NO Initial ITS Start location: l3 0: l0 -> l1 : x^0'=x^post0, __const_110^0'=__const_110^post0, __const_3000^0'=__const_3000^post0, __const_1000^0'=__const_1000^post0, y^0'=y^post0, __const_2000^0'=__const_2000^post0, (__const_110^0-__const_110^post0 == 0 /\ 1+__const_110^0-x^post0 <= 0 /\ -__const_3000^post0+__const_3000^0 == 0 /\ -__const_1000^post0+__const_1000^0 == 0 /\ -__const_2000^post0+__const_2000^0 == 0 /\ y^0-y^post0 == 0 /\ 1+y^0-__const_2000^0 <= 0 /\ -x^0+x^post0-__const_1000^0 == 0), cost: 1 1: l1 -> l0 : x^0'=x^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_1000^0'=__const_1000^post1, y^0'=y^post1, __const_2000^0'=__const_2000^post1, (-y^post1+y^0 == 0 /\ -__const_1000^post1+__const_1000^0 == 0 /\ -__const_2000^post1+__const_2000^0 == 0 /\ x^0-x^post1 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ __const_110^0-__const_110^post1 == 0), cost: 1 2: l2 -> l0 : x^0'=x^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_1000^0'=__const_1000^post2, y^0'=y^post2, __const_2000^0'=__const_2000^post2, (-__const_2000^post2+__const_2000^0 == 0 /\ __const_1000^0-__const_1000^post2 == 0 /\ __const_110^0-__const_110^post2 == 0 /\ y^post2-__const_3000^0 == 0 /\ x^0-x^post2 == 0 /\ __const_3000^0-__const_3000^post2 == 0), cost: 1 3: l3 -> l2 : x^0'=x^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_1000^0'=__const_1000^post3, y^0'=y^post3, __const_2000^0'=__const_2000^post3, (__const_1000^0-__const_1000^post3 == 0 /\ -__const_2000^post3+__const_2000^0 == 0 /\ __const_3000^0-__const_3000^post3 == 0 /\ __const_110^0-__const_110^post3 == 0 /\ x^0-x^post3 == 0 /\ -y^post3+y^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : x^0'=x^post0, __const_110^0'=__const_110^post0, __const_3000^0'=__const_3000^post0, __const_1000^0'=__const_1000^post0, y^0'=y^post0, __const_2000^0'=__const_2000^post0, (__const_110^0-__const_110^post0 == 0 /\ 1+__const_110^0-x^post0 <= 0 /\ -__const_3000^post0+__const_3000^0 == 0 /\ -__const_1000^post0+__const_1000^0 == 0 /\ -__const_2000^post0+__const_2000^0 == 0 /\ y^0-y^post0 == 0 /\ 1+y^0-__const_2000^0 <= 0 /\ -x^0+x^post0-__const_1000^0 == 0), cost: 1 New rule: l0 -> l1 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 1 Applied preprocessing Original rule: l1 -> l0 : x^0'=x^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_1000^0'=__const_1000^post1, y^0'=y^post1, __const_2000^0'=__const_2000^post1, (-y^post1+y^0 == 0 /\ -__const_1000^post1+__const_1000^0 == 0 /\ -__const_2000^post1+__const_2000^0 == 0 /\ x^0-x^post1 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ __const_110^0-__const_110^post1 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l0 : x^0'=x^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_1000^0'=__const_1000^post2, y^0'=y^post2, __const_2000^0'=__const_2000^post2, (-__const_2000^post2+__const_2000^0 == 0 /\ __const_1000^0-__const_1000^post2 == 0 /\ __const_110^0-__const_110^post2 == 0 /\ y^post2-__const_3000^0 == 0 /\ x^0-x^post2 == 0 /\ __const_3000^0-__const_3000^post2 == 0), cost: 1 New rule: l2 -> l0 : y^0'=__const_3000^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l2 : x^0'=x^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_1000^0'=__const_1000^post3, y^0'=y^post3, __const_2000^0'=__const_2000^post3, (__const_1000^0-__const_1000^post3 == 0 /\ -__const_2000^post3+__const_2000^0 == 0 /\ __const_3000^0-__const_3000^post3 == 0 /\ __const_110^0-__const_110^post3 == 0 /\ x^0-x^post3 == 0 /\ -y^post3+y^0 == 0), cost: 1 New rule: l3 -> l2 : TRUE, cost: 1 Simplified rules Start location: l3 4: l0 -> l1 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 1 5: l1 -> l0 : TRUE, cost: 1 6: l2 -> l0 : y^0'=__const_3000^0, 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 : y^0'=__const_3000^0, TRUE, cost: 1 New rule: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 Applied deletion Removed the following rules: 6 7 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: l3 9: l0 -> l0 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 2 8: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 Applied acceleration Original rule: l0 -> l0 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 2 New rule: l0 -> l0 : x^0'=x^0+n*__const_1000^0, (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ n >= 0 /\ -1+x^0-__const_110^0+__const_1000^0+__const_1000^0*(-1+n) >= 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_kNLOBa.txt Applied nonterm Original rule: l0 -> l0 : x^0'=x^0+__const_1000^0, (1+y^0-__const_2000^0 <= 0 /\ 1-x^0+__const_110^0-__const_1000^0 <= 0), cost: 2 New rule: l0 -> [4] : (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -__const_1000^0 <= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_CpGdnl.txt Applied simplification Original rule: l0 -> [4] : (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -__const_1000^0 <= 0), cost: NONTERM New rule: l0 -> [4] : (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ __const_1000^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 9 Accelerated simple loops Start location: l3 10: l0 -> l0 : x^0'=x^0+n*__const_1000^0, (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ n >= 0 /\ -1+x^0-__const_110^0+__const_1000^0+__const_1000^0*(-1+n) >= 0), cost: 2*n 12: l0 -> [4] : (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ __const_1000^0 >= 0), cost: NONTERM 8: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 Applied chaining First rule: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 Second rule: l0 -> l0 : x^0'=x^0+n*__const_1000^0, (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ n >= 0 /\ -1+x^0-__const_110^0+__const_1000^0+__const_1000^0*(-1+n) >= 0), cost: 2*n New rule: l3 -> l0 : x^0'=x^0+n*__const_1000^0, y^0'=__const_3000^0, (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ n >= 0 /\ -1+x^0-__const_110^0+__const_1000^0+__const_1000^0*(-1+n) >= 0), cost: 2+2*n Applied chaining First rule: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 Second rule: l0 -> [4] : (-1-y^0+__const_2000^0 >= 0 /\ -1+x^0-__const_110^0+__const_1000^0 >= 0 /\ __const_1000^0 >= 0), cost: NONTERM New rule: l3 -> [4] : (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ __const_1000^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 10 12 Chained accelerated rules with incoming rules Start location: l3 8: l3 -> l0 : y^0'=__const_3000^0, TRUE, cost: 2 13: l3 -> l0 : x^0'=x^0+n*__const_1000^0, y^0'=__const_3000^0, (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ n >= 0 /\ -1+x^0-__const_110^0+__const_1000^0+__const_1000^0*(-1+n) >= 0), cost: 2+2*n 14: l3 -> [4] : (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ __const_1000^0 >= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l3 14: l3 -> [4] : (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ __const_1000^0 >= 0), 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: (-1+x^0-__const_110^0+__const_1000^0 >= 0 /\ -1-__const_3000^0+__const_2000^0 >= 0 /\ __const_1000^0 >= 0)