NO Initial ITS Start location: l5 0: l0 -> l2 : b^0'=b^post0, (-1+b^post0 == 0 /\ -b^0 <= 0), cost: 1 1: l2 -> l3 : b^0'=b^post1, (1+b^0 <= 0 /\ b^0-b^post1 == 0), cost: 1 2: l2 -> l3 : b^0'=b^post2, (1-b^0 <= 0 /\ b^0-b^post2 == 0), cost: 1 3: l3 -> l1 : b^0'=b^post3, b^post3 == 0, cost: 1 4: l1 -> l0 : b^0'=b^post4, b^0-b^post4 == 0, cost: 1 5: l4 -> l0 : b^0'=b^post5, b^0-b^post5 == 0, cost: 1 6: l5 -> l4 : b^0'=b^post6, b^0-b^post6 == 0, cost: 1 Applied preprocessing Original rule: l0 -> l2 : b^0'=b^post0, (-1+b^post0 == 0 /\ -b^0 <= 0), cost: 1 New rule: l0 -> l2 : b^0'=1, b^0 >= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : b^0'=b^post1, (1+b^0 <= 0 /\ b^0-b^post1 == 0), cost: 1 New rule: l2 -> l3 : 1+b^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : b^0'=b^post2, (1-b^0 <= 0 /\ b^0-b^post2 == 0), cost: 1 New rule: l2 -> l3 : -1+b^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : b^0'=b^post3, b^post3 == 0, cost: 1 New rule: l3 -> l1 : b^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l0 : b^0'=b^post4, b^0-b^post4 == 0, cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l0 : b^0'=b^post5, b^0-b^post5 == 0, cost: 1 New rule: l4 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : b^0'=b^post6, b^0-b^post6 == 0, cost: 1 New rule: l5 -> l4 : TRUE, cost: 1 Simplified rules Start location: l5 7: l0 -> l2 : b^0'=1, b^0 >= 0, cost: 1 8: l2 -> l3 : 1+b^0 <= 0, cost: 1 9: l2 -> l3 : -1+b^0 >= 0, cost: 1 10: l3 -> l1 : b^0'=0, TRUE, cost: 1 11: l1 -> l0 : TRUE, cost: 1 12: l4 -> l0 : TRUE, cost: 1 13: l5 -> l4 : TRUE, cost: 1 Eliminating location l4 by chaining: Applied chaining First rule: l5 -> l4 : TRUE, cost: 1 Second rule: l4 -> l0 : TRUE, cost: 1 New rule: l5 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 12 13 Eliminating location l1 by chaining: Applied chaining First rule: l3 -> l1 : b^0'=0, TRUE, cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l3 -> l0 : b^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminated locations on linear paths Start location: l5 7: l0 -> l2 : b^0'=1, b^0 >= 0, cost: 1 8: l2 -> l3 : 1+b^0 <= 0, cost: 1 9: l2 -> l3 : -1+b^0 >= 0, cost: 1 15: l3 -> l0 : b^0'=0, TRUE, cost: 2 14: l5 -> l0 : TRUE, cost: 2 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : b^0'=1, b^0 >= 0, cost: 1 Second rule: l2 -> l3 : -1+b^0 >= 0, cost: 1 New rule: l0 -> l3 : b^0'=1, (0 >= 0 /\ b^0 >= 0), cost: 2 Applied simplification Original rule: l0 -> l3 : b^0'=1, (0 >= 0 /\ b^0 >= 0), cost: 2 New rule: l0 -> l3 : b^0'=1, b^0 >= 0, cost: 2 Applied deletion Removed the following rules: 7 8 9 Eliminated locations on tree-shaped paths Start location: l5 16: l0 -> l3 : b^0'=1, b^0 >= 0, cost: 2 15: l3 -> l0 : b^0'=0, TRUE, cost: 2 14: l5 -> l0 : TRUE, cost: 2 Eliminating location l3 by chaining: Applied chaining First rule: l0 -> l3 : b^0'=1, b^0 >= 0, cost: 2 Second rule: l3 -> l0 : b^0'=0, TRUE, cost: 2 New rule: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4 Applied deletion Removed the following rules: 15 16 Eliminated locations on linear paths Start location: l5 17: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4 14: l5 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4 New rule: l0 -> [6] : b^0 >= 0, cost: NONTERM Applied acceleration Original rule: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4 New rule: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4*n0 Applied deletion Removed the following rules: 17 Accelerated simple loops Start location: l5 18: l0 -> [6] : b^0 >= 0, cost: NONTERM 19: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4*n0 14: l5 -> l0 : TRUE, cost: 2 Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> [6] : b^0 >= 0, cost: NONTERM New rule: l5 -> [6] : b^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : b^0'=0, b^0 >= 0, cost: 4*n0 New rule: l5 -> l0 : b^0'=0, b^0 >= 0, cost: 2+4*n0 Applied deletion Removed the following rules: 18 19 Chained accelerated rules with incoming rules Start location: l5 14: l5 -> l0 : TRUE, cost: 2 20: l5 -> [6] : b^0 >= 0, cost: NONTERM 21: l5 -> l0 : b^0'=0, b^0 >= 0, cost: 2+4*n0 Removed unreachable locations and irrelevant leafs Start location: l5 20: l5 -> [6] : b^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 20 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: b^0 >= 0