NO Initial ITS Start location: l4 0: l0 -> l1 : __const_100^0'=__const_100^post0, __const_11^0'=__const_11^post0, n^0'=n^post0, __const_10^0'=__const_10^post0, e^0'=e^post0, (-1+e^post0-e^0 == 0 /\ -__const_100^0+n^0 <= 0 /\ -__const_11^0-n^0+n^post0 == 0 /\ __const_100^0-__const_100^post0 == 0 /\ -__const_10^post0+__const_10^0 == 0 /\ __const_11^0-__const_11^post0 == 0 /\ 1-e^0 <= 0), cost: 1 2: l0 -> l2 : __const_100^0'=__const_100^post2, __const_11^0'=__const_11^post2, n^0'=n^post2, __const_10^0'=__const_10^post2, e^0'=e^post2, (1+__const_100^0-n^0 <= 0 /\ __const_100^0-__const_100^post2 == 0 /\ -__const_10^post2+__const_10^0 == 0 /\ __const_11^0-__const_11^post2 == 0 /\ 1+e^post2-e^0 == 0 /\ n^post2-n^0+__const_10^0 == 0 /\ 1-e^0 <= 0), cost: 1 1: l1 -> l0 : __const_100^0'=__const_100^post1, __const_11^0'=__const_11^post1, n^0'=n^post1, __const_10^0'=__const_10^post1, e^0'=e^post1, (-n^post1+n^0 == 0 /\ __const_100^0-__const_100^post1 == 0 /\ __const_10^0-__const_10^post1 == 0 /\ -e^post1+e^0 == 0 /\ -__const_11^post1+__const_11^0 == 0), cost: 1 3: l2 -> l0 : __const_100^0'=__const_100^post3, __const_11^0'=__const_11^post3, n^0'=n^post3, __const_10^0'=__const_10^post3, e^0'=e^post3, (-e^post3+e^0 == 0 /\ n^0-n^post3 == 0 /\ __const_10^0-__const_10^post3 == 0 /\ __const_11^0-__const_11^post3 == 0 /\ __const_100^0-__const_100^post3 == 0), cost: 1 4: l3 -> l0 : __const_100^0'=__const_100^post4, __const_11^0'=__const_11^post4, n^0'=n^post4, __const_10^0'=__const_10^post4, e^0'=e^post4, (0 == 0 /\ -__const_10^post4+__const_10^0 == 0 /\ __const_100^0-__const_100^post4 == 0 /\ __const_11^0-__const_11^post4 == 0 /\ -1+e^post4 == 0), cost: 1 5: l4 -> l3 : __const_100^0'=__const_100^post5, __const_11^0'=__const_11^post5, n^0'=n^post5, __const_10^0'=__const_10^post5, e^0'=e^post5, (-e^post5+e^0 == 0 /\ n^0-n^post5 == 0 /\ __const_100^0-__const_100^post5 == 0 /\ -__const_10^post5+__const_10^0 == 0 /\ __const_11^0-__const_11^post5 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : __const_100^0'=__const_100^post0, __const_11^0'=__const_11^post0, n^0'=n^post0, __const_10^0'=__const_10^post0, e^0'=e^post0, (-1+e^post0-e^0 == 0 /\ -__const_100^0+n^0 <= 0 /\ -__const_11^0-n^0+n^post0 == 0 /\ __const_100^0-__const_100^post0 == 0 /\ -__const_10^post0+__const_10^0 == 0 /\ __const_11^0-__const_11^post0 == 0 /\ 1-e^0 <= 0), cost: 1 New rule: l0 -> l1 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 Applied preprocessing Original rule: l1 -> l0 : __const_100^0'=__const_100^post1, __const_11^0'=__const_11^post1, n^0'=n^post1, __const_10^0'=__const_10^post1, e^0'=e^post1, (-n^post1+n^0 == 0 /\ __const_100^0-__const_100^post1 == 0 /\ __const_10^0-__const_10^post1 == 0 /\ -e^post1+e^0 == 0 /\ -__const_11^post1+__const_11^0 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l2 : __const_100^0'=__const_100^post2, __const_11^0'=__const_11^post2, n^0'=n^post2, __const_10^0'=__const_10^post2, e^0'=e^post2, (1+__const_100^0-n^0 <= 0 /\ __const_100^0-__const_100^post2 == 0 /\ -__const_10^post2+__const_10^0 == 0 /\ __const_11^0-__const_11^post2 == 0 /\ 1+e^post2-e^0 == 0 /\ n^post2-n^0+__const_10^0 == 0 /\ 1-e^0 <= 0), cost: 1 New rule: l0 -> l2 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 Applied preprocessing Original rule: l2 -> l0 : __const_100^0'=__const_100^post3, __const_11^0'=__const_11^post3, n^0'=n^post3, __const_10^0'=__const_10^post3, e^0'=e^post3, (-e^post3+e^0 == 0 /\ n^0-n^post3 == 0 /\ __const_10^0-__const_10^post3 == 0 /\ __const_11^0-__const_11^post3 == 0 /\ __const_100^0-__const_100^post3 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : __const_100^0'=__const_100^post4, __const_11^0'=__const_11^post4, n^0'=n^post4, __const_10^0'=__const_10^post4, e^0'=e^post4, (0 == 0 /\ -__const_10^post4+__const_10^0 == 0 /\ __const_100^0-__const_100^post4 == 0 /\ __const_11^0-__const_11^post4 == 0 /\ -1+e^post4 == 0), cost: 1 New rule: l3 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : __const_100^0'=__const_100^post5, __const_11^0'=__const_11^post5, n^0'=n^post5, __const_10^0'=__const_10^post5, e^0'=e^post5, (-e^post5+e^0 == 0 /\ n^0-n^post5 == 0 /\ __const_100^0-__const_100^post5 == 0 /\ -__const_10^post5+__const_10^0 == 0 /\ __const_11^0-__const_11^post5 == 0), cost: 1 New rule: l4 -> l3 : TRUE, cost: 1 Simplified rules Start location: l4 6: l0 -> l1 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 8: l0 -> l2 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 7: l1 -> l0 : TRUE, cost: 1 9: l2 -> l0 : TRUE, cost: 1 10: l3 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 1 11: l4 -> l3 : TRUE, cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 1 New rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Applied deletion Removed the following rules: 6 7 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Applied deletion Removed the following rules: 8 9 Eliminated locations on linear paths Start location: l4 13: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 14: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 12: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Applied acceleration Original rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 New rule: l0 -> l0 : n^0'=__const_11^0*n1+n^0, e^0'=n1+e^0, (__const_100^0-n^0 >= 0 /\ __const_100^0-__const_11^0*(-1+n1)-n^0 >= 0 /\ n1 >= 0 /\ -1+e^0 >= 0), cost: 2*n1 Applied recurrent set Original rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 New rule: l0 -> [5] : (-__const_100^0+n^0 <= 0 /\ 1+__const_11^0 <= 0 /\ -1+e^0 >= 0), cost: NONTERM Applied acceleration Original rule: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 New rule: l0 -> l0 : n^0'=n^0-__const_10^0*n3, e^0'=e^0-n3, (e^0-n3 >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ n3 >= 0 /\ -1-__const_100^0-(-1+n3)*__const_10^0+n^0 >= 0), cost: 2*n3 Applied instantiation Original rule: l0 -> l0 : n^0'=n^0-__const_10^0*n3, e^0'=e^0-n3, (e^0-n3 >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ n3 >= 0 /\ -1-__const_100^0-(-1+n3)*__const_10^0+n^0 >= 0), cost: 2*n3 New rule: l0 -> l0 : n^0'=n^0-__const_10^0*e^0, e^0'=0, (0 >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ -1-__const_100^0+n^0-__const_10^0*(-1+e^0) >= 0 /\ e^0 >= 0), cost: 2*e^0 Applied chaining First rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Second rule: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 New rule: l0 -> l0 : n^0'=__const_11^0+n^0-__const_10^0, (1+__const_100^0-__const_11^0-n^0 <= 0 /\ -__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 4 Applied acceleration Original rule: l0 -> l0 : n^0'=__const_11^0+n^0-__const_10^0, (1+__const_100^0-__const_11^0-n^0 <= 0 /\ -__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 4 New rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0*n5, (__const_100^0-n^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0+__const_11^0*(-1+n5) >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 4*n5 Applied chaining First rule: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0*n5, (__const_100^0-n^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0+__const_11^0*(-1+n5) >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 4*n5 New rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0-__const_10^0*n5, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0-__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0-__const_10^0+__const_11^0*(-1+n5) >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0+__const_10^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 2+4*n5 Applied chaining First rule: l0 -> l0 : n^0'=n^0-__const_10^0, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 New rule: l0 -> l0 : n^0'=__const_11^0+n^0-__const_10^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ -__const_100^0+n^0-__const_10^0 <= 0), cost: 4 Applied acceleration Original rule: l0 -> l0 : n^0'=__const_11^0+n^0-__const_10^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ -__const_100^0+n^0-__const_10^0 <= 0), cost: 4 New rule: l0 -> l0 : n^0'=__const_11^0*n7+n^0-__const_10^0*n7, (-2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+n^0+__const_11^0*(-1+n7) >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ __const_100^0+__const_10^0*(-1+n7)-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ n7 >= 0), cost: 4*n7 Applied chaining First rule: l0 -> l0 : n^0'=__const_11^0+n^0, e^0'=1+e^0, (-__const_100^0+n^0 <= 0 /\ -1+e^0 >= 0), cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0*n7+n^0-__const_10^0*n7, (-2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+n^0+__const_11^0*(-1+n7) >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ __const_100^0+__const_10^0*(-1+n7)-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ n7 >= 0), cost: 4*n7 New rule: l0 -> l0 : n^0'=__const_11^0*n7+__const_11^0+n^0-__const_10^0*n7, e^0'=1+e^0, (__const_100^0-__const_11^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+__const_11^0+n^0+__const_11^0*(-1+n7) >= 0 /\ -__const_100^0+n^0 <= 0 /\ __const_100^0+__const_10^0*(-1+n7)-__const_11^0-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ n7 >= 0 /\ -1+e^0 >= 0), cost: 2+4*n7 Applied simplification Original rule: l0 -> l0 : n^0'=n^0-__const_10^0*e^0, e^0'=0, (0 >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ -1-__const_100^0+n^0-__const_10^0*(-1+e^0) >= 0 /\ e^0 >= 0), cost: 2*e^0 New rule: l0 -> l0 : n^0'=n^0-__const_10^0*e^0, e^0'=0, (-1-__const_100^0+n^0 >= 0 /\ -1-__const_100^0+n^0-__const_10^0*(-1+e^0) >= 0 /\ e^0 >= 0), cost: 2*e^0 Applied simplification Original rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0-__const_10^0*n5, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0-__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0-__const_10^0+__const_11^0*(-1+n5) >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0+__const_10^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 2+4*n5 New rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0-__const_10^0*n5, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0-__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0-__const_10^0+__const_11^0*(-1+n5) >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0+__const_10^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0), cost: 2+4*n5 Applied deletion Removed the following rules: 13 14 Accelerated simple loops Start location: l4 15: l0 -> l0 : n^0'=__const_11^0*n1+n^0, e^0'=n1+e^0, (__const_100^0-n^0 >= 0 /\ __const_100^0-__const_11^0*(-1+n1)-n^0 >= 0 /\ n1 >= 0 /\ -1+e^0 >= 0), cost: 2*n1 16: l0 -> [5] : (-__const_100^0+n^0 <= 0 /\ 1+__const_11^0 <= 0 /\ -1+e^0 >= 0), cost: NONTERM 18: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0*n5, (__const_100^0-n^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0+__const_11^0*(-1+n5) >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 4*n5 20: l0 -> l0 : n^0'=__const_11^0*n7+n^0-__const_10^0*n7, (-2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+n^0+__const_11^0*(-1+n7) >= 0 /\ -1-__const_100^0+n^0 >= 0 /\ __const_100^0+__const_10^0*(-1+n7)-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ n7 >= 0), cost: 4*n7 21: l0 -> l0 : n^0'=__const_11^0*n7+__const_11^0+n^0-__const_10^0*n7, e^0'=1+e^0, (__const_100^0-__const_11^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+__const_11^0+n^0+__const_11^0*(-1+n7) >= 0 /\ -__const_100^0+n^0 <= 0 /\ __const_100^0+__const_10^0*(-1+n7)-__const_11^0-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ n7 >= 0 /\ -1+e^0 >= 0), cost: 2+4*n7 22: l0 -> l0 : n^0'=n^0-__const_10^0*e^0, e^0'=0, (-1-__const_100^0+n^0 >= 0 /\ -1-__const_100^0+n^0-__const_10^0*(-1+e^0) >= 0 /\ e^0 >= 0), cost: 2*e^0 23: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0-__const_10^0*n5, e^0'=-1+e^0, (1+__const_100^0-n^0 <= 0 /\ -2+e^0 >= 0 /\ __const_100^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0-__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0-__const_10^0+__const_11^0*(-1+n5) >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0+__const_10^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0), cost: 2+4*n5 12: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Applied chaining First rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0*n1+n^0, e^0'=n1+e^0, (__const_100^0-n^0 >= 0 /\ __const_100^0-__const_11^0*(-1+n1)-n^0 >= 0 /\ n1 >= 0 /\ -1+e^0 >= 0), cost: 2*n1 New rule: l4 -> l0 : n^0'=n^post4+__const_11^0*n1, e^0'=1+n1, (__const_100^0-n^post4-__const_11^0*(-1+n1) >= 0 /\ __const_100^0-n^post4 >= 0 /\ n1 >= 0), cost: 2+2*n1 Applied chaining First rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Second rule: l0 -> [5] : (-__const_100^0+n^0 <= 0 /\ 1+__const_11^0 <= 0 /\ -1+e^0 >= 0), cost: NONTERM New rule: l4 -> [5] : 1+__const_11^0 <= 0, cost: NONTERM Applied chaining First rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0*n5+n^0-__const_10^0*n5, (__const_100^0-n^0 >= 0 /\ -1-__const_100^0+__const_11^0-(-1+n5)*__const_10^0+n^0+__const_11^0*(-1+n5) >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ __const_100^0+(-1+n5)*__const_10^0-n^0-__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ -1+e^0 >= 0), cost: 4*n5 New rule: l4 -> l0 : n^0'=n^post4+__const_11^0*n5-__const_10^0*n5, e^0'=1, (-1-__const_100^0+n^post4+__const_11^0 >= 0 /\ __const_100^0-n^post4 >= 0 /\ -1-__const_100^0+n^post4+__const_11^0-(-1+n5)*__const_10^0+__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ __const_100^0-n^post4+(-1+n5)*__const_10^0-__const_11^0*(-1+n5) >= 0), cost: 2+4*n5 Applied chaining First rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Second rule: l0 -> l0 : n^0'=__const_11^0*n7+__const_11^0+n^0-__const_10^0*n7, e^0'=1+e^0, (__const_100^0-__const_11^0-n^0+__const_10^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+__const_11^0+n^0+__const_11^0*(-1+n7) >= 0 /\ -__const_100^0+n^0 <= 0 /\ __const_100^0+__const_10^0*(-1+n7)-__const_11^0-n^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ -1-__const_100^0+__const_11^0+n^0 >= 0 /\ n7 >= 0 /\ -1+e^0 >= 0), cost: 2+4*n7 New rule: l4 -> l0 : n^0'=__const_11^0*n7+n^post4+__const_11^0-__const_10^0*n7, e^0'=2, (-1-__const_100^0+n^post4+__const_11^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+n^post4+__const_11^0+__const_11^0*(-1+n7) >= 0 /\ __const_100^0-n^post4-__const_11^0+__const_10^0 >= 0 /\ -__const_100^0+n^post4 <= 0 /\ __const_100^0+__const_10^0*(-1+n7)-n^post4-__const_11^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ n7 >= 0), cost: 4+4*n7 Applied chaining First rule: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 Second rule: l0 -> l0 : n^0'=n^0-__const_10^0*e^0, e^0'=0, (-1-__const_100^0+n^0 >= 0 /\ -1-__const_100^0+n^0-__const_10^0*(-1+e^0) >= 0 /\ e^0 >= 0), cost: 2*e^0 New rule: l4 -> l0 : n^0'=n^post4-__const_10^0, e^0'=0, -1-__const_100^0+n^post4 >= 0, cost: 4 Applied deletion Removed the following rules: 15 16 18 20 21 22 23 Chained accelerated rules with incoming rules Start location: l4 12: l4 -> l0 : n^0'=n^post4, e^0'=1, 0 == 0, cost: 2 24: l4 -> l0 : n^0'=n^post4+__const_11^0*n1, e^0'=1+n1, (__const_100^0-n^post4-__const_11^0*(-1+n1) >= 0 /\ __const_100^0-n^post4 >= 0 /\ n1 >= 0), cost: 2+2*n1 25: l4 -> [5] : 1+__const_11^0 <= 0, cost: NONTERM 26: l4 -> l0 : n^0'=n^post4+__const_11^0*n5-__const_10^0*n5, e^0'=1, (-1-__const_100^0+n^post4+__const_11^0 >= 0 /\ __const_100^0-n^post4 >= 0 /\ -1-__const_100^0+n^post4+__const_11^0-(-1+n5)*__const_10^0+__const_11^0*(-1+n5) >= 0 /\ n5 >= 0 /\ __const_100^0-n^post4+(-1+n5)*__const_10^0-__const_11^0*(-1+n5) >= 0), cost: 2+4*n5 27: l4 -> l0 : n^0'=__const_11^0*n7+n^post4+__const_11^0-__const_10^0*n7, e^0'=2, (-1-__const_100^0+n^post4+__const_11^0 >= 0 /\ -1-__const_100^0-__const_10^0*(-1+n7)+n^post4+__const_11^0+__const_11^0*(-1+n7) >= 0 /\ __const_100^0-n^post4-__const_11^0+__const_10^0 >= 0 /\ -__const_100^0+n^post4 <= 0 /\ __const_100^0+__const_10^0*(-1+n7)-n^post4-__const_11^0-__const_11^0*(-1+n7)+__const_10^0 >= 0 /\ n7 >= 0), cost: 4+4*n7 28: l4 -> l0 : n^0'=n^post4-__const_10^0, e^0'=0, -1-__const_100^0+n^post4 >= 0, cost: 4 Removed unreachable locations and irrelevant leafs Start location: l4 25: l4 -> [5] : 1+__const_11^0 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 25 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 1+__const_11^0 <= 0