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