NO Initial ITS Start location: l7 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 /\ x_5^0-x_5^post1 == 0 /\ 1+x_5^0 <= 0 /\ tmp_6^0-tmp_6^post1 == 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 /\ -x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l1 -> l5 : tmp_6^0'=tmp_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+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: l5 -> l6 : 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: l5 -> l6 : 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: l6 -> l4 : tmp_6^0'=tmp_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (1+x_5^post7-x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ tmp_6^0-tmp_6^post7 == 0), cost: 1 8: l4 -> l1 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0 /\ tmp_6^0-tmp_6^post8 == 0), cost: 1 9: l7 -> l0 : 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 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l7 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 /\ -x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l1 -> l5 : tmp_6^0'=tmp_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+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: l5 -> l6 : 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: l5 -> l6 : 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: l6 -> l4 : tmp_6^0'=tmp_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (1+x_5^post7-x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ tmp_6^0-tmp_6^post7 == 0), cost: 1 8: l4 -> l1 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0 /\ tmp_6^0-tmp_6^post8 == 0), cost: 1 9: l7 -> l0 : 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 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 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 /\ -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, 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 -> l5 : tmp_6^0'=tmp_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 New rule: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l5 -> l6 : 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 New rule: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l5 -> l6 : 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 New rule: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 Applied preprocessing Original rule: l6 -> l4 : tmp_6^0'=tmp_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (1+x_5^post7-x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ tmp_6^0-tmp_6^post7 == 0), cost: 1 New rule: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l1 : tmp_6^0'=tmp_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (Result_4^0-Result_4^post8 == 0 /\ -x_5^post8+x_5^0 == 0 /\ tmp_6^0-tmp_6^post8 == 0), cost: 1 New rule: l4 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l0 : 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 /\ Result_4^0-Result_4^post9 == 0 /\ -x_5^post9+x_5^0 == 0), cost: 1 New rule: l7 -> l0 : TRUE, cost: 1 Simplified rules Start location: l7 10: l0 -> l1 : TRUE, cost: 1 11: l1 -> l3 : tmp_6^0'=0, x_5^0 >= 0, cost: 1 13: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 12: l3 -> l1 : TRUE, cost: 1 14: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 15: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 16: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 17: l4 -> l1 : TRUE, cost: 1 18: l7 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l7 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l7 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 10 18 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : tmp_6^0'=0, x_5^0 >= 0, cost: 1 Second rule: l3 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 11 12 Eliminating location l4 by chaining: Applied chaining First rule: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Second rule: l4 -> l1 : TRUE, cost: 1 New rule: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 Applied deletion Removed the following rules: 16 17 Eliminated locations on linear paths Start location: l7 13: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 20: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 14: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 15: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 21: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 19: l7 -> l1 : TRUE, cost: 2 Applied nonterm Original rule: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 New rule: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_mOkAOA.txt Applied deletion Removed the following rules: 20 Accelerated simple loops Start location: l7 13: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 22: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM 14: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 15: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 21: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 19: l7 -> l1 : TRUE, cost: 2 Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 Second rule: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l6 -> [8] : -1+x_5^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 22 Chained accelerated rules with incoming rules Start location: l7 13: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 14: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 15: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 21: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 24: l6 -> [8] : -1+x_5^0 >= 0, cost: NONTERM 19: l7 -> l1 : TRUE, cost: 2 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Eliminating location l5 by chaining: Applied chaining First rule: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 Second rule: l5 -> l6 : 1+tmp_6^0 <= 0, cost: 1 New rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 2 Applied chaining First rule: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 Second rule: l5 -> l6 : -1+tmp_6^0 >= 0, cost: 1 New rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 2 Applied deletion Removed the following rules: 13 14 15 Eliminated locations on tree-shaped paths Start location: l7 25: l1 -> l6 : tmp_6^0'=tmp_6^post4, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 2 26: l1 -> l6 : tmp_6^0'=tmp_6^post4, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 2 21: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 24: l6 -> [8] : -1+x_5^0 >= 0, cost: NONTERM 19: l7 -> l1 : TRUE, cost: 2 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Eliminating location l6 by chaining: Applied chaining First rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 2 Second rule: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4 Applied chaining First rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 2 Second rule: l6 -> [8] : -1+x_5^0 >= 0, cost: NONTERM New rule: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0 /\ x_5^0 >= 0), cost: NONTERM Applied simplification Original rule: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0 /\ x_5^0 >= 0), cost: NONTERM New rule: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM Applied chaining First rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 2 Second rule: l6 -> l1 : x_5^0'=-1+x_5^0, TRUE, cost: 2 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4 Applied chaining First rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 2 Second rule: l6 -> [8] : -1+x_5^0 >= 0, cost: NONTERM New rule: l1 -> [8] : (-1+x_5^0 >= 0 /\ x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM Applied simplification Original rule: l1 -> [8] : (-1+x_5^0 >= 0 /\ x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM New rule: l1 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM Applied deletion Removed the following rules: 21 24 25 26 Eliminated locations on tree-shaped paths Start location: l7 27: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4 28: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM 29: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4 30: l1 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM 19: l7 -> l1 : TRUE, cost: 2 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Applied acceleration Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-n0+x_5^0, (-1-tmp_6^post4 >= 0 /\ 1-n0+x_5^0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_nhANPe.txt Applied instantiation Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-n0+x_5^0, (-1-tmp_6^post4 >= 0 /\ 1-n0+x_5^0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (0 >= 0 /\ -1-tmp_6^post4 >= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 Applied acceleration Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1+x_5^0, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-n1+x_5^0, (-1+n1 >= 0 /\ -1+tmp_6^post4 >= 0 /\ 1-n1+x_5^0 >= 0), cost: 4*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_hKjdCF.txt Applied instantiation Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-n1+x_5^0, (-1+n1 >= 0 /\ -1+tmp_6^post4 >= 0 /\ 1-n1+x_5^0 >= 0), cost: 4*n1 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (0 >= 0 /\ x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4+4*x_5^0 Applied simplification Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (0 >= 0 /\ -1-tmp_6^post4 >= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 Applied simplification Original rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (0 >= 0 /\ x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4+4*x_5^0 New rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4+4*x_5^0 Applied deletion Removed the following rules: 27 29 Accelerated simple loops Start location: l7 28: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM 30: l1 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM 33: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 34: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4+4*x_5^0 19: l7 -> l1 : TRUE, cost: 2 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 New rule: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 6+4*x_5^0 Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 4+4*x_5^0 New rule: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 6+4*x_5^0 Applied deletion Removed the following rules: 33 34 Chained accelerated rules with incoming rules Start location: l7 28: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM 30: l1 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM 19: l7 -> l1 : TRUE, cost: 2 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM 35: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 6+4*x_5^0 36: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 6+4*x_5^0 Eliminating location l1 by chaining: Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM New rule: l7 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM New rule: l7 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM Applied partial deletion Original rule: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 6+4*x_5^0 New rule: l7 -> [10] : (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 6+4*x_5^0 Applied partial deletion Original rule: l7 -> l1 : tmp_6^0'=tmp_6^post4, x_5^0'=-1, (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 6+4*x_5^0 New rule: l7 -> [10] : (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 6+4*x_5^0 Applied deletion Removed the following rules: 19 28 30 35 36 Eliminated locations on tree-shaped paths Start location: l7 23: l7 -> [8] : x_5^0 >= 0, cost: NONTERM 37: l7 -> [8] : (1+tmp_6^post4 <= 0 /\ -1+x_5^0 >= 0), cost: NONTERM 38: l7 -> [8] : (-1+x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: NONTERM 39: l7 -> [10] : (1+tmp_6^post4 <= 0 /\ x_5^0 >= 0), cost: 6+4*x_5^0 40: l7 -> [10] : (x_5^0 >= 0 /\ -1+tmp_6^post4 >= 0), cost: 6+4*x_5^0 Computing asymptotic complexity Proved nontermination of rule 23 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: x_5^0 >= 0