NO Initial ITS Start location: l4 0: l0 -> l2 : __disjvr_0^0'=__disjvr_0^post0, __const_100^0'=__const_100^post0, x^0'=x^post0, (1-x^0+x^post0 == 0 /\ __const_100^0-__const_100^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0), cost: 1 1: l2 -> l1 : __disjvr_0^0'=__disjvr_0^post1, __const_100^0'=__const_100^post1, x^0'=x^post1, (x^0-x^post1 == 0 /\ __const_100^0-__const_100^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ -__disjvr_0^0+__disjvr_0^post1 == 0), cost: 1 2: l1 -> l0 : __disjvr_0^0'=__disjvr_0^post2, __const_100^0'=__const_100^post2, x^0'=x^post2, (x^0-x^post2 == 0 /\ __disjvr_0^0-__disjvr_0^post2 == 0 /\ -__const_100^post2+__const_100^0 == 0), cost: 1 3: l3 -> l0 : __disjvr_0^0'=__disjvr_0^post3, __const_100^0'=__const_100^post3, x^0'=x^post3, (-__const_100^post3+__const_100^0 == 0 /\ -__disjvr_0^post3+__disjvr_0^0 == 0 /\ -__const_100^0+x^post3 == 0), cost: 1 4: l4 -> l3 : __disjvr_0^0'=__disjvr_0^post4, __const_100^0'=__const_100^post4, x^0'=x^post4, (-__const_100^post4+__const_100^0 == 0 /\ -x^post4+x^0 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : __disjvr_0^0'=__disjvr_0^post0, __const_100^0'=__const_100^post0, x^0'=x^post0, (1-x^0+x^post0 == 0 /\ __const_100^0-__const_100^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0), cost: 1 New rule: l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l1 : __disjvr_0^0'=__disjvr_0^post1, __const_100^0'=__const_100^post1, x^0'=x^post1, (x^0-x^post1 == 0 /\ __const_100^0-__const_100^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ -__disjvr_0^0+__disjvr_0^post1 == 0), cost: 1 New rule: l2 -> l1 : 0 == 0, cost: 1 Applied preprocessing Original rule: l1 -> l0 : __disjvr_0^0'=__disjvr_0^post2, __const_100^0'=__const_100^post2, x^0'=x^post2, (x^0-x^post2 == 0 /\ __disjvr_0^0-__disjvr_0^post2 == 0 /\ -__const_100^post2+__const_100^0 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : __disjvr_0^0'=__disjvr_0^post3, __const_100^0'=__const_100^post3, x^0'=x^post3, (-__const_100^post3+__const_100^0 == 0 /\ -__disjvr_0^post3+__disjvr_0^0 == 0 /\ -__const_100^0+x^post3 == 0), cost: 1 New rule: l3 -> l0 : x^0'=__const_100^0, TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l3 : __disjvr_0^0'=__disjvr_0^post4, __const_100^0'=__const_100^post4, x^0'=x^post4, (-__const_100^post4+__const_100^0 == 0 /\ -x^post4+x^0 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0), cost: 1 New rule: l4 -> l3 : TRUE, cost: 1 Simplified rules Start location: l4 5: l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1 6: l2 -> l1 : 0 == 0, cost: 1 7: l1 -> l0 : TRUE, cost: 1 8: l3 -> l0 : x^0'=__const_100^0, TRUE, cost: 1 9: l4 -> l3 : TRUE, cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : x^0'=__const_100^0, TRUE, cost: 1 New rule: l4 -> l0 : x^0'=__const_100^0, TRUE, cost: 2 Applied deletion Removed the following rules: 8 9 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1 Second rule: l2 -> l1 : 0 == 0, cost: 1 New rule: l0 -> l1 : x^0'=-1+x^0, 0 == 0, cost: 2 Applied deletion Removed the following rules: 5 6 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : x^0'=-1+x^0, 0 == 0, cost: 2 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x^0'=-1+x^0, 0 == 0, cost: 3 Applied deletion Removed the following rules: 7 11 Eliminated locations on linear paths Start location: l4 12: l0 -> l0 : x^0'=-1+x^0, 0 == 0, cost: 3 10: l4 -> l0 : x^0'=__const_100^0, TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : x^0'=-1+x^0, 0 == 0, cost: 3 New rule: l0 -> [5] : (0 >= 0 /\ n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_CfkCOL.txt Applied simplification Original rule: l0 -> [5] : (0 >= 0 /\ n >= 0), cost: NONTERM New rule: l0 -> [5] : n >= 0, cost: NONTERM Applied deletion Removed the following rules: 12 Accelerated simple loops Start location: l4 14: l0 -> [5] : n >= 0, cost: NONTERM 10: l4 -> l0 : x^0'=__const_100^0, TRUE, cost: 2 Applied chaining First rule: l4 -> l0 : x^0'=__const_100^0, TRUE, cost: 2 Second rule: l0 -> [5] : n >= 0, cost: NONTERM New rule: l4 -> [5] : TRUE, cost: NONTERM Applied deletion Removed the following rules: 14 Chained accelerated rules with incoming rules Start location: l4 10: l4 -> l0 : x^0'=__const_100^0, TRUE, cost: 2 15: l4 -> [5] : TRUE, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 15: l4 -> [5] : TRUE, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 15 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: TRUE