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, (0 == 0 /\ -x1^0+oldX1^post0 == 0 /\ oldX2^post0-x2^0 == 0 /\ -oldX5^post0+x2^post0 == 0 /\ -oldX4^post0+x1^post0 == 0 /\ -oldX3^post0+x0^post0 == 0 /\ -x0^0+oldX0^post0 == 0), cost: 1 1: l2 -> l3 : 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, (-1+x2^post1-oldX2^post1 == 0 /\ -oldX3^post1+oldX3^0 == 0 /\ oldX0^post1-x0^0 == 0 /\ oldX2^post1-x2^0 == 0 /\ oldX5^0-oldX5^post1 == 0 /\ -1+x1^post1-oldX1^post1 == 0 /\ -x1^0+oldX1^post1 == 0 /\ x0^post1-oldX0^post1 == 0 /\ -oldX4^post1+oldX4^0 == 0), cost: 1 2: l3 -> l0 : 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, (oldX5^0-oldX5^post2 == 0 /\ x1^post2-oldX1^post2 == 0 /\ oldX0^post2-oldX1^post2 <= 0 /\ -oldX3^post2+oldX3^0 == 0 /\ oldX0^post2-x0^0 == 0 /\ x0^post2-oldX0^post2 == 0 /\ oldX2^post2-x2^0 == 0 /\ -oldX2^post2+x2^post2 == 0 /\ oldX4^0-oldX4^post2 == 0 /\ -x1^0+oldX1^post2 == 0), cost: 1 3: l3 -> l2 : 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 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ 1-oldX0^post3+oldX1^post3 <= 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 4: l4 -> 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 /\ -x1^0+oldX1^post4 == 0 /\ x2^post4 == 0 /\ -oldX4^post4+x1^post4 == 0 /\ oldX5^0-oldX5^post4 == 0 /\ oldX2^post4-x2^0 == 0 /\ -oldX3^post4+x0^post4 == 0 /\ -x0^0+oldX0^post4 == 0), cost: 1 5: l5 -> l4 : 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, (0 == 0 /\ oldX2^post5-x2^0 == 0 /\ x0^post5-oldX3^post5 == 0 /\ -oldX4^post5+x1^post5 == 0 /\ -x1^0+oldX1^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x2^post5-oldX5^post5 == 0), cost: 1 6: l5 -> 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, (oldX2^0-oldX2^post6 == 0 /\ -oldX1^post6+oldX1^0 == 0 /\ oldX5^0-oldX5^post6 == 0 /\ oldX3^0-oldX3^post6 == 0 /\ -x1^post6+x1^0 == 0 /\ -x2^post6+x2^0 == 0 /\ oldX4^0-oldX4^post6 == 0 /\ oldX0^0-oldX0^post6 == 0 /\ -x0^post6+x0^0 == 0), cost: 1 7: l5 -> l0 : 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, (-oldX1^post7+oldX1^0 == 0 /\ oldX0^0-oldX0^post7 == 0 /\ -x1^post7+x1^0 == 0 /\ oldX2^0-oldX2^post7 == 0 /\ oldX4^0-oldX4^post7 == 0 /\ x2^0-x2^post7 == 0 /\ oldX5^0-oldX5^post7 == 0 /\ -oldX3^post7+oldX3^0 == 0 /\ -x0^post7+x0^0 == 0), cost: 1 8: l5 -> l2 : 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, (-oldX3^post8+oldX3^0 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ -x2^post8+x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ x1^0-x1^post8 == 0 /\ -oldX1^post8+oldX1^0 == 0 /\ x0^0-x0^post8 == 0 /\ -oldX2^post8+oldX2^0 == 0 /\ oldX0^0-oldX0^post8 == 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 -> l4 : 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: l6 -> l5 : 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 Removed unreachable rules and leafs Start location: l6 1: l2 -> l3 : 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, (-1+x2^post1-oldX2^post1 == 0 /\ -oldX3^post1+oldX3^0 == 0 /\ oldX0^post1-x0^0 == 0 /\ oldX2^post1-x2^0 == 0 /\ oldX5^0-oldX5^post1 == 0 /\ -1+x1^post1-oldX1^post1 == 0 /\ -x1^0+oldX1^post1 == 0 /\ x0^post1-oldX0^post1 == 0 /\ -oldX4^post1+oldX4^0 == 0), cost: 1 3: l3 -> l2 : 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 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ 1-oldX0^post3+oldX1^post3 <= 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 4: l4 -> 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 /\ -x1^0+oldX1^post4 == 0 /\ x2^post4 == 0 /\ -oldX4^post4+x1^post4 == 0 /\ oldX5^0-oldX5^post4 == 0 /\ oldX2^post4-x2^0 == 0 /\ -oldX3^post4+x0^post4 == 0 /\ -x0^0+oldX0^post4 == 0), cost: 1 5: l5 -> l4 : 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, (0 == 0 /\ oldX2^post5-x2^0 == 0 /\ x0^post5-oldX3^post5 == 0 /\ -oldX4^post5+x1^post5 == 0 /\ -x1^0+oldX1^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x2^post5-oldX5^post5 == 0), cost: 1 8: l5 -> l2 : 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, (-oldX3^post8+oldX3^0 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ -x2^post8+x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ x1^0-x1^post8 == 0 /\ -oldX1^post8+oldX1^0 == 0 /\ x0^0-x0^post8 == 0 /\ -oldX2^post8+oldX2^0 == 0 /\ oldX0^0-oldX0^post8 == 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 -> l4 : 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: l6 -> l5 : 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 Applied preprocessing Original rule: l2 -> l3 : 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, (-1+x2^post1-oldX2^post1 == 0 /\ -oldX3^post1+oldX3^0 == 0 /\ oldX0^post1-x0^0 == 0 /\ oldX2^post1-x2^0 == 0 /\ oldX5^0-oldX5^post1 == 0 /\ -1+x1^post1-oldX1^post1 == 0 /\ -x1^0+oldX1^post1 == 0 /\ x0^post1-oldX0^post1 == 0 /\ -oldX4^post1+oldX4^0 == 0), cost: 1 New rule: l2 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l2 : 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 /\ -oldX1^post3+x1^post3 == 0 /\ -oldX3^post3+oldX3^0 == 0 /\ 1-oldX0^post3+oldX1^post3 <= 0 /\ x2^post3-oldX2^post3 == 0 /\ oldX0^post3-x0^0 == 0 /\ -oldX4^post3+oldX4^0 == 0 /\ oldX2^post3-x2^0 == 0 /\ -oldX0^post3+x0^post3 == 0), cost: 1 New rule: l3 -> l2 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, 1+x1^0-x0^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> 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 /\ -x1^0+oldX1^post4 == 0 /\ x2^post4 == 0 /\ -oldX4^post4+x1^post4 == 0 /\ oldX5^0-oldX5^post4 == 0 /\ oldX2^post4-x2^0 == 0 /\ -oldX3^post4+x0^post4 == 0 /\ -x0^0+oldX0^post4 == 0), cost: 1 New rule: l4 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 1 Applied preprocessing Original rule: l5 -> l4 : 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, (0 == 0 /\ oldX2^post5-x2^0 == 0 /\ x0^post5-oldX3^post5 == 0 /\ -oldX4^post5+x1^post5 == 0 /\ -x1^0+oldX1^post5 == 0 /\ oldX0^post5-x0^0 == 0 /\ x2^post5-oldX5^post5 == 0), cost: 1 New rule: l5 -> l4 : oldX0^0'=x0^0, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 1 Applied preprocessing Original rule: l5 -> l2 : 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, (-oldX3^post8+oldX3^0 == 0 /\ oldX4^0-oldX4^post8 == 0 /\ -x2^post8+x2^0 == 0 /\ oldX5^0-oldX5^post8 == 0 /\ x1^0-x1^post8 == 0 /\ -oldX1^post8+oldX1^0 == 0 /\ x0^0-x0^post8 == 0 /\ -oldX2^post8+oldX2^0 == 0 /\ oldX0^0-oldX0^post8 == 0), cost: 1 New rule: l5 -> l2 : TRUE, cost: 1 Applied preprocessing Original rule: 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 New rule: l5 -> l3 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : 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 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : 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: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 12: l2 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 1 13: l3 -> l2 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, 1+x1^0-x0^0 <= 0, cost: 1 14: l4 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 1 15: l5 -> l4 : oldX0^0'=x0^0, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 1 16: l5 -> l2 : TRUE, cost: 1 17: l5 -> l3 : TRUE, cost: 1 18: l5 -> l4 : TRUE, cost: 1 19: 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, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 1 New rule: l6 -> l4 : oldX0^0'=x0^0, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 2 Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l2 : TRUE, cost: 1 New rule: l6 -> l2 : TRUE, cost: 2 Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l3 : TRUE, cost: 1 New rule: l6 -> l3 : 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: 15 16 17 18 19 Eliminated locations on tree-shaped paths Start location: l6 12: l2 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 1 13: l3 -> l2 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, 1+x1^0-x0^0 <= 0, cost: 1 14: l4 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 1 20: l6 -> l4 : oldX0^0'=x0^0, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 2 21: l6 -> l2 : TRUE, cost: 2 22: l6 -> l3 : TRUE, cost: 2 23: l6 -> l4 : TRUE, cost: 2 Eliminating location l4 by chaining: Applied chaining First rule: l6 -> l4 : oldX0^0'=x0^0, oldX5^0'=oldX5^post5, oldX2^0'=x2^0, x1^0'=x1^post5, oldX4^0'=x1^post5, oldX1^0'=x1^0, x0^0'=oldX3^post5, oldX3^0'=oldX3^post5, x2^0'=oldX5^post5, 0 == 0, cost: 2 Second rule: l4 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 1 New rule: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 Applied chaining First rule: l6 -> l4 : TRUE, cost: 2 Second rule: l4 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 1 New rule: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 Applied deletion Removed the following rules: 14 20 23 Eliminated locations on tree-shaped paths Start location: l6 12: l2 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 1 13: l3 -> l2 : oldX0^0'=x0^0, oldX2^0'=x2^0, oldX1^0'=x1^0, 1+x1^0-x0^0 <= 0, cost: 1 21: l6 -> l2 : TRUE, cost: 2 22: l6 -> l3 : TRUE, cost: 2 24: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 25: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 Eliminated location l2 Start location: l6 26: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, 1+x1^0-x0^0 <= 0, cost: 2 22: l6 -> l3 : TRUE, cost: 2 24: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 25: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 27: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 3 Applied acceleration Original rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, 1+x1^0-x0^0 <= 0, cost: 2 New rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1+n0+x2^0, x1^0'=n0+x1^0, oldX1^0'=-1+n0+x1^0, x2^0'=n0+x2^0, (-1+n0 >= 0 /\ -n0-x1^0+x0^0 >= 0), cost: 2*n0 Applied instantiation Original rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1+n0+x2^0, x1^0'=n0+x1^0, oldX1^0'=-1+n0+x1^0, x2^0'=n0+x2^0, (-1+n0 >= 0 /\ -n0-x1^0+x0^0 >= 0), cost: 2*n0 New rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, (0 >= 0 /\ -1-x1^0+x0^0 >= 0), cost: -2*x1^0+2*x0^0 Applied simplification Original rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, (0 >= 0 /\ -1-x1^0+x0^0 >= 0), cost: -2*x1^0+2*x0^0 New rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 Applied deletion Removed the following rules: 26 Accelerated simple loops Start location: l6 29: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 22: l6 -> l3 : TRUE, cost: 2 24: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 25: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 27: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 3 Applied chaining First rule: l6 -> l3 : TRUE, cost: 2 Second rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 New rule: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: 2-2*x1^0+2*x0^0 Applied chaining First rule: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 Second rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 New rule: l6 -> l3 : oldX0^0'=x0^post4, oldX5^0'=oldX5^post5, oldX2^0'=-1+x0^post4-x1^post4, x1^0'=x0^post4, oldX4^0'=x1^post4, oldX1^0'=-1+x0^post4, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=x0^post4-x1^post4, -1+x0^post4-x1^post4 >= 0, cost: 3+2*x0^post4-2*x1^post4 Applied chaining First rule: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 Second rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 New rule: l6 -> l3 : oldX0^0'=x0^post4, oldX2^0'=-1+x0^post4-x1^post4, x1^0'=x0^post4, oldX4^0'=x1^post4, oldX1^0'=-1+x0^post4, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=x0^post4-x1^post4, -1+x0^post4-x1^post4 >= 0, cost: 3+2*x0^post4-2*x1^post4 Applied chaining First rule: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 3 Second rule: l3 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: -2*x1^0+2*x0^0 New rule: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -2-x1^0+x0^0 >= 0, cost: 1-2*x1^0+2*x0^0 Applied deletion Removed the following rules: 29 Chained accelerated rules with incoming rules Start location: l6 22: l6 -> l3 : TRUE, cost: 2 24: l6 -> l3 : oldX0^0'=oldX3^post5, oldX5^0'=oldX5^post5, oldX2^0'=oldX5^post5, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^post5, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 25: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=x1^post4, oldX4^0'=x1^post4, oldX1^0'=x1^0, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=0, 0 == 0, cost: 3 27: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=x2^0, x1^0'=1+x1^0, oldX1^0'=x1^0, x2^0'=1+x2^0, TRUE, cost: 3 30: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -1-x1^0+x0^0 >= 0, cost: 2-2*x1^0+2*x0^0 31: l6 -> l3 : oldX0^0'=x0^post4, oldX5^0'=oldX5^post5, oldX2^0'=-1+x0^post4-x1^post4, x1^0'=x0^post4, oldX4^0'=x1^post4, oldX1^0'=-1+x0^post4, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=x0^post4-x1^post4, -1+x0^post4-x1^post4 >= 0, cost: 3+2*x0^post4-2*x1^post4 32: l6 -> l3 : oldX0^0'=x0^post4, oldX2^0'=-1+x0^post4-x1^post4, x1^0'=x0^post4, oldX4^0'=x1^post4, oldX1^0'=-1+x0^post4, x0^0'=x0^post4, oldX3^0'=x0^post4, x2^0'=x0^post4-x1^post4, -1+x0^post4-x1^post4 >= 0, cost: 3+2*x0^post4-2*x1^post4 33: l6 -> l3 : oldX0^0'=x0^0, oldX2^0'=-1-x1^0+x0^0+x2^0, x1^0'=x0^0, oldX1^0'=-1+x0^0, x2^0'=-x1^0+x0^0+x2^0, -2-x1^0+x0^0 >= 0, cost: 1-2*x1^0+2*x0^0 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