 1+tmp_6^0 <= 0, cost: 1 New rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, (0 == 0 /\ 1+tmp_6^post8 <= 0), cost: 2 Applied simplification Original rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, (0 == 0 /\ 1+tmp_6^post8 <= 0), cost: 2 New rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, 1+tmp_6^post8 <= 0, cost: 2 Applied chaining First rule: l1 -> l7 : tmp_6^0'=tmp_6^post8, 0 == 0, cost: 1 Second rule: l7 -> l8 : -1+tmp_6^0 >= 0, cost: 1 New rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, (0 == 0 /\ -1+tmp_6^post8 >= 0), cost: 2 Applied simplification Original rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, (0 == 0 /\ -1+tmp_6^post8 >= 0), cost: 2 New rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, -1+tmp_6^post8 >= 0, cost: 2 Applied deletion Removed the following rules: 17 18 19 Eliminated locations on tree-shaped paths Start location: l9 29: l1 -> l8 : tmp_6^0'=tmp_6^post8, 1+tmp_6^post8 <= 0, cost: 2 30: l1 -> l8 : tmp_6^0'=tmp_6^post8, -1+tmp_6^post8 >= 0, cost: 2 25: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 28: l8 -> [10] : -2+x_5^0 >= 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM Eliminating location l8 by chaining: Applied chaining First rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, 1+tmp_6^post8 <= 0, cost: 2 Second rule: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: 4 Applied chaining First rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, 1+tmp_6^post8 <= 0, cost: 2 Second rule: l8 -> [10] : -2+x_5^0 >= 0, cost: NONTERM New rule: l1 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM Applied chaining First rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, -1+tmp_6^post8 >= 0, cost: 2 Second rule: l8 -> l1 : x_5^0'=-1+x_5^0, -2+x_5^0 >= 0, cost: 2 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: 4 Applied chaining First rule: l1 -> l8 : tmp_6^0'=tmp_6^post8, -1+tmp_6^post8 >= 0, cost: 2 Second rule: l8 -> [10] : -2+x_5^0 >= 0, cost: NONTERM New rule: l1 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM Applied deletion Removed the following rules: 25 28 29 30 Eliminated locations on tree-shaped paths Start location: l9 31: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: 4 32: l1 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM 33: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: 4 34: l1 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM Applied acceleration Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: 4 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-n0+x_5^0, (-1-tmp_6^post8 >= 0 /\ -1+n0 >= 0 /\ -1-n0+x_5^0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_bLOLJp.txt Applied instantiation Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-n0+x_5^0, (-1-tmp_6^post8 >= 0 /\ -1+n0 >= 0 /\ -1-n0+x_5^0 >= 0), cost: 4*n0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (0 >= 0 /\ -1-tmp_6^post8 >= 0 /\ -2+x_5^0 >= 0), cost: -4+4*x_5^0 Applied acceleration Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-1+x_5^0, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: 4 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-n1+x_5^0, (-1+tmp_6^post8 >= 0 /\ -1+n1 >= 0 /\ -1-n1+x_5^0 >= 0), cost: 4*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_CHpooi.txt Applied instantiation Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=-n1+x_5^0, (-1+tmp_6^post8 >= 0 /\ -1+n1 >= 0 /\ -1-n1+x_5^0 >= 0), cost: 4*n1 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (0 >= 0 /\ -2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -4+4*x_5^0 Applied simplification Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (0 >= 0 /\ -1-tmp_6^post8 >= 0 /\ -2+x_5^0 >= 0), cost: -4+4*x_5^0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -4+4*x_5^0 Applied simplification Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (0 >= 0 /\ -2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -4+4*x_5^0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -4+4*x_5^0 Applied deletion Removed the following rules: 31 33 Accelerated simple loops Start location: l9 32: l1 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM 34: l1 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM 37: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -4+4*x_5^0 38: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -4+4*x_5^0 23: l9 -> l1 : TRUE, cost: 2 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -4+4*x_5^0 New rule: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -2+4*x_5^0 Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -4+4*x_5^0 New rule: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -2+4*x_5^0 Applied deletion Removed the following rules: 37 38 Chained accelerated rules with incoming rules Start location: l9 32: l1 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM 34: l1 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM 39: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -2+4*x_5^0 40: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -2+4*x_5^0 Eliminating location l1 by chaining: Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM New rule: l9 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM New rule: l9 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM Applied partial deletion Original rule: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -2+4*x_5^0 New rule: l9 -> [12] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -2+4*x_5^0 Applied partial deletion Original rule: l9 -> l1 : tmp_6^0'=tmp_6^post8, x_5^0'=1, (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -2+4*x_5^0 New rule: l9 -> [12] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -2+4*x_5^0 Applied deletion Removed the following rules: 23 32 34 39 40 Eliminated locations on tree-shaped paths Start location: l9 27: l9 -> [10] : -1+x_5^0 >= 0, cost: NONTERM 41: l9 -> [10] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: NONTERM 42: l9 -> [10] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: NONTERM 43: l9 -> [12] : (1+tmp_6^post8 <= 0 /\ -2+x_5^0 >= 0), cost: -2+4*x_5^0 44: l9 -> [12] : (-2+x_5^0 >= 0 /\ -1+tmp_6^post8 >= 0), cost: -2+4*x_5^0 Computing asymptotic complexity Proved nontermination of rule 27 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1+x_5^0 >= 0