NO Initial ITS Start location: l5 0: l0 -> l1 : a_19^0'=a_19^post0, i_20^0'=i_20^post0, st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, (i_13^post0 <= 0 /\ i_13^post0 == 0 /\ -i_13^post0 <= 0 /\ st_14^0-st_14^post0 == 0 /\ a_19^0-a_19^post0 == 0 /\ -rt_11^post0+rt_11^0 == 0 /\ i_20^0-i_20^post0 == 0), cost: 1 2: l1 -> l3 : a_19^0'=a_19^post2, i_20^0'=i_20^post2, st_14^0'=st_14^post2, i_13^0'=i_13^post2, rt_11^0'=rt_11^post2, (-st_14^0+rt_11^post2 == 0 /\ a_19^0-a_19^post2 == 0 /\ i_20^0-i_20^post2 == 0 /\ -st_14^post2+st_14^0 == 0 /\ 10-i_13^0 <= 0 /\ -i_13^post2+i_13^0 == 0), cost: 1 3: l1 -> l4 : a_19^0'=a_19^post3, i_20^0'=i_20^post3, st_14^0'=st_14^post3, i_13^0'=i_13^post3, rt_11^0'=rt_11^post3, (0 == 0 /\ 1-i_13^0+i_13^post3 == 0 /\ a_19^0-a_19^post3 == 0 /\ st_14^0-st_14^post3 == 0 /\ -9+i_20^post3 <= 0 /\ 1-i_20^post3+i_13^post3 <= 0 /\ -9+i_13^0 <= 0 /\ -rt_11^post3+rt_11^0 == 0 /\ -1+i_20^post3-i_13^post3 <= 0), cost: 1 1: l2 -> l1 : a_19^0'=a_19^post1, i_20^0'=i_20^post1, st_14^0'=st_14^post1, i_13^0'=i_13^post1, rt_11^0'=rt_11^post1, (0 == 0 /\ -a_19^post1+i_13^post1 <= 0 /\ i_20^0-i_20^post1 == 0 /\ 1-i_13^0+i_13^10 == 0 /\ -rt_11^post1+rt_11^0 == 0 /\ a_19^post1-i_13^post1 <= 0 /\ 1+i_13^post1 <= 0 /\ -1-i_13^post1 <= 0 /\ -st_14^post1+st_14^0 == 0 /\ -9+i_13^0 <= 0), cost: 1 4: l4 -> l1 : a_19^0'=a_19^post4, i_20^0'=i_20^post4, st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, (-rt_11^post4+rt_11^0 == 0 /\ -i_13^post4+i_13^0 == 0 /\ i_20^0-i_20^post4 == 0 /\ -st_14^post4+st_14^0 == 0 /\ a_19^0-a_19^post4 == 0), cost: 1 5: l5 -> l0 : a_19^0'=a_19^post5, i_20^0'=i_20^post5, st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, (-rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ i_13^0-i_13^post5 == 0 /\ i_20^0-i_20^post5 == 0 /\ a_19^0-a_19^post5 == 0), cost: 1 Removed unreachable rules and leafs Start location: l5 0: l0 -> l1 : a_19^0'=a_19^post0, i_20^0'=i_20^post0, st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, (i_13^post0 <= 0 /\ i_13^post0 == 0 /\ -i_13^post0 <= 0 /\ st_14^0-st_14^post0 == 0 /\ a_19^0-a_19^post0 == 0 /\ -rt_11^post0+rt_11^0 == 0 /\ i_20^0-i_20^post0 == 0), cost: 1 3: l1 -> l4 : a_19^0'=a_19^post3, i_20^0'=i_20^post3, st_14^0'=st_14^post3, i_13^0'=i_13^post3, rt_11^0'=rt_11^post3, (0 == 0 /\ 1-i_13^0+i_13^post3 == 0 /\ a_19^0-a_19^post3 == 0 /\ st_14^0-st_14^post3 == 0 /\ -9+i_20^post3 <= 0 /\ 1-i_20^post3+i_13^post3 <= 0 /\ -9+i_13^0 <= 0 /\ -rt_11^post3+rt_11^0 == 0 /\ -1+i_20^post3-i_13^post3 <= 0), cost: 1 4: l4 -> l1 : a_19^0'=a_19^post4, i_20^0'=i_20^post4, st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, (-rt_11^post4+rt_11^0 == 0 /\ -i_13^post4+i_13^0 == 0 /\ i_20^0-i_20^post4 == 0 /\ -st_14^post4+st_14^0 == 0 /\ a_19^0-a_19^post4 == 0), cost: 1 5: l5 -> l0 : a_19^0'=a_19^post5, i_20^0'=i_20^post5, st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, (-rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ i_13^0-i_13^post5 == 0 /\ i_20^0-i_20^post5 == 0 /\ a_19^0-a_19^post5 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : a_19^0'=a_19^post0, i_20^0'=i_20^post0, st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, (i_13^post0 <= 0 /\ i_13^post0 == 0 /\ -i_13^post0 <= 0 /\ st_14^0-st_14^post0 == 0 /\ a_19^0-a_19^post0 == 0 /\ -rt_11^post0+rt_11^0 == 0 /\ i_20^0-i_20^post0 == 0), cost: 1 New rule: l0 -> l1 : i_13^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l4 : a_19^0'=a_19^post3, i_20^0'=i_20^post3, st_14^0'=st_14^post3, i_13^0'=i_13^post3, rt_11^0'=rt_11^post3, (0 == 0 /\ 1-i_13^0+i_13^post3 == 0 /\ a_19^0-a_19^post3 == 0 /\ st_14^0-st_14^post3 == 0 /\ -9+i_20^post3 <= 0 /\ 1-i_20^post3+i_13^post3 <= 0 /\ -9+i_13^0 <= 0 /\ -rt_11^post3+rt_11^0 == 0 /\ -1+i_20^post3-i_13^post3 <= 0), cost: 1 New rule: l1 -> l4 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l1 : a_19^0'=a_19^post4, i_20^0'=i_20^post4, st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, (-rt_11^post4+rt_11^0 == 0 /\ -i_13^post4+i_13^0 == 0 /\ i_20^0-i_20^post4 == 0 /\ -st_14^post4+st_14^0 == 0 /\ a_19^0-a_19^post4 == 0), cost: 1 New rule: l4 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l0 : a_19^0'=a_19^post5, i_20^0'=i_20^post5, st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, (-rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ i_13^0-i_13^post5 == 0 /\ i_20^0-i_20^post5 == 0 /\ a_19^0-a_19^post5 == 0), cost: 1 New rule: l5 -> l0 : TRUE, cost: 1 Simplified rules Start location: l5 6: l0 -> l1 : i_13^0'=0, TRUE, cost: 1 7: l1 -> l4 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 1 8: l4 -> l1 : TRUE, cost: 1 9: l5 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l5 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : i_13^0'=0, TRUE, cost: 1 New rule: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 6 9 Eliminating location l4 by chaining: Applied chaining First rule: l1 -> l4 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 1 Second rule: l4 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminated locations on linear paths Start location: l5 11: l1 -> l1 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 2 10: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 Applied nonterm Original rule: l1 -> l1 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 2 New rule: l1 -> [6] : 9-i_13^0 >= 0, cost: NONTERM Applied acceleration Original rule: l1 -> l1 : i_20^0'=i_13^0, i_13^0'=-1+i_13^0, -9+i_13^0 <= 0, cost: 2 New rule: l1 -> l1 : i_20^0'=1-n0+i_13^0, i_13^0'=-n0+i_13^0, 9-i_13^0 >= 0, cost: 2*n0 Applied simplification Original rule: l1 -> [6] : 9-i_13^0 >= 0, cost: NONTERM New rule: l1 -> [6] : -9+i_13^0 <= 0, cost: NONTERM Applied simplification Original rule: l1 -> l1 : i_20^0'=1-n0+i_13^0, i_13^0'=-n0+i_13^0, 9-i_13^0 >= 0, cost: 2*n0 New rule: l1 -> l1 : i_20^0'=1-n0+i_13^0, i_13^0'=-n0+i_13^0, -9+i_13^0 <= 0, cost: 2*n0 Applied deletion Removed the following rules: 11 Accelerated simple loops Start location: l5 14: l1 -> [6] : -9+i_13^0 <= 0, cost: NONTERM 15: l1 -> l1 : i_20^0'=1-n0+i_13^0, i_13^0'=-n0+i_13^0, -9+i_13^0 <= 0, cost: 2*n0 10: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 Applied chaining First rule: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 Second rule: l1 -> [6] : -9+i_13^0 <= 0, cost: NONTERM New rule: l5 -> [6] : -9 <= 0, cost: NONTERM Applied chaining First rule: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : i_20^0'=1-n0+i_13^0, i_13^0'=-n0+i_13^0, -9+i_13^0 <= 0, cost: 2*n0 New rule: l5 -> l1 : i_20^0'=1-n0, i_13^0'=-n0, -9 <= 0, cost: 2+2*n0 Applied deletion Removed the following rules: 14 15 Chained accelerated rules with incoming rules Start location: l5 10: l5 -> l1 : i_13^0'=0, TRUE, cost: 2 16: l5 -> [6] : -9 <= 0, cost: NONTERM 17: l5 -> l1 : i_20^0'=1-n0, i_13^0'=-n0, -9 <= 0, cost: 2+2*n0 Removed unreachable locations and irrelevant leafs Start location: l5 16: l5 -> [6] : -9 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 16 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -9 <= 0