NO Initial ITS Start location: l6 0: l0 -> l1 : tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, (tmp^0-tmp^post0 == 0 /\ -low6^post0+low6^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -up5^post0+up5^0 == 0 /\ -fvalue3^post0+fvalue3^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post0 == 0 /\ x2^0-x2^post0 == 0), cost: 1 1: l0 -> l2 : tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, (0 == 0 /\ x2^0-x2^post1 == 0 /\ tmp^0-tmp^post1 == 0 /\ low6^0-low6^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ -mid4^post1+mid4^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post1 == 0), cost: 1 2: l0 -> l1 : tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, (low6^0-low6^post2 == 0 /\ mid4^0-mid4^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -up5^post2+up5^0 == 0 /\ x2^0-x2^post2 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ -fvalue3^post2+fvalue3^0 == 0), cost: 1 6: l1 -> l2 : tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, (tmp^0-tmp^post6 == 0 /\ -fvalue3^post6+fvalue3^0 == 0 /\ -up5^post6+up5^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ -mid4^post6+mid4^0 == 0 /\ -1+low6^post6-mid4^0 == 0 /\ x2^0-x2^post6 == 0), cost: 1 7: l1 -> l2 : tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, (-ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ -mid4^post7+mid4^0 == 0 /\ x2^0-x2^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -fvalue3^post7+fvalue3^0 == 0 /\ 1+up5^post7-mid4^0 == 0 /\ low6^0-low6^post7 == 0), cost: 1 5: l2 -> l3 : tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, (ret_binary_search7^0-ret_binary_search7^post5 == 0 /\ -x2^post5+x2^0 == 0 /\ -mid4^post5+mid4^0 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -up5^post5+up5^0 == 0 /\ low6^0-low6^post5 == 0 /\ tmp^0-tmp^post5 == 0), cost: 1 3: l3 -> l4 : tmp^0'=tmp^post3, low6^0'=low6^post3, x2^0'=x2^post3, ret_binary_search7^0'=ret_binary_search7^post3, fvalue3^0'=fvalue3^post3, up5^0'=up5^post3, mid4^0'=mid4^post3, (1-low6^0+up5^0 <= 0 /\ -mid4^post3+mid4^0 == 0 /\ -x2^post3+x2^0 == 0 /\ low6^0-low6^post3 == 0 /\ -ret_binary_search7^post3+tmp^post3 == 0 /\ up5^0-up5^post3 == 0 /\ fvalue3^0-fvalue3^post3 == 0 /\ ret_binary_search7^post3-fvalue3^0 == 0), cost: 1 4: l3 -> l0 : tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, (0 == 0 /\ -x2^post4+x2^0 == 0 /\ low6^0-up5^0 <= 0 /\ tmp^0-tmp^post4 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ up5^0-up5^post4 == 0 /\ low6^0-low6^post4 == 0), cost: 1 8: l5 -> l2 : tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, (-8+x2^post8 == 0 /\ mid4^0-mid4^post8 == 0 /\ low6^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ 1+fvalue3^post8 == 0 /\ tmp^0-tmp^post8 == 0 /\ -14+up5^post8 == 0), cost: 1 9: l6 -> l5 : tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, (low6^0-low6^post9 == 0 /\ tmp^0-tmp^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ up5^0-up5^post9 == 0 /\ x2^0-x2^post9 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -fvalue3^post9+fvalue3^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 0: l0 -> l1 : tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, (tmp^0-tmp^post0 == 0 /\ -low6^post0+low6^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -up5^post0+up5^0 == 0 /\ -fvalue3^post0+fvalue3^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post0 == 0 /\ x2^0-x2^post0 == 0), cost: 1 1: l0 -> l2 : tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, (0 == 0 /\ x2^0-x2^post1 == 0 /\ tmp^0-tmp^post1 == 0 /\ low6^0-low6^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ -mid4^post1+mid4^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post1 == 0), cost: 1 2: l0 -> l1 : tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, (low6^0-low6^post2 == 0 /\ mid4^0-mid4^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -up5^post2+up5^0 == 0 /\ x2^0-x2^post2 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ -fvalue3^post2+fvalue3^0 == 0), cost: 1 6: l1 -> l2 : tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, (tmp^0-tmp^post6 == 0 /\ -fvalue3^post6+fvalue3^0 == 0 /\ -up5^post6+up5^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ -mid4^post6+mid4^0 == 0 /\ -1+low6^post6-mid4^0 == 0 /\ x2^0-x2^post6 == 0), cost: 1 7: l1 -> l2 : tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, (-ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ -mid4^post7+mid4^0 == 0 /\ x2^0-x2^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -fvalue3^post7+fvalue3^0 == 0 /\ 1+up5^post7-mid4^0 == 0 /\ low6^0-low6^post7 == 0), cost: 1 5: l2 -> l3 : tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, (ret_binary_search7^0-ret_binary_search7^post5 == 0 /\ -x2^post5+x2^0 == 0 /\ -mid4^post5+mid4^0 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -up5^post5+up5^0 == 0 /\ low6^0-low6^post5 == 0 /\ tmp^0-tmp^post5 == 0), cost: 1 4: l3 -> l0 : tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, (0 == 0 /\ -x2^post4+x2^0 == 0 /\ low6^0-up5^0 <= 0 /\ tmp^0-tmp^post4 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ up5^0-up5^post4 == 0 /\ low6^0-low6^post4 == 0), cost: 1 8: l5 -> l2 : tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, (-8+x2^post8 == 0 /\ mid4^0-mid4^post8 == 0 /\ low6^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ 1+fvalue3^post8 == 0 /\ tmp^0-tmp^post8 == 0 /\ -14+up5^post8 == 0), cost: 1 9: l6 -> l5 : tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, (low6^0-low6^post9 == 0 /\ tmp^0-tmp^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ up5^0-up5^post9 == 0 /\ x2^0-x2^post9 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -fvalue3^post9+fvalue3^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, (tmp^0-tmp^post0 == 0 /\ -low6^post0+low6^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -up5^post0+up5^0 == 0 /\ -fvalue3^post0+fvalue3^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post0 == 0 /\ x2^0-x2^post0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l2 : tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, (0 == 0 /\ x2^0-x2^post1 == 0 /\ tmp^0-tmp^post1 == 0 /\ low6^0-low6^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ -mid4^post1+mid4^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post1 == 0), cost: 1 New rule: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 Applied preprocessing Original rule: l0 -> l1 : tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, (low6^0-low6^post2 == 0 /\ mid4^0-mid4^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -up5^post2+up5^0 == 0 /\ x2^0-x2^post2 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ -fvalue3^post2+fvalue3^0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, (0 == 0 /\ -x2^post4+x2^0 == 0 /\ low6^0-up5^0 <= 0 /\ tmp^0-tmp^post4 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ up5^0-up5^post4 == 0 /\ low6^0-low6^post4 == 0), cost: 1 New rule: l3 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, (ret_binary_search7^0-ret_binary_search7^post5 == 0 /\ -x2^post5+x2^0 == 0 /\ -mid4^post5+mid4^0 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -up5^post5+up5^0 == 0 /\ low6^0-low6^post5 == 0 /\ tmp^0-tmp^post5 == 0), cost: 1 New rule: l2 -> l3 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, (tmp^0-tmp^post6 == 0 /\ -fvalue3^post6+fvalue3^0 == 0 /\ -up5^post6+up5^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ -mid4^post6+mid4^0 == 0 /\ -1+low6^post6-mid4^0 == 0 /\ x2^0-x2^post6 == 0), cost: 1 New rule: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, (-ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ -mid4^post7+mid4^0 == 0 /\ x2^0-x2^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -fvalue3^post7+fvalue3^0 == 0 /\ 1+up5^post7-mid4^0 == 0 /\ low6^0-low6^post7 == 0), cost: 1 New rule: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l2 : tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, (-8+x2^post8 == 0 /\ mid4^0-mid4^post8 == 0 /\ low6^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ 1+fvalue3^post8 == 0 /\ tmp^0-tmp^post8 == 0 /\ -14+up5^post8 == 0), cost: 1 New rule: l5 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, (low6^0-low6^post9 == 0 /\ tmp^0-tmp^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ up5^0-up5^post9 == 0 /\ x2^0-x2^post9 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -fvalue3^post9+fvalue3^0 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 10: l0 -> l1 : TRUE, cost: 1 11: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 14: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 15: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 13: l2 -> l3 : TRUE, cost: 1 12: l3 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 1 16: l5 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 1 17: l6 -> l5 : TRUE, cost: 1 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 1 New rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Applied deletion Removed the following rules: 16 17 Eliminating location l3 by chaining: Applied chaining First rule: l2 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 1 New rule: l2 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 12 13 Eliminated locations on linear paths Start location: l6 10: l0 -> l1 : TRUE, cost: 1 11: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 14: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 15: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 19: l2 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 2 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Eliminating location l0 by chaining: Applied chaining First rule: l2 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 2 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Applied chaining First rule: l2 -> l0 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 2 Second rule: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (0 == 0 /\ low6^0-up5^0 <= 0), cost: 3 Applied simplification Original rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (0 == 0 /\ low6^0-up5^0 <= 0), cost: 3 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Applied deletion Removed the following rules: 10 11 19 Eliminated locations on tree-shaped paths Start location: l6 14: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 15: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 20: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 21: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Accelerated simple loops Start location: l6 14: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 15: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 20: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 21: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Applied chaining First rule: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 New rule: l1 -> l2 : low6^0'=1+mid4^0, fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, 1-up5^0+mid4^0 <= 0, cost: 4 Applied chaining First rule: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 New rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1+low6^0-mid4^0 <= 0, cost: 4 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 New rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -14 <= 0, cost: 5 Applied deletion Removed the following rules: 21 Chained accelerated rules with incoming rules Start location: l6 14: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 15: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 22: l1 -> l2 : low6^0'=1+mid4^0, fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, 1-up5^0+mid4^0 <= 0, cost: 4 23: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1+low6^0-mid4^0 <= 0, cost: 4 20: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 24: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -14 <= 0, cost: 5 Eliminating location l1 by chaining: Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Second rule: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 New rule: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Second rule: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 New rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Second rule: l1 -> l2 : low6^0'=1+mid4^0, fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, 1-up5^0+mid4^0 <= 0, cost: 4 New rule: l2 -> l2 : low6^0'=1+mid4^post4, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+mid4^post4-up5^0 <= 0), cost: 7 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 3 Second rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1+low6^0-mid4^0 <= 0, cost: 4 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+low6^0-mid4^post4 <= 0), cost: 7 Applied deletion Removed the following rules: 14 15 20 22 23 Eliminated locations on tree-shaped paths Start location: l6 25: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 26: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 27: l2 -> l2 : low6^0'=1+mid4^post4, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+mid4^post4-up5^0 <= 0), cost: 7 28: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+low6^0-mid4^post4 <= 0), cost: 7 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 24: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -14 <= 0, cost: 5 Applied acceleration Original rule: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 New rule: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, (-low6^0+up5^0 >= 0 /\ -1-mid4^post4+up5^0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_aCdAbk.txt Applied nonterm Original rule: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 New rule: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-low6^0+mid4^post4 <= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_KDJiOO.txt Applied acceleration Original rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 New rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ -low6^0+up5^0 >= 0 /\ -1+n1 >= 0), cost: 4*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_DhckJn.txt Applied nonterm Original rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0-up5^0 <= 0, cost: 4 New rule: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-mid4^post4+up5^0 <= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_GnMbfj.txt Applied deletion Removed the following rules: 25 26 Accelerated simple loops Start location: l6 27: l2 -> l2 : low6^0'=1+mid4^post4, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+mid4^post4-up5^0 <= 0), cost: 7 28: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+low6^0-mid4^post4 <= 0), cost: 7 29: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, (-low6^0+up5^0 >= 0 /\ -1-mid4^post4+up5^0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 30: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-low6^0+mid4^post4 <= 0), cost: NONTERM 31: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ -low6^0+up5^0 >= 0 /\ -1+n1 >= 0), cost: 4*n1 32: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-mid4^post4+up5^0 <= 0), cost: NONTERM 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 24: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -14 <= 0, cost: 5 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> l2 : low6^0'=1+mid4^post4, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+mid4^post4-up5^0 <= 0), cost: 7 New rule: l6 -> l2 : low6^0'=1+mid4^post4, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, -13+mid4^post4 <= 0, cost: 9 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (low6^0-up5^0 <= 0 /\ 1+low6^0-mid4^post4 <= 0), cost: 7 New rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -1+mid4^post4 >= 0, cost: 9 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> l2 : low6^0'=1+mid4^post4, mid4^0'=mid4^post4, (-low6^0+up5^0 >= 0 /\ -1-mid4^post4+up5^0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 New rule: l6 -> l2 : low6^0'=1+mid4^post4, x2^0'=8, fvalue3^0'=-1, up5^0'=14, mid4^0'=mid4^post4, (-1+n0 >= 0 /\ -13+mid4^post4 <= 0), cost: 2+4*n0 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-low6^0+mid4^post4 <= 0), cost: NONTERM New rule: l6 -> [8] : 14 >= 0, cost: NONTERM Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ -low6^0+up5^0 >= 0 /\ -1+n1 >= 0), cost: 4*n1 New rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1+mid4^post4 >= 0 /\ -1+n1 >= 0), cost: 2+4*n1 Applied chaining First rule: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 Second rule: l2 -> [8] : (-low6^0+up5^0 >= 0 /\ 1-mid4^post4+up5^0 <= 0), cost: NONTERM New rule: l6 -> [8] : 14 >= 0, cost: NONTERM Applied deletion Removed the following rules: 27 28 29 30 31 32 Chained accelerated rules with incoming rules Start location: l6 18: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=14, TRUE, cost: 2 24: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -14 <= 0, cost: 5 33: l6 -> l2 : low6^0'=1+mid4^post4, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, -13+mid4^post4 <= 0, cost: 9 34: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, -1+mid4^post4 >= 0, cost: 9 35: l6 -> l2 : low6^0'=1+mid4^post4, x2^0'=8, fvalue3^0'=-1, up5^0'=14, mid4^0'=mid4^post4, (-1+n0 >= 0 /\ -13+mid4^post4 <= 0), cost: 2+4*n0 36: l6 -> [8] : 14 >= 0, cost: NONTERM 37: l6 -> l2 : low6^0'=0, x2^0'=8, fvalue3^0'=-1, up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1+mid4^post4 >= 0 /\ -1+n1 >= 0), cost: 2+4*n1 Removed unreachable locations and irrelevant leafs Start location: l6 36: l6 -> [8] : 14 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 36 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 14 >= 0