NO Initial ITS Start location: l3 0: l0 -> l1 : __const_200^0'=__const_200^post0, x^0'=x^post0, (__const_200^0-__const_200^post0 == 0 /\ 1+__const_200^0-x^post0 <= 0 /\ -1-x^0+x^post0 == 0), cost: 1 1: l1 -> l0 : __const_200^0'=__const_200^post1, x^0'=x^post1, (-x^post1+x^0 == 0 /\ __const_200^0-__const_200^post1 == 0), cost: 1 2: l2 -> l0 : __const_200^0'=__const_200^post2, x^0'=x^post2, (-x^post2+x^0 == 0 /\ __const_200^0-__const_200^post2 == 0), cost: 1 3: l3 -> l2 : __const_200^0'=__const_200^post3, x^0'=x^post3, (__const_200^0-__const_200^post3 == 0 /\ x^0-x^post3 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : __const_200^0'=__const_200^post0, x^0'=x^post0, (__const_200^0-__const_200^post0 == 0 /\ 1+__const_200^0-x^post0 <= 0 /\ -1-x^0+x^post0 == 0), cost: 1 New rule: l0 -> l1 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 1 Applied preprocessing Original rule: l1 -> l0 : __const_200^0'=__const_200^post1, x^0'=x^post1, (-x^post1+x^0 == 0 /\ __const_200^0-__const_200^post1 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l0 : __const_200^0'=__const_200^post2, x^0'=x^post2, (-x^post2+x^0 == 0 /\ __const_200^0-__const_200^post2 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l2 : __const_200^0'=__const_200^post3, x^0'=x^post3, (__const_200^0-__const_200^post3 == 0 /\ x^0-x^post3 == 0), cost: 1 New rule: l3 -> l2 : TRUE, cost: 1 Simplified rules Start location: l3 4: l0 -> l1 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 1 5: l1 -> l0 : TRUE, cost: 1 6: l2 -> l0 : 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 : TRUE, cost: 1 New rule: l3 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 6 7 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: l3 9: l0 -> l0 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 2 8: l3 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 2 New rule: l0 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM Applied acceleration Original rule: l0 -> l0 : x^0'=1+x^0, __const_200^0-x^0 <= 0, cost: 2 New rule: l0 -> l0 : x^0'=n0+x^0, -__const_200^0+x^0 >= 0, cost: 2*n0 Applied deletion Removed the following rules: 9 Accelerated simple loops Start location: l3 10: l0 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM 11: l0 -> l0 : x^0'=n0+x^0, -__const_200^0+x^0 >= 0, cost: 2*n0 8: l3 -> l0 : TRUE, cost: 2 Applied chaining First rule: l3 -> l0 : TRUE, cost: 2 Second rule: l0 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM New rule: l3 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM Applied chaining First rule: l3 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : x^0'=n0+x^0, -__const_200^0+x^0 >= 0, cost: 2*n0 New rule: l3 -> l0 : x^0'=n0+x^0, -__const_200^0+x^0 >= 0, cost: 2+2*n0 Applied deletion Removed the following rules: 10 11 Chained accelerated rules with incoming rules Start location: l3 8: l3 -> l0 : TRUE, cost: 2 12: l3 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM 13: l3 -> l0 : x^0'=n0+x^0, -__const_200^0+x^0 >= 0, cost: 2+2*n0 Removed unreachable locations and irrelevant leafs Start location: l3 12: l3 -> [4] : -__const_200^0+x^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 12 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -__const_200^0+x^0 >= 0