NO Initial ITS Start location: l6 0: l0 -> l1 : fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, (up5^0-up5^post0 == 0 /\ fvalue3^0-fvalue3^post0 == 0 /\ -x2^post0+x2^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -ret_binary_search7^post0+ret_binary_search7^0 == 0 /\ low6^0-low6^post0 == 0 /\ -tmp^post0+tmp^0 == 0), cost: 1 1: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, (0 == 0 /\ tmp^0-tmp^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ low6^0-low6^post1 == 0 /\ -ret_binary_search7^post1+ret_binary_search7^0 == 0 /\ mid4^0-mid4^post1 == 0 /\ -x2^post1+x2^0 == 0), cost: 1 2: l0 -> l1 : fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, (-x2^post2+x2^0 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -low6^post2+low6^0 == 0 /\ up5^0-up5^post2 == 0 /\ mid4^0-mid4^post2 == 0), cost: 1 6: l1 -> l2 : fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, (-x2^post6+x2^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ fvalue3^0-fvalue3^post6 == 0 /\ -1-mid4^0+low6^post6 == 0 /\ up5^0-up5^post6 == 0 /\ mid4^0-mid4^post6 == 0 /\ -tmp^post6+tmp^0 == 0), cost: 1 7: l1 -> l2 : fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, (-tmp^post7+tmp^0 == 0 /\ fvalue3^0-fvalue3^post7 == 0 /\ 1-mid4^0+up5^post7 == 0 /\ -ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ x2^0-x2^post7 == 0 /\ low6^0-low6^post7 == 0 /\ -mid4^post7+mid4^0 == 0), cost: 1 5: l2 -> l3 : fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, (-ret_binary_search7^post5+ret_binary_search7^0 == 0 /\ -x2^post5+x2^0 == 0 /\ up5^0-up5^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ mid4^0-mid4^post5 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -low6^post5+low6^0 == 0), cost: 1 3: l3 -> l4 : fvalue3^0'=fvalue3^post3, up5^0'=up5^post3, mid4^0'=mid4^post3, tmp^0'=tmp^post3, low6^0'=low6^post3, x2^0'=x2^post3, ret_binary_search7^0'=ret_binary_search7^post3, (fvalue3^0-fvalue3^post3 == 0 /\ up5^0-up5^post3 == 0 /\ mid4^0-mid4^post3 == 0 /\ -low6^post3+low6^0 == 0 /\ 1+up5^0-low6^0 <= 0 /\ -x2^post3+x2^0 == 0 /\ -ret_binary_search7^post3+tmp^post3 == 0 /\ -fvalue3^0+ret_binary_search7^post3 == 0), cost: 1 4: l3 -> l0 : fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, (0 == 0 /\ -low6^post4+low6^0 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ up5^0-up5^post4 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -x2^post4+x2^0 == 0 /\ -up5^0+low6^0 <= 0), cost: 1 8: l5 -> l2 : fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, (tmp^0-tmp^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ -mid4^post8+mid4^0 == 0 /\ 1+fvalue3^post8 == 0 /\ -8+x2^post8 == 0 /\ -14+up5^post8 == 0 /\ low6^post8 == 0), cost: 1 9: l6 -> l5 : fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, (up5^0-up5^post9 == 0 /\ fvalue3^0-fvalue3^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ -low6^post9+low6^0 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -x2^post9+x2^0 == 0 /\ tmp^0-tmp^post9 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 0: l0 -> l1 : fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, (up5^0-up5^post0 == 0 /\ fvalue3^0-fvalue3^post0 == 0 /\ -x2^post0+x2^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -ret_binary_search7^post0+ret_binary_search7^0 == 0 /\ low6^0-low6^post0 == 0 /\ -tmp^post0+tmp^0 == 0), cost: 1 1: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, (0 == 0 /\ tmp^0-tmp^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ low6^0-low6^post1 == 0 /\ -ret_binary_search7^post1+ret_binary_search7^0 == 0 /\ mid4^0-mid4^post1 == 0 /\ -x2^post1+x2^0 == 0), cost: 1 2: l0 -> l1 : fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, (-x2^post2+x2^0 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -low6^post2+low6^0 == 0 /\ up5^0-up5^post2 == 0 /\ mid4^0-mid4^post2 == 0), cost: 1 6: l1 -> l2 : fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, (-x2^post6+x2^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ fvalue3^0-fvalue3^post6 == 0 /\ -1-mid4^0+low6^post6 == 0 /\ up5^0-up5^post6 == 0 /\ mid4^0-mid4^post6 == 0 /\ -tmp^post6+tmp^0 == 0), cost: 1 7: l1 -> l2 : fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, (-tmp^post7+tmp^0 == 0 /\ fvalue3^0-fvalue3^post7 == 0 /\ 1-mid4^0+up5^post7 == 0 /\ -ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ x2^0-x2^post7 == 0 /\ low6^0-low6^post7 == 0 /\ -mid4^post7+mid4^0 == 0), cost: 1 5: l2 -> l3 : fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, (-ret_binary_search7^post5+ret_binary_search7^0 == 0 /\ -x2^post5+x2^0 == 0 /\ up5^0-up5^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ mid4^0-mid4^post5 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -low6^post5+low6^0 == 0), cost: 1 4: l3 -> l0 : fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, (0 == 0 /\ -low6^post4+low6^0 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ up5^0-up5^post4 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -x2^post4+x2^0 == 0 /\ -up5^0+low6^0 <= 0), cost: 1 8: l5 -> l2 : fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, (tmp^0-tmp^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ -mid4^post8+mid4^0 == 0 /\ 1+fvalue3^post8 == 0 /\ -8+x2^post8 == 0 /\ -14+up5^post8 == 0 /\ low6^post8 == 0), cost: 1 9: l6 -> l5 : fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, (up5^0-up5^post9 == 0 /\ fvalue3^0-fvalue3^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ -low6^post9+low6^0 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -x2^post9+x2^0 == 0 /\ tmp^0-tmp^post9 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : fvalue3^0'=fvalue3^post0, up5^0'=up5^post0, mid4^0'=mid4^post0, tmp^0'=tmp^post0, low6^0'=low6^post0, x2^0'=x2^post0, ret_binary_search7^0'=ret_binary_search7^post0, (up5^0-up5^post0 == 0 /\ fvalue3^0-fvalue3^post0 == 0 /\ -x2^post0+x2^0 == 0 /\ -mid4^post0+mid4^0 == 0 /\ -ret_binary_search7^post0+ret_binary_search7^0 == 0 /\ low6^0-low6^post0 == 0 /\ -tmp^post0+tmp^0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=up5^post1, mid4^0'=mid4^post1, tmp^0'=tmp^post1, low6^0'=low6^post1, x2^0'=x2^post1, ret_binary_search7^0'=ret_binary_search7^post1, (0 == 0 /\ tmp^0-tmp^post1 == 0 /\ 1-low6^0+up5^post1 == 0 /\ low6^0-low6^post1 == 0 /\ -ret_binary_search7^post1+ret_binary_search7^0 == 0 /\ mid4^0-mid4^post1 == 0 /\ -x2^post1+x2^0 == 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 : fvalue3^0'=fvalue3^post2, up5^0'=up5^post2, mid4^0'=mid4^post2, tmp^0'=tmp^post2, low6^0'=low6^post2, x2^0'=x2^post2, ret_binary_search7^0'=ret_binary_search7^post2, (-x2^post2+x2^0 == 0 /\ -ret_binary_search7^post2+ret_binary_search7^0 == 0 /\ fvalue3^0-fvalue3^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ -low6^post2+low6^0 == 0 /\ up5^0-up5^post2 == 0 /\ mid4^0-mid4^post2 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : fvalue3^0'=fvalue3^post4, up5^0'=up5^post4, mid4^0'=mid4^post4, tmp^0'=tmp^post4, low6^0'=low6^post4, x2^0'=x2^post4, ret_binary_search7^0'=ret_binary_search7^post4, (0 == 0 /\ -low6^post4+low6^0 == 0 /\ -ret_binary_search7^post4+ret_binary_search7^0 == 0 /\ up5^0-up5^post4 == 0 /\ fvalue3^0-fvalue3^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -x2^post4+x2^0 == 0 /\ -up5^0+low6^0 <= 0), cost: 1 New rule: l3 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : fvalue3^0'=fvalue3^post5, up5^0'=up5^post5, mid4^0'=mid4^post5, tmp^0'=tmp^post5, low6^0'=low6^post5, x2^0'=x2^post5, ret_binary_search7^0'=ret_binary_search7^post5, (-ret_binary_search7^post5+ret_binary_search7^0 == 0 /\ -x2^post5+x2^0 == 0 /\ up5^0-up5^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ mid4^0-mid4^post5 == 0 /\ fvalue3^0-fvalue3^post5 == 0 /\ -low6^post5+low6^0 == 0), cost: 1 New rule: l2 -> l3 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : fvalue3^0'=fvalue3^post6, up5^0'=up5^post6, mid4^0'=mid4^post6, tmp^0'=tmp^post6, low6^0'=low6^post6, x2^0'=x2^post6, ret_binary_search7^0'=ret_binary_search7^post6, (-x2^post6+x2^0 == 0 /\ ret_binary_search7^0-ret_binary_search7^post6 == 0 /\ fvalue3^0-fvalue3^post6 == 0 /\ -1-mid4^0+low6^post6 == 0 /\ up5^0-up5^post6 == 0 /\ mid4^0-mid4^post6 == 0 /\ -tmp^post6+tmp^0 == 0), cost: 1 New rule: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : fvalue3^0'=fvalue3^post7, up5^0'=up5^post7, mid4^0'=mid4^post7, tmp^0'=tmp^post7, low6^0'=low6^post7, x2^0'=x2^post7, ret_binary_search7^0'=ret_binary_search7^post7, (-tmp^post7+tmp^0 == 0 /\ fvalue3^0-fvalue3^post7 == 0 /\ 1-mid4^0+up5^post7 == 0 /\ -ret_binary_search7^post7+ret_binary_search7^0 == 0 /\ x2^0-x2^post7 == 0 /\ low6^0-low6^post7 == 0 /\ -mid4^post7+mid4^0 == 0), cost: 1 New rule: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l2 : fvalue3^0'=fvalue3^post8, up5^0'=up5^post8, mid4^0'=mid4^post8, tmp^0'=tmp^post8, low6^0'=low6^post8, x2^0'=x2^post8, ret_binary_search7^0'=ret_binary_search7^post8, (tmp^0-tmp^post8 == 0 /\ -ret_binary_search7^post8+ret_binary_search7^0 == 0 /\ -mid4^post8+mid4^0 == 0 /\ 1+fvalue3^post8 == 0 /\ -8+x2^post8 == 0 /\ -14+up5^post8 == 0 /\ low6^post8 == 0), cost: 1 New rule: l5 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : fvalue3^0'=fvalue3^post9, up5^0'=up5^post9, mid4^0'=mid4^post9, tmp^0'=tmp^post9, low6^0'=low6^post9, x2^0'=x2^post9, ret_binary_search7^0'=ret_binary_search7^post9, (up5^0-up5^post9 == 0 /\ fvalue3^0-fvalue3^post9 == 0 /\ mid4^0-mid4^post9 == 0 /\ -low6^post9+low6^0 == 0 /\ -ret_binary_search7^post9+ret_binary_search7^0 == 0 /\ -x2^post9+x2^0 == 0 /\ tmp^0-tmp^post9 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Applied deletion Removed the following rules: 10 Simplified rules Start location: l6 11: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 12: l0 -> l1 : TRUE, cost: 1 15: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 16: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 14: l2 -> l3 : TRUE, cost: 1 13: l3 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 1 17: l5 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 1 18: l6 -> l5 : TRUE, cost: 1 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 1 New rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Applied deletion Removed the following rules: 17 18 Eliminating location l3 by chaining: Applied chaining First rule: l2 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 1 New rule: l2 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 2 Applied deletion Removed the following rules: 13 14 Eliminated locations on linear paths Start location: l6 11: l0 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, 0 == 0, cost: 1 12: l0 -> l1 : TRUE, cost: 1 15: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 16: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 20: l2 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 2 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Eliminating location l0 by chaining: Applied chaining First rule: l2 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 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 /\ -up5^0+low6^0 <= 0), cost: 3 Applied simplification Original rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (0 == 0 /\ -up5^0+low6^0 <= 0), cost: 3 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 Applied chaining First rule: l2 -> l0 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 2 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 Applied deletion Removed the following rules: 11 12 20 Eliminated locations on tree-shaped paths Start location: l6 15: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 16: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 21: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 22: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Accelerated simple loops Start location: l6 15: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 16: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 21: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 22: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, 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, -up5^0+low6^0 <= 0, cost: 3 New rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, low6^0'=1+mid4^0, 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, -up5^0+low6^0 <= 0, cost: 3 New rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1-mid4^0+low6^0 <= 0, cost: 4 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 New rule: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -14 <= 0, cost: 5 Applied deletion Removed the following rules: 21 Chained accelerated rules with incoming rules Start location: l6 15: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 16: l1 -> l2 : up5^0'=-1+mid4^0, TRUE, cost: 1 23: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, low6^0'=1+mid4^0, 1-up5^0+mid4^0 <= 0, cost: 4 24: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1-mid4^0+low6^0 <= 0, cost: 4 22: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 25: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -14 <= 0, cost: 5 Eliminating location l1 by chaining: Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 Second rule: l1 -> l2 : low6^0'=1+mid4^0, TRUE, cost: 1 New rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, -up5^0+low6^0 <= 0, cost: 4 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 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, -up5^0+low6^0 <= 0, cost: 4 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 Second rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^0, mid4^0'=mid4^post4, low6^0'=1+mid4^0, 1-up5^0+mid4^0 <= 0, cost: 4 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 Applied chaining First rule: l2 -> l1 : mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 3 Second rule: l1 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, 1-mid4^0+low6^0 <= 0, cost: 4 New rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 Applied deletion Removed the following rules: 15 16 22 23 24 Eliminated locations on tree-shaped paths Start location: l6 26: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, -up5^0+low6^0 <= 0, cost: 4 27: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 4 28: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 29: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 25: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -14 <= 0, cost: 5 Applied acceleration Original rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, -up5^0+low6^0 <= 0, cost: 4 New rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (-1+n5 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+up5^0-mid4^post4 >= 0), cost: 4*n5 Applied unrolling Original rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, -up5^0+low6^0 <= 0, cost: 4 New rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 8 Applied non-termination processor Original rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 8 New rule: l2 -> [8] : (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM Applied acceleration Original rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 4 New rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7 Applied unrolling Original rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, -up5^0+low6^0 <= 0, cost: 4 New rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 8 Applied non-termination processor Original rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 8 New rule: l2 -> [8] : (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 26 27 Accelerated simple loops Start location: l6 28: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 29: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 30: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (-1+n5 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+up5^0-mid4^post4 >= 0), cost: 4*n5 31: l2 -> [8] : (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM 32: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7 33: l2 -> [8] : (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 25: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -14 <= 0, cost: 5 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 New rule: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, x2^0'=8, -13+mid4^post4 <= 0, cost: 9 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1+low6^0, mid4^0'=mid4^post4, (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: 7 New rule: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -1+mid4^post4 >= 0, cost: 9 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> l2 : mid4^0'=mid4^post4, low6^0'=1+mid4^post4, (-1+n5 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+up5^0-mid4^post4 >= 0), cost: 4*n5 New rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, x2^0'=8, (-13+mid4^post4 <= 0 /\ -1+n5 >= 0), cost: 2+4*n5 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> [8] : (1-up5^0+mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM New rule: l6 -> [8] : -14 <= 0, cost: NONTERM Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> l2 : up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, (-1-low6^0+mid4^post4 >= 0 /\ up5^0-low6^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7 New rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, (-1+mid4^post4 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7 Applied chaining First rule: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 Second rule: l2 -> [8] : (1+low6^0-mid4^post4 <= 0 /\ -up5^0+low6^0 <= 0), cost: NONTERM New rule: l6 -> [8] : -14 <= 0, cost: NONTERM Applied deletion Removed the following rules: 28 29 30 31 32 33 Chained accelerated rules with incoming rules Start location: l6 19: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, low6^0'=0, x2^0'=8, TRUE, cost: 2 25: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -14 <= 0, cost: 5 34: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=mid4^post4, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, x2^0'=8, -13+mid4^post4 <= 0, cost: 9 35: l6 -> l2 : fvalue3^0'=fvalue3^post1, up5^0'=-1, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, -1+mid4^post4 >= 0, cost: 9 36: l6 -> l2 : fvalue3^0'=-1, up5^0'=14, mid4^0'=mid4^post4, low6^0'=1+mid4^post4, x2^0'=8, (-13+mid4^post4 <= 0 /\ -1+n5 >= 0), cost: 2+4*n5 37: l6 -> [8] : -14 <= 0, cost: NONTERM 38: l6 -> l2 : fvalue3^0'=-1, up5^0'=-1+mid4^post4, mid4^0'=mid4^post4, low6^0'=0, x2^0'=8, (-1+mid4^post4 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7 39: l6 -> [8] : -14 <= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l6 37: l6 -> [8] : -14 <= 0, cost: NONTERM 39: l6 -> [8] : -14 <= 0, cost: NONTERM Removed duplicate rules (ignoring updates) Start location: l6 39: l6 -> [8] : -14 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 39 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -14 <= 0