WORST_CASE(Omega(0),?) Initial ITS Start location: l6 0: l0 -> l1 : oldX0^0'=oldX0^post0, oldX5^0'=oldX5^post0, oldX2^0'=oldX2^post0, x1^0'=x1^post0, oldX4^0'=oldX4^post0, oldX1^0'=oldX1^post0, x0^0'=x0^post0, oldX3^0'=oldX3^post0, x2^0'=x2^post0, (-oldX3^post0+oldX3^0 == 0 /\ -x1^0+oldX1^post0 == 0 /\ -oldX4^post0+oldX4^0 == 0 /\ oldX2^post0-x2^0 == 0 /\ x2^post0-oldX2^post0+oldX1^post0 == 0 /\ x0^post0-oldX0^post0 == 0 /\ x1^post0-oldX1^post0 == 0 /\ -x0^0+oldX0^post0 == 0 /\ oldX5^0-oldX5^post0 == 0), cost: 1 1: l1 -> l2 : oldX0^0'=oldX0^post1, oldX5^0'=oldX5^post1, oldX2^0'=oldX2^post1, x1^0'=x1^post1, oldX4^0'=oldX4^post1, oldX1^0'=oldX1^post1, x0^0'=x0^post1, oldX3^0'=oldX3^post1, x2^0'=x2^post1, (0 == 0 /\ -oldX3^post1+x2^post1 == 0 /\ oldX0^post1-x0^0 == 0 /\ oldX2^post1-x2^0 == 0 /\ oldX5^0-oldX5^post1 == 0 /\ -x1^0+oldX1^post1 == 0 /\ x1^post1-oldX1^post1 == 0 /\ oldX1^post1 <= 0 /\ x0^post1-oldX0^post1 == 0 /\ -oldX4^post1+oldX4^0 == 0), cost: 1 2: l1 -> l2 : oldX0^0'=oldX0^post2, oldX5^0'=oldX5^post2, oldX2^0'=oldX2^post2, x1^0'=x1^post2, oldX4^0'=oldX4^post2, oldX1^0'=oldX1^post2, x0^0'=x0^post2, oldX3^0'=oldX3^post2, x2^0'=x2^post2, (0 == 0 /\ oldX5^0-oldX5^post2 == 0 /\ x1^post2-oldX1^post2 == 0 /\ oldX2^post2 <= 0 /\ -oldX3^post2+x2^post2 == 0 /\ oldX0^post2-x0^0 == 0 /\ x0^post2-oldX0^post2 == 0 /\ oldX2^post2-x2^0 == 0 /\ oldX4^0-oldX4^post2 == 0 /\ -x1^0+oldX1^post2 == 0), cost: 1 3: l1 -> l0 : oldX0^0'=oldX0^post3, oldX5^0'=oldX5^post3, oldX2^0'=oldX2^post3, x1^0'=x1^post3, oldX4^0'=oldX4^post3, oldX1^0'=oldX1^post3, x0^0'=x0^post3, oldX3^0'=oldX3^post3, x2^0'=x2^post3, (oldX1^post3-x1^0 == 0 /\ oldX5^0-oldX5^post3 == 0 /\ 1-oldX1^post3 <= 0 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ 1-oldX2^post3 <= 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 4: l2 -> l3 : oldX0^0'=oldX0^post4, oldX5^0'=oldX5^post4, oldX2^0'=oldX2^post4, x1^0'=x1^post4, oldX4^0'=oldX4^post4, oldX1^0'=oldX1^post4, x0^0'=x0^post4, oldX3^0'=oldX3^post4, x2^0'=x2^post4, (0 == 0 /\ -oldX5^post4+x2^post4 == 0 /\ -x1^0+oldX1^post4 == 0 /\ -oldX4^post4+x1^post4 == 0 /\ oldX2^post4-x2^0 == 0 /\ -oldX3^post4+x0^post4 == 0 /\ -x0^0+oldX0^post4 == 0), cost: 1 5: l4 -> l1 : oldX0^0'=oldX0^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX2^post5, x1^0'=x1^post5, oldX4^0'=oldX4^post5, oldX1^0'=oldX1^post5, x0^0'=x0^post5, oldX3^0'=oldX3^post5, x2^0'=x2^post5, (oldX2^post5-x2^0 == 0 /\ x2^post5-oldX0^post5 == 0 /\ oldX5^0-oldX5^post5 == 0 /\ 1-oldX0^post5 <= 0 /\ oldX3^0-oldX3^post5 == 0 /\ -oldX4^post5+oldX4^0 == 0 /\ -x1^0+oldX1^post5 == 0 /\ x0^post5-oldX0^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x1^post5-oldX1^post5 == 0), cost: 1 6: l4 -> l1 : oldX0^0'=oldX0^post6, oldX5^0'=oldX5^post6, oldX2^0'=oldX2^post6, x1^0'=x1^post6, oldX4^0'=oldX4^post6, oldX1^0'=oldX1^post6, x0^0'=x0^post6, oldX3^0'=oldX3^post6, x2^0'=x2^post6, (oldX2^post6-x2^0 == 0 /\ x2^post6-oldX0^post6 == 0 /\ -x1^0+oldX1^post6 == 0 /\ oldX5^0-oldX5^post6 == 0 /\ x1^post6-oldX1^post6 == 0 /\ oldX3^0-oldX3^post6 == 0 /\ 1+oldX0^post6 <= 0 /\ oldX4^0-oldX4^post6 == 0 /\ oldX0^post6-x0^0 == 0 /\ x0^post6-oldX0^post6 == 0), cost: 1 7: l4 -> l2 : oldX0^0'=oldX0^post7, oldX5^0'=oldX5^post7, oldX2^0'=oldX2^post7, x1^0'=x1^post7, oldX4^0'=oldX4^post7, oldX1^0'=oldX1^post7, x0^0'=x0^post7, oldX3^0'=oldX3^post7, x2^0'=x2^post7, (0 == 0 /\ -x1^0+oldX1^post7 == 0 /\ oldX2^post7-x2^0 == 0 /\ oldX0^post7 <= 0 /\ x0^post7-oldX0^post7 == 0 /\ x1^post7-oldX1^post7 == 0 /\ -oldX3^post7+x2^post7 == 0 /\ oldX4^0-oldX4^post7 == 0 /\ oldX5^0-oldX5^post7 == 0 /\ -oldX0^post7 <= 0 /\ oldX0^post7-x0^0 == 0), cost: 1 8: l5 -> l4 : oldX0^0'=oldX0^post8, oldX5^0'=oldX5^post8, oldX2^0'=oldX2^post8, x1^0'=x1^post8, oldX4^0'=oldX4^post8, oldX1^0'=oldX1^post8, x0^0'=x0^post8, oldX3^0'=oldX3^post8, x2^0'=x2^post8, (0 == 0 /\ oldX0^post8-x0^0 == 0 /\ -oldX3^post8+x2^post8 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ oldX2^post8-x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ -oldX0^post8+x0^post8 == 0 /\ -oldX1^post8+x1^post8 == 0 /\ oldX1^post8-x1^0 == 0), cost: 1 9: l5 -> l3 : oldX0^0'=oldX0^post9, oldX5^0'=oldX5^post9, oldX2^0'=oldX2^post9, x1^0'=x1^post9, oldX4^0'=oldX4^post9, oldX1^0'=oldX1^post9, x0^0'=x0^post9, oldX3^0'=oldX3^post9, x2^0'=x2^post9, (-oldX3^post9+oldX3^0 == 0 /\ oldX0^0-oldX0^post9 == 0 /\ oldX2^0-oldX2^post9 == 0 /\ -x2^post9+x2^0 == 0 /\ -oldX1^post9+oldX1^0 == 0 /\ -x0^post9+x0^0 == 0 /\ -oldX4^post9+oldX4^0 == 0 /\ x1^0-x1^post9 == 0 /\ oldX5^0-oldX5^post9 == 0), cost: 1 10: l5 -> l0 : oldX0^0'=oldX0^post10, oldX5^0'=oldX5^post10, oldX2^0'=oldX2^post10, x1^0'=x1^post10, oldX4^0'=oldX4^post10, oldX1^0'=oldX1^post10, x0^0'=x0^post10, oldX3^0'=oldX3^post10, x2^0'=x2^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX5^0-oldX5^post10 == 0 /\ -x2^post10+x2^0 == 0 /\ oldX3^0-oldX3^post10 == 0 /\ -x0^post10+x0^0 == 0 /\ -oldX1^post10+oldX1^0 == 0 /\ oldX2^0-oldX2^post10 == 0 /\ oldX4^0-oldX4^post10 == 0 /\ -x1^post10+x1^0 == 0), cost: 1 11: l5 -> l1 : oldX0^0'=oldX0^post11, oldX5^0'=oldX5^post11, oldX2^0'=oldX2^post11, x1^0'=x1^post11, oldX4^0'=oldX4^post11, oldX1^0'=oldX1^post11, x0^0'=x0^post11, oldX3^0'=oldX3^post11, x2^0'=x2^post11, (-oldX2^post11+oldX2^0 == 0 /\ -x1^post11+x1^0 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ oldX4^0-oldX4^post11 == 0 /\ -oldX3^post11+oldX3^0 == 0 /\ oldX5^0-oldX5^post11 == 0 /\ -x2^post11+x2^0 == 0 /\ -oldX1^post11+oldX1^0 == 0 /\ x0^0-x0^post11 == 0), cost: 1 12: l5 -> l2 : oldX0^0'=oldX0^post12, oldX5^0'=oldX5^post12, oldX2^0'=oldX2^post12, x1^0'=x1^post12, oldX4^0'=oldX4^post12, oldX1^0'=oldX1^post12, x0^0'=x0^post12, oldX3^0'=oldX3^post12, x2^0'=x2^post12, (oldX4^0-oldX4^post12 == 0 /\ x1^0-x1^post12 == 0 /\ oldX5^0-oldX5^post12 == 0 /\ x0^0-x0^post12 == 0 /\ -oldX3^post12+oldX3^0 == 0 /\ -x2^post12+x2^0 == 0 /\ oldX2^0-oldX2^post12 == 0 /\ -oldX1^post12+oldX1^0 == 0 /\ oldX0^0-oldX0^post12 == 0), cost: 1 13: l5 -> l4 : oldX0^0'=oldX0^post13, oldX5^0'=oldX5^post13, oldX2^0'=oldX2^post13, x1^0'=x1^post13, oldX4^0'=oldX4^post13, oldX1^0'=oldX1^post13, x0^0'=x0^post13, oldX3^0'=oldX3^post13, x2^0'=x2^post13, (oldX5^0-oldX5^post13 == 0 /\ x0^0-x0^post13 == 0 /\ oldX1^0-oldX1^post13 == 0 /\ -oldX4^post13+oldX4^0 == 0 /\ x1^0-x1^post13 == 0 /\ -oldX3^post13+oldX3^0 == 0 /\ -x2^post13+x2^0 == 0 /\ oldX2^0-oldX2^post13 == 0 /\ oldX0^0-oldX0^post13 == 0), cost: 1 14: l6 -> l5 : oldX0^0'=oldX0^post14, oldX5^0'=oldX5^post14, oldX2^0'=oldX2^post14, x1^0'=x1^post14, oldX4^0'=oldX4^post14, oldX1^0'=oldX1^post14, x0^0'=x0^post14, oldX3^0'=oldX3^post14, x2^0'=x2^post14, (oldX0^0-oldX0^post14 == 0 /\ oldX1^0-oldX1^post14 == 0 /\ -oldX4^post14+oldX4^0 == 0 /\ -x2^post14+x2^0 == 0 /\ x1^0-x1^post14 == 0 /\ oldX2^0-oldX2^post14 == 0 /\ -oldX3^post14+oldX3^0 == 0 /\ oldX5^0-oldX5^post14 == 0 /\ -x0^post14+x0^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 0: l0 -> l1 : oldX0^0'=oldX0^post0, oldX5^0'=oldX5^post0, oldX2^0'=oldX2^post0, x1^0'=x1^post0, oldX4^0'=oldX4^post0, oldX1^0'=oldX1^post0, x0^0'=x0^post0, oldX3^0'=oldX3^post0, x2^0'=x2^post0, (-oldX3^post0+oldX3^0 == 0 /\ -x1^0+oldX1^post0 == 0 /\ -oldX4^post0+oldX4^0 == 0 /\ oldX2^post0-x2^0 == 0 /\ x2^post0-oldX2^post0+oldX1^post0 == 0 /\ x0^post0-oldX0^post0 == 0 /\ x1^post0-oldX1^post0 == 0 /\ -x0^0+oldX0^post0 == 0 /\ oldX5^0-oldX5^post0 == 0), cost: 1 3: l1 -> l0 : oldX0^0'=oldX0^post3, oldX5^0'=oldX5^post3, oldX2^0'=oldX2^post3, x1^0'=x1^post3, oldX4^0'=oldX4^post3, oldX1^0'=oldX1^post3, x0^0'=x0^post3, oldX3^0'=oldX3^post3, x2^0'=x2^post3, (oldX1^post3-x1^0 == 0 /\ oldX5^0-oldX5^post3 == 0 /\ 1-oldX1^post3 <= 0 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ 1-oldX2^post3 <= 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 5: l4 -> l1 : oldX0^0'=oldX0^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX2^post5, x1^0'=x1^post5, oldX4^0'=oldX4^post5, oldX1^0'=oldX1^post5, x0^0'=x0^post5, oldX3^0'=oldX3^post5, x2^0'=x2^post5, (oldX2^post5-x2^0 == 0 /\ x2^post5-oldX0^post5 == 0 /\ oldX5^0-oldX5^post5 == 0 /\ 1-oldX0^post5 <= 0 /\ oldX3^0-oldX3^post5 == 0 /\ -oldX4^post5+oldX4^0 == 0 /\ -x1^0+oldX1^post5 == 0 /\ x0^post5-oldX0^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x1^post5-oldX1^post5 == 0), cost: 1 6: l4 -> l1 : oldX0^0'=oldX0^post6, oldX5^0'=oldX5^post6, oldX2^0'=oldX2^post6, x1^0'=x1^post6, oldX4^0'=oldX4^post6, oldX1^0'=oldX1^post6, x0^0'=x0^post6, oldX3^0'=oldX3^post6, x2^0'=x2^post6, (oldX2^post6-x2^0 == 0 /\ x2^post6-oldX0^post6 == 0 /\ -x1^0+oldX1^post6 == 0 /\ oldX5^0-oldX5^post6 == 0 /\ x1^post6-oldX1^post6 == 0 /\ oldX3^0-oldX3^post6 == 0 /\ 1+oldX0^post6 <= 0 /\ oldX4^0-oldX4^post6 == 0 /\ oldX0^post6-x0^0 == 0 /\ x0^post6-oldX0^post6 == 0), cost: 1 8: l5 -> l4 : oldX0^0'=oldX0^post8, oldX5^0'=oldX5^post8, oldX2^0'=oldX2^post8, x1^0'=x1^post8, oldX4^0'=oldX4^post8, oldX1^0'=oldX1^post8, x0^0'=x0^post8, oldX3^0'=oldX3^post8, x2^0'=x2^post8, (0 == 0 /\ oldX0^post8-x0^0 == 0 /\ -oldX3^post8+x2^post8 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ oldX2^post8-x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ -oldX0^post8+x0^post8 == 0 /\ -oldX1^post8+x1^post8 == 0 /\ oldX1^post8-x1^0 == 0), cost: 1 10: l5 -> l0 : oldX0^0'=oldX0^post10, oldX5^0'=oldX5^post10, oldX2^0'=oldX2^post10, x1^0'=x1^post10, oldX4^0'=oldX4^post10, oldX1^0'=oldX1^post10, x0^0'=x0^post10, oldX3^0'=oldX3^post10, x2^0'=x2^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX5^0-oldX5^post10 == 0 /\ -x2^post10+x2^0 == 0 /\ oldX3^0-oldX3^post10 == 0 /\ -x0^post10+x0^0 == 0 /\ -oldX1^post10+oldX1^0 == 0 /\ oldX2^0-oldX2^post10 == 0 /\ oldX4^0-oldX4^post10 == 0 /\ -x1^post10+x1^0 == 0), cost: 1 11: l5 -> l1 : oldX0^0'=oldX0^post11, oldX5^0'=oldX5^post11, oldX2^0'=oldX2^post11, x1^0'=x1^post11, oldX4^0'=oldX4^post11, oldX1^0'=oldX1^post11, x0^0'=x0^post11, oldX3^0'=oldX3^post11, x2^0'=x2^post11, (-oldX2^post11+oldX2^0 == 0 /\ -x1^post11+x1^0 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ oldX4^0-oldX4^post11 == 0 /\ -oldX3^post11+oldX3^0 == 0 /\ oldX5^0-oldX5^post11 == 0 /\ -x2^post11+x2^0 == 0 /\ -oldX1^post11+oldX1^0 == 0 /\ x0^0-x0^post11 == 0), cost: 1 13: l5 -> l4 : oldX0^0'=oldX0^post13, oldX5^0'=oldX5^post13, oldX2^0'=oldX2^post13, x1^0'=x1^post13, oldX4^0'=oldX4^post13, oldX1^0'=oldX1^post13, x0^0'=x0^post13, oldX3^0'=oldX3^post13, x2^0'=x2^post13, (oldX5^0-oldX5^post13 == 0 /\ x0^0-x0^post13 == 0 /\ oldX1^0-oldX1^post13 == 0 /\ -oldX4^post13+oldX4^0 == 0 /\ x1^0-x1^post13 == 0 /\ -oldX3^post13+oldX3^0 == 0 /\ -x2^post13+x2^0 == 0 /\ oldX2^0-oldX2^post13 == 0 /\ oldX0^0-oldX0^post13 == 0), cost: 1 14: l6 -> l5 : oldX0^0'=oldX0^post14, oldX5^0'=oldX5^post14, oldX2^0'=oldX2^post14, x1^0'=x1^post14, oldX4^0'=oldX4^post14, oldX1^0'=oldX1^post14, x0^0'=x0^post14, oldX3^0'=oldX3^post14, x2^0'=x2^post14, (oldX0^0-oldX0^post14 == 0 /\ oldX1^0-oldX1^post14 == 0 /\ -oldX4^post14+oldX4^0 == 0 /\ -x2^post14+x2^0 == 0 /\ x1^0-x1^post14 == 0 /\ oldX2^0-oldX2^post14 == 0 /\ -oldX3^post14+oldX3^0 == 0 /\ oldX5^0-oldX5^post14 == 0 /\ -x0^post14+x0^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : oldX0^0'=oldX0^post0, oldX5^0'=oldX5^post0, oldX2^0'=oldX2^post0, x1^0'=x1^post0, oldX4^0'=oldX4^post0, oldX1^0'=oldX1^post0, x0^0'=x0^post0, oldX3^0'=oldX3^post0, x2^0'=x2^post0, (-oldX3^post0+oldX3^0 == 0 /\ -x1^0+oldX1^post0 == 0 /\ -oldX4^post0+oldX4^0 == 0 /\ oldX2^post0-x2^0 == 0 /\ x2^post0-oldX2^post0+oldX1^post0 == 0 /\ x0^post0-oldX0^post0 == 0 /\ x1^post0-oldX1^post0 == 0 /\ -x0^0+oldX0^post0 == 0 /\ oldX5^0-oldX5^post0 == 0), cost: 1 New rule: l0 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l0 : oldX0^0'=oldX0^post3, oldX5^0'=oldX5^post3, oldX2^0'=oldX2^post3, x1^0'=x1^post3, oldX4^0'=oldX4^post3, oldX1^0'=oldX1^post3, x0^0'=x0^post3, oldX3^0'=oldX3^post3, x2^0'=x2^post3, (oldX1^post3-x1^0 == 0 /\ oldX5^0-oldX5^post3 == 0 /\ 1-oldX1^post3 <= 0 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ 1-oldX2^post3 <= 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 New rule: l1 -> l0 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 1 Applied preprocessing Original rule: l4 -> l1 : oldX0^0'=oldX0^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX2^post5, x1^0'=x1^post5, oldX4^0'=oldX4^post5, oldX1^0'=oldX1^post5, x0^0'=x0^post5, oldX3^0'=oldX3^post5, x2^0'=x2^post5, (oldX2^post5-x2^0 == 0 /\ x2^post5-oldX0^post5 == 0 /\ oldX5^0-oldX5^post5 == 0 /\ 1-oldX0^post5 <= 0 /\ oldX3^0-oldX3^post5 == 0 /\ -oldX4^post5+oldX4^0 == 0 /\ -x1^0+oldX1^post5 == 0 /\ x0^post5-oldX0^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x1^post5-oldX1^post5 == 0), cost: 1 New rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 1 Applied preprocessing Original rule: l4 -> l1 : oldX0^0'=oldX0^post6, oldX5^0'=oldX5^post6, oldX2^0'=oldX2^post6, x1^0'=x1^post6, oldX4^0'=oldX4^post6, oldX1^0'=oldX1^post6, x0^0'=x0^post6, oldX3^0'=oldX3^post6, x2^0'=x2^post6, (oldX2^post6-x2^0 == 0 /\ x2^post6-oldX0^post6 == 0 /\ -x1^0+oldX1^post6 == 0 /\ oldX5^0-oldX5^post6 == 0 /\ x1^post6-oldX1^post6 == 0 /\ oldX3^0-oldX3^post6 == 0 /\ 1+oldX0^post6 <= 0 /\ oldX4^0-oldX4^post6 == 0 /\ oldX0^post6-x0^0 == 0 /\ x0^post6-oldX0^post6 == 0), cost: 1 New rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 1 Applied preprocessing Original rule: l5 -> l4 : oldX0^0'=oldX0^post8, oldX5^0'=oldX5^post8, oldX2^0'=oldX2^post8, x1^0'=x1^post8, oldX4^0'=oldX4^post8, oldX1^0'=oldX1^post8, x0^0'=x0^post8, oldX3^0'=oldX3^post8, x2^0'=x2^post8, (0 == 0 /\ oldX0^post8-x0^0 == 0 /\ -oldX3^post8+x2^post8 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ oldX2^post8-x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ -oldX0^post8+x0^post8 == 0 /\ -oldX1^post8+x1^post8 == 0 /\ oldX1^post8-x1^0 == 0), cost: 1 New rule: l5 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 1 Applied preprocessing Original rule: l5 -> l0 : oldX0^0'=oldX0^post10, oldX5^0'=oldX5^post10, oldX2^0'=oldX2^post10, x1^0'=x1^post10, oldX4^0'=oldX4^post10, oldX1^0'=oldX1^post10, x0^0'=x0^post10, oldX3^0'=oldX3^post10, x2^0'=x2^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX5^0-oldX5^post10 == 0 /\ -x2^post10+x2^0 == 0 /\ oldX3^0-oldX3^post10 == 0 /\ -x0^post10+x0^0 == 0 /\ -oldX1^post10+oldX1^0 == 0 /\ oldX2^0-oldX2^post10 == 0 /\ oldX4^0-oldX4^post10 == 0 /\ -x1^post10+x1^0 == 0), cost: 1 New rule: l5 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l1 : oldX0^0'=oldX0^post11, oldX5^0'=oldX5^post11, oldX2^0'=oldX2^post11, x1^0'=x1^post11, oldX4^0'=oldX4^post11, oldX1^0'=oldX1^post11, x0^0'=x0^post11, oldX3^0'=oldX3^post11, x2^0'=x2^post11, (-oldX2^post11+oldX2^0 == 0 /\ -x1^post11+x1^0 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ oldX4^0-oldX4^post11 == 0 /\ -oldX3^post11+oldX3^0 == 0 /\ oldX5^0-oldX5^post11 == 0 /\ -x2^post11+x2^0 == 0 /\ -oldX1^post11+oldX1^0 == 0 /\ x0^0-x0^post11 == 0), cost: 1 New rule: l5 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : oldX0^0'=oldX0^post13, oldX5^0'=oldX5^post13, oldX2^0'=oldX2^post13, x1^0'=x1^post13, oldX4^0'=oldX4^post13, oldX1^0'=oldX1^post13, x0^0'=x0^post13, oldX3^0'=oldX3^post13, x2^0'=x2^post13, (oldX5^0-oldX5^post13 == 0 /\ x0^0-x0^post13 == 0 /\ oldX1^0-oldX1^post13 == 0 /\ -oldX4^post13+oldX4^0 == 0 /\ x1^0-x1^post13 == 0 /\ -oldX3^post13+oldX3^0 == 0 /\ -x2^post13+x2^0 == 0 /\ oldX2^0-oldX2^post13 == 0 /\ oldX0^0-oldX0^post13 == 0), cost: 1 New rule: l5 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : oldX0^0'=oldX0^post14, oldX5^0'=oldX5^post14, oldX2^0'=oldX2^post14, x1^0'=x1^post14, oldX4^0'=oldX4^post14, oldX1^0'=oldX1^post14, x0^0'=x0^post14, oldX3^0'=oldX3^post14, x2^0'=x2^post14, (oldX0^0-oldX0^post14 == 0 /\ oldX1^0-oldX1^post14 == 0 /\ -oldX4^post14+oldX4^0 == 0 /\ -x2^post14+x2^0 == 0 /\ x1^0-x1^post14 == 0 /\ oldX2^0-oldX2^post14 == 0 /\ -oldX3^post14+oldX3^0 == 0 /\ oldX5^0-oldX5^post14 == 0 /\ -x0^post14+x0^0 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 15: l0 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 1 16: l1 -> l0 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 1 17: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 1 18: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 1 19: l5 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 1 20: l5 -> l0 : TRUE, cost: 1 21: l5 -> l1 : TRUE, cost: 1 22: l5 -> l4 : TRUE, cost: 1 23: l6 -> l5 : TRUE, cost: 1 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 1 New rule: l6 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 2 Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l0 : TRUE, cost: 1 New rule: l6 -> l0 : TRUE, cost: 2 Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l1 : TRUE, cost: 1 New rule: l6 -> l1 : TRUE, cost: 2 Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l4 : TRUE, cost: 1 New rule: l6 -> l4 : TRUE, cost: 2 Applied deletion Removed the following rules: 19 20 21 22 23 Eliminated locations on tree-shaped paths Start location: l6 15: l0 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 1 16: l1 -> l0 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 1 17: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 1 18: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 1 24: l6 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 2 25: l6 -> l0 : TRUE, cost: 2 26: l6 -> l1 : TRUE, cost: 2 27: l6 -> l4 : TRUE, cost: 2 Eliminating location l4 by chaining: Applied chaining First rule: l6 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 2 Second rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 1 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, (0 == 0 /\ -1+x0^0 >= 0), cost: 3 Applied simplification Original rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, (0 == 0 /\ -1+x0^0 >= 0), cost: 3 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 Applied chaining First rule: l6 -> l4 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x2^post8, 0 == 0, cost: 2 Second rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 1 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, (0 == 0 /\ 1+x0^0 <= 0), cost: 3 Applied simplification Original rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, (0 == 0 /\ 1+x0^0 <= 0), cost: 3 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 Applied chaining First rule: l6 -> l4 : TRUE, cost: 2 Second rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 1 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 Applied chaining First rule: l6 -> l4 : TRUE, cost: 2 Second rule: l4 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 1 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 Applied deletion Removed the following rules: 17 18 24 27 Eliminated locations on tree-shaped paths Start location: l6 15: l0 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 1 16: l1 -> l0 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 1 25: l6 -> l0 : TRUE, cost: 2 26: l6 -> l1 : TRUE, cost: 2 28: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 29: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 30: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 31: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 Eliminated location l0 Start location: l6 32: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 2 26: l6 -> l1 : TRUE, cost: 2 28: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 29: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 30: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 31: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 33: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 3 Applied acceleration Original rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, (-1+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 2 New rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1+n0 >= 0 /\ -1+x1^0 >= 0 /\ ((-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x1^0 >= 0) \/ (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x2^0 >= 0))), cost: 2*n0 Applied simplification Original rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1+n0 >= 0 /\ -1+x1^0 >= 0 /\ ((-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x1^0 >= 0) \/ (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x2^0 >= 0))), cost: 2*n0 New rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 Applied deletion Removed the following rules: 32 Accelerated simple loops Start location: l6 35: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 26: l6 -> l1 : TRUE, cost: 2 28: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 29: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 30: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 31: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 33: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 3 Applied chaining First rule: l6 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2+2*n0 Applied chaining First rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 Second rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x0^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=-x1^0*n0+x0^0, (-1+n0 >= 0 /\ -1-x1^0*(-1+n0)+x0^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 Applied chaining First rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 Second rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x0^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x0^0, (-1+n0 >= 0 /\ -1-x1^0*(-1+n0)+x0^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 Applied chaining First rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 3 Second rule: l1 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2*n0 New rule: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0-x1^0*n0+x2^0, (-1+n0 >= 0 /\ -1-x1^0-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 Applied deletion Removed the following rules: 35 Chained accelerated rules with incoming rules Start location: l6 26: l6 -> l1 : TRUE, cost: 2 28: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 29: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^post8, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 30: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, -1+x0^0 >= 0, cost: 3 31: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=x0^0, 1+x0^0 <= 0, cost: 3 33: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, x2^0'=-x1^0+x2^0, TRUE, cost: 3 36: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x2^0, (-1-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+n0 >= 0 /\ -1+x1^0 >= 0), cost: 2+2*n0 37: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x0^0, oldX1^0'=x1^0, oldX3^0'=x2^post8, x2^0'=-x1^0*n0+x0^0, (-1+n0 >= 0 /\ -1-x1^0*(-1+n0)+x0^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 38: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0*(-1+n0)+x0^0, oldX1^0'=x1^0, x2^0'=-x1^0*n0+x0^0, (-1+n0 >= 0 /\ -1-x1^0*(-1+n0)+x0^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 39: l6 -> l1 : oldX0^0'=x0^0, oldX2^0'=-x1^0-x1^0*(-1+n0)+x2^0, oldX1^0'=x1^0, x2^0'=-x1^0-x1^0*n0+x2^0, (-1+n0 >= 0 /\ -1-x1^0-x1^0*(-1+n0)+x2^0 >= 0 /\ -1+x1^0 >= 0), cost: 3+2*n0 Removed unreachable locations and irrelevant leafs Start location: l6 Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0