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