WORST_CASE(Omega(0),?) Initial ITS Start location: l11 0: l0 -> l1 : b_16^0'=b_16^post0, st_15^0'=st_15^post0, rt_11^0'=rt_11^post0, x_14^0'=x_14^post0, (-x_14^post0+x_14^0 == 0 /\ -1+b_16^post0 == 0 /\ rt_11^0-rt_11^post0 == 0 /\ st_15^0-st_15^post0 == 0 /\ 1-x_14^0 <= 0), cost: 1 4: l1 -> l5 : b_16^0'=b_16^post4, st_15^0'=st_15^post4, rt_11^0'=rt_11^post4, x_14^0'=x_14^post4, (b_16^0-b_16^post4 == 0 /\ -x_14^post4+x_14^0 == 0 /\ x_14^0 <= 0 /\ rt_11^post4-st_15^0 == 0 /\ -x_14^0 <= 0 /\ -st_15^post4+st_15^0 == 0), cost: 1 5: l1 -> l6 : b_16^0'=b_16^post5, st_15^0'=st_15^post5, rt_11^0'=rt_11^post5, x_14^0'=x_14^post5, (b_16^0-b_16^post5 == 0 /\ st_15^0-st_15^post5 == 0 /\ -x_14^post5+x_14^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 6: l1 -> l6 : b_16^0'=b_16^post6, st_15^0'=st_15^post6, rt_11^0'=rt_11^post6, x_14^0'=x_14^post6, (st_15^0-st_15^post6 == 0 /\ 1+x_14^0 <= 0 /\ x_14^0-x_14^post6 == 0 /\ b_16^0-b_16^post6 == 0 /\ -rt_11^post6+rt_11^0 == 0), cost: 1 1: l2 -> l4 : b_16^0'=b_16^post1, st_15^0'=st_15^post1, rt_11^0'=rt_11^post1, x_14^0'=x_14^post1, (-rt_11^post1+rt_11^0 == 0 /\ b_16^0-b_16^post1 == 0 /\ -st_15^post1+st_15^0 == 0 /\ -x_14^post1+x_14^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 2: l2 -> l4 : b_16^0'=b_16^post2, st_15^0'=st_15^post2, rt_11^0'=rt_11^post2, x_14^0'=x_14^post2, (1+x_14^0 <= 0 /\ -rt_11^post2+rt_11^0 == 0 /\ st_15^0-st_15^post2 == 0 /\ -x_14^post2+x_14^0 == 0 /\ b_16^0-b_16^post2 == 0), cost: 1 3: l4 -> l3 : b_16^0'=b_16^post3, st_15^0'=st_15^post3, rt_11^0'=rt_11^post3, x_14^0'=x_14^post3, (1-b_16^0 <= 0 /\ -1+b_16^0 <= 0 /\ b_16^post3 == 0 /\ st_15^0-st_15^post3 == 0 /\ 1+x_14^post3-x_14^0 == 0 /\ rt_11^0-rt_11^post3 == 0), cost: 1 14: l3 -> l7 : b_16^0'=b_16^post14, st_15^0'=st_15^post14, rt_11^0'=rt_11^post14, x_14^0'=x_14^post14, (-rt_11^post14+rt_11^0 == 0 /\ x_14^post14+x_14^0 == 0 /\ b_16^0-b_16^post14 == 0 /\ -st_15^post14+st_15^0 == 0), cost: 1 7: l6 -> l3 : b_16^0'=b_16^post7, st_15^0'=st_15^post7, rt_11^0'=rt_11^post7, x_14^0'=x_14^post7, (rt_11^0-rt_11^post7 == 0 /\ 1-b_16^0 <= 0 /\ -1+b_16^0 <= 0 /\ b_16^post7 == 0 /\ st_15^0-st_15^post7 == 0 /\ 1+x_14^post7-x_14^0 == 0), cost: 1 8: l7 -> l5 : b_16^0'=b_16^post8, st_15^0'=st_15^post8, rt_11^0'=rt_11^post8, x_14^0'=x_14^post8, (-x_14^post8+x_14^0 == 0 /\ rt_11^post8-st_15^0 == 0 /\ b_16^0-b_16^post8 == 0 /\ x_14^0 <= 0 /\ st_15^0-st_15^post8 == 0 /\ -x_14^0 <= 0), cost: 1 9: l7 -> l8 : b_16^0'=b_16^post9, st_15^0'=st_15^post9, rt_11^0'=rt_11^post9, x_14^0'=x_14^post9, (-st_15^post9+st_15^0 == 0 /\ b_16^0-b_16^post9 == 0 /\ -x_14^post9+x_14^0 == 0 /\ -rt_11^post9+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 10: l7 -> l8 : b_16^0'=b_16^post10, st_15^0'=st_15^post10, rt_11^0'=rt_11^post10, x_14^0'=x_14^post10, (1+x_14^0 <= 0 /\ -x_14^post10+x_14^0 == 0 /\ b_16^0-b_16^post10 == 0 /\ -rt_11^post10+rt_11^0 == 0 /\ st_15^0-st_15^post10 == 0), cost: 1 11: l8 -> l9 : b_16^0'=b_16^post11, st_15^0'=st_15^post11, rt_11^0'=rt_11^post11, x_14^0'=x_14^post11, (rt_11^0-rt_11^post11 == 0 /\ 2-b_16^0 <= 0 /\ -x_14^post11+x_14^0 == 0 /\ b_16^0-b_16^post11 == 0 /\ st_15^0-st_15^post11 == 0), cost: 1 12: l8 -> l9 : b_16^0'=b_16^post12, st_15^0'=st_15^post12, rt_11^0'=rt_11^post12, x_14^0'=x_14^post12, (b_16^0 <= 0 /\ rt_11^0-rt_11^post12 == 0 /\ b_16^0-b_16^post12 == 0 /\ -x_14^post12+x_14^0 == 0 /\ st_15^0-st_15^post12 == 0), cost: 1 13: l9 -> l1 : b_16^0'=b_16^post13, st_15^0'=st_15^post13, rt_11^0'=rt_11^post13, x_14^0'=x_14^post13, (-1+x_14^10-x_14^0 == 0 /\ -1+b_16^post13 == 0 /\ x_14^post13+x_14^10 == 0 /\ rt_11^0-rt_11^post13 == 0 /\ st_15^0-st_15^post13 == 0), cost: 1 15: l10 -> l7 : b_16^0'=b_16^post15, st_15^0'=st_15^post15, rt_11^0'=rt_11^post15, x_14^0'=x_14^post15, (-rt_11^post15+rt_11^0 == 0 /\ x_14^post15+x_14^0 == 0 /\ st_15^0-st_15^post15 == 0 /\ b_16^0-b_16^post15 == 0), cost: 1 16: l11 -> l0 : b_16^0'=b_16^post16, st_15^0'=st_15^post16, rt_11^0'=rt_11^post16, x_14^0'=x_14^post16, (st_15^0-st_15^post16 == 0 /\ b_16^0-b_16^post16 == 0 /\ x_14^0-x_14^post16 == 0 /\ rt_11^0-rt_11^post16 == 0), cost: 1 Removed unreachable rules and leafs Start location: l11 0: l0 -> l1 : b_16^0'=b_16^post0, st_15^0'=st_15^post0, rt_11^0'=rt_11^post0, x_14^0'=x_14^post0, (-x_14^post0+x_14^0 == 0 /\ -1+b_16^post0 == 0 /\ rt_11^0-rt_11^post0 == 0 /\ st_15^0-st_15^post0 == 0 /\ 1-x_14^0 <= 0), cost: 1 5: l1 -> l6 : b_16^0'=b_16^post5, st_15^0'=st_15^post5, rt_11^0'=rt_11^post5, x_14^0'=x_14^post5, (b_16^0-b_16^post5 == 0 /\ st_15^0-st_15^post5 == 0 /\ -x_14^post5+x_14^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 6: l1 -> l6 : b_16^0'=b_16^post6, st_15^0'=st_15^post6, rt_11^0'=rt_11^post6, x_14^0'=x_14^post6, (st_15^0-st_15^post6 == 0 /\ 1+x_14^0 <= 0 /\ x_14^0-x_14^post6 == 0 /\ b_16^0-b_16^post6 == 0 /\ -rt_11^post6+rt_11^0 == 0), cost: 1 14: l3 -> l7 : b_16^0'=b_16^post14, st_15^0'=st_15^post14, rt_11^0'=rt_11^post14, x_14^0'=x_14^post14, (-rt_11^post14+rt_11^0 == 0 /\ x_14^post14+x_14^0 == 0 /\ b_16^0-b_16^post14 == 0 /\ -st_15^post14+st_15^0 == 0), cost: 1 7: l6 -> l3 : b_16^0'=b_16^post7, st_15^0'=st_15^post7, rt_11^0'=rt_11^post7, x_14^0'=x_14^post7, (rt_11^0-rt_11^post7 == 0 /\ 1-b_16^0 <= 0 /\ -1+b_16^0 <= 0 /\ b_16^post7 == 0 /\ st_15^0-st_15^post7 == 0 /\ 1+x_14^post7-x_14^0 == 0), cost: 1 9: l7 -> l8 : b_16^0'=b_16^post9, st_15^0'=st_15^post9, rt_11^0'=rt_11^post9, x_14^0'=x_14^post9, (-st_15^post9+st_15^0 == 0 /\ b_16^0-b_16^post9 == 0 /\ -x_14^post9+x_14^0 == 0 /\ -rt_11^post9+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 10: l7 -> l8 : b_16^0'=b_16^post10, st_15^0'=st_15^post10, rt_11^0'=rt_11^post10, x_14^0'=x_14^post10, (1+x_14^0 <= 0 /\ -x_14^post10+x_14^0 == 0 /\ b_16^0-b_16^post10 == 0 /\ -rt_11^post10+rt_11^0 == 0 /\ st_15^0-st_15^post10 == 0), cost: 1 11: l8 -> l9 : b_16^0'=b_16^post11, st_15^0'=st_15^post11, rt_11^0'=rt_11^post11, x_14^0'=x_14^post11, (rt_11^0-rt_11^post11 == 0 /\ 2-b_16^0 <= 0 /\ -x_14^post11+x_14^0 == 0 /\ b_16^0-b_16^post11 == 0 /\ st_15^0-st_15^post11 == 0), cost: 1 12: l8 -> l9 : b_16^0'=b_16^post12, st_15^0'=st_15^post12, rt_11^0'=rt_11^post12, x_14^0'=x_14^post12, (b_16^0 <= 0 /\ rt_11^0-rt_11^post12 == 0 /\ b_16^0-b_16^post12 == 0 /\ -x_14^post12+x_14^0 == 0 /\ st_15^0-st_15^post12 == 0), cost: 1 13: l9 -> l1 : b_16^0'=b_16^post13, st_15^0'=st_15^post13, rt_11^0'=rt_11^post13, x_14^0'=x_14^post13, (-1+x_14^10-x_14^0 == 0 /\ -1+b_16^post13 == 0 /\ x_14^post13+x_14^10 == 0 /\ rt_11^0-rt_11^post13 == 0 /\ st_15^0-st_15^post13 == 0), cost: 1 16: l11 -> l0 : b_16^0'=b_16^post16, st_15^0'=st_15^post16, rt_11^0'=rt_11^post16, x_14^0'=x_14^post16, (st_15^0-st_15^post16 == 0 /\ b_16^0-b_16^post16 == 0 /\ x_14^0-x_14^post16 == 0 /\ rt_11^0-rt_11^post16 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : b_16^0'=b_16^post0, st_15^0'=st_15^post0, rt_11^0'=rt_11^post0, x_14^0'=x_14^post0, (-x_14^post0+x_14^0 == 0 /\ -1+b_16^post0 == 0 /\ rt_11^0-rt_11^post0 == 0 /\ st_15^0-st_15^post0 == 0 /\ 1-x_14^0 <= 0), cost: 1 New rule: l0 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l6 : b_16^0'=b_16^post5, st_15^0'=st_15^post5, rt_11^0'=rt_11^post5, x_14^0'=x_14^post5, (b_16^0-b_16^post5 == 0 /\ st_15^0-st_15^post5 == 0 /\ -x_14^post5+x_14^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 New rule: l1 -> l6 : -1+x_14^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l6 : b_16^0'=b_16^post6, st_15^0'=st_15^post6, rt_11^0'=rt_11^post6, x_14^0'=x_14^post6, (st_15^0-st_15^post6 == 0 /\ 1+x_14^0 <= 0 /\ x_14^0-x_14^post6 == 0 /\ b_16^0-b_16^post6 == 0 /\ -rt_11^post6+rt_11^0 == 0), cost: 1 New rule: l1 -> l6 : 1+x_14^0 <= 0, cost: 1 Applied preprocessing Original rule: l6 -> l3 : b_16^0'=b_16^post7, st_15^0'=st_15^post7, rt_11^0'=rt_11^post7, x_14^0'=x_14^post7, (rt_11^0-rt_11^post7 == 0 /\ 1-b_16^0 <= 0 /\ -1+b_16^0 <= 0 /\ b_16^post7 == 0 /\ st_15^0-st_15^post7 == 0 /\ 1+x_14^post7-x_14^0 == 0), cost: 1 New rule: l6 -> l3 : b_16^0'=0, x_14^0'=-1+x_14^0, -1+b_16^0 == 0, cost: 1 Applied preprocessing Original rule: l7 -> l8 : b_16^0'=b_16^post9, st_15^0'=st_15^post9, rt_11^0'=rt_11^post9, x_14^0'=x_14^post9, (-st_15^post9+st_15^0 == 0 /\ b_16^0-b_16^post9 == 0 /\ -x_14^post9+x_14^0 == 0 /\ -rt_11^post9+rt_11^0 == 0 /\ 1-x_14^0 <= 0), cost: 1 New rule: l7 -> l8 : -1+x_14^0 >= 0, cost: 1 Applied preprocessing Original rule: l7 -> l8 : b_16^0'=b_16^post10, st_15^0'=st_15^post10, rt_11^0'=rt_11^post10, x_14^0'=x_14^post10, (1+x_14^0 <= 0 /\ -x_14^post10+x_14^0 == 0 /\ b_16^0-b_16^post10 == 0 /\ -rt_11^post10+rt_11^0 == 0 /\ st_15^0-st_15^post10 == 0), cost: 1 New rule: l7 -> l8 : 1+x_14^0 <= 0, cost: 1 Applied preprocessing Original rule: l8 -> l9 : b_16^0'=b_16^post11, st_15^0'=st_15^post11, rt_11^0'=rt_11^post11, x_14^0'=x_14^post11, (rt_11^0-rt_11^post11 == 0 /\ 2-b_16^0 <= 0 /\ -x_14^post11+x_14^0 == 0 /\ b_16^0-b_16^post11 == 0 /\ st_15^0-st_15^post11 == 0), cost: 1 New rule: l8 -> l9 : -2+b_16^0 >= 0, cost: 1 Applied preprocessing Original rule: l8 -> l9 : b_16^0'=b_16^post12, st_15^0'=st_15^post12, rt_11^0'=rt_11^post12, x_14^0'=x_14^post12, (b_16^0 <= 0 /\ rt_11^0-rt_11^post12 == 0 /\ b_16^0-b_16^post12 == 0 /\ -x_14^post12+x_14^0 == 0 /\ st_15^0-st_15^post12 == 0), cost: 1 New rule: l8 -> l9 : b_16^0 <= 0, cost: 1 Applied preprocessing Original rule: l9 -> l1 : b_16^0'=b_16^post13, st_15^0'=st_15^post13, rt_11^0'=rt_11^post13, x_14^0'=x_14^post13, (-1+x_14^10-x_14^0 == 0 /\ -1+b_16^post13 == 0 /\ x_14^post13+x_14^10 == 0 /\ rt_11^0-rt_11^post13 == 0 /\ st_15^0-st_15^post13 == 0), cost: 1 New rule: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l7 : b_16^0'=b_16^post14, st_15^0'=st_15^post14, rt_11^0'=rt_11^post14, x_14^0'=x_14^post14, (-rt_11^post14+rt_11^0 == 0 /\ x_14^post14+x_14^0 == 0 /\ b_16^0-b_16^post14 == 0 /\ -st_15^post14+st_15^0 == 0), cost: 1 New rule: l3 -> l7 : x_14^0'=-x_14^0, TRUE, cost: 1 Applied preprocessing Original rule: l11 -> l0 : b_16^0'=b_16^post16, st_15^0'=st_15^post16, rt_11^0'=rt_11^post16, x_14^0'=x_14^post16, (st_15^0-st_15^post16 == 0 /\ b_16^0-b_16^post16 == 0 /\ x_14^0-x_14^post16 == 0 /\ rt_11^0-rt_11^post16 == 0), cost: 1 New rule: l11 -> l0 : TRUE, cost: 1 Simplified rules Start location: l11 17: l0 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 1 18: l1 -> l6 : -1+x_14^0 >= 0, cost: 1 19: l1 -> l6 : 1+x_14^0 <= 0, cost: 1 26: l3 -> l7 : x_14^0'=-x_14^0, TRUE, cost: 1 20: l6 -> l3 : b_16^0'=0, x_14^0'=-1+x_14^0, -1+b_16^0 == 0, cost: 1 21: l7 -> l8 : -1+x_14^0 >= 0, cost: 1 22: l7 -> l8 : 1+x_14^0 <= 0, cost: 1 23: l8 -> l9 : -2+b_16^0 >= 0, cost: 1 24: l8 -> l9 : b_16^0 <= 0, cost: 1 25: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 27: l11 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l11 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 1 New rule: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Applied deletion Removed the following rules: 17 27 Eliminating location l3 by chaining: Applied chaining First rule: l6 -> l3 : b_16^0'=0, x_14^0'=-1+x_14^0, -1+b_16^0 == 0, cost: 1 Second rule: l3 -> l7 : x_14^0'=-x_14^0, TRUE, cost: 1 New rule: l6 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, -1+b_16^0 == 0, cost: 2 Applied deletion Removed the following rules: 20 26 Eliminated locations on linear paths Start location: l11 18: l1 -> l6 : -1+x_14^0 >= 0, cost: 1 19: l1 -> l6 : 1+x_14^0 <= 0, cost: 1 29: l6 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, -1+b_16^0 == 0, cost: 2 21: l7 -> l8 : -1+x_14^0 >= 0, cost: 1 22: l7 -> l8 : 1+x_14^0 <= 0, cost: 1 23: l8 -> l9 : -2+b_16^0 >= 0, cost: 1 24: l8 -> l9 : b_16^0 <= 0, cost: 1 25: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Eliminating location l6 by chaining: Applied chaining First rule: l1 -> l6 : -1+x_14^0 >= 0, cost: 1 Second rule: l6 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, -1+b_16^0 == 0, cost: 2 New rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0), cost: 3 Applied chaining First rule: l1 -> l6 : 1+x_14^0 <= 0, cost: 1 Second rule: l6 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, -1+b_16^0 == 0, cost: 2 New rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (1+x_14^0 <= 0 /\ -1+b_16^0 == 0), cost: 3 Applied deletion Removed the following rules: 18 19 29 Eliminating location l8 by chaining: Applied chaining First rule: l7 -> l8 : -1+x_14^0 >= 0, cost: 1 Second rule: l8 -> l9 : -2+b_16^0 >= 0, cost: 1 New rule: l7 -> l9 : (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0), cost: 2 Applied chaining First rule: l7 -> l8 : -1+x_14^0 >= 0, cost: 1 Second rule: l8 -> l9 : b_16^0 <= 0, cost: 1 New rule: l7 -> l9 : (b_16^0 <= 0 /\ -1+x_14^0 >= 0), cost: 2 Applied chaining First rule: l7 -> l8 : 1+x_14^0 <= 0, cost: 1 Second rule: l8 -> l9 : -2+b_16^0 >= 0, cost: 1 New rule: l7 -> l9 : (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0), cost: 2 Applied chaining First rule: l7 -> l8 : 1+x_14^0 <= 0, cost: 1 Second rule: l8 -> l9 : b_16^0 <= 0, cost: 1 New rule: l7 -> l9 : (b_16^0 <= 0 /\ 1+x_14^0 <= 0), cost: 2 Applied deletion Removed the following rules: 21 22 23 24 Eliminated locations on tree-shaped paths Start location: l11 30: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0), cost: 3 31: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (1+x_14^0 <= 0 /\ -1+b_16^0 == 0), cost: 3 32: l7 -> l9 : (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0), cost: 2 33: l7 -> l9 : (b_16^0 <= 0 /\ -1+x_14^0 >= 0), cost: 2 34: l7 -> l9 : (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0), cost: 2 35: l7 -> l9 : (b_16^0 <= 0 /\ 1+x_14^0 <= 0), cost: 2 25: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Applied merging first rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0), cost: 3 second rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, (1+x_14^0 <= 0 /\ -1+b_16^0 == 0), cost: 3 new rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, ((-1+b_16^0 == 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -1+b_16^0 == 0)), cost: 3 Applied merging first rule: l7 -> l9 : (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0), cost: 2 second rule: l7 -> l9 : (b_16^0 <= 0 /\ -1+x_14^0 >= 0), cost: 2 new rule: l7 -> l9 : ((b_16^0 <= 0 /\ -1+x_14^0 >= 0) \/ (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0)), cost: 2 Applied merging first rule: l7 -> l9 : (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0), cost: 2 second rule: l7 -> l9 : (b_16^0 <= 0 /\ 1+x_14^0 <= 0), cost: 2 new rule: l7 -> l9 : ((1+x_14^0 <= 0 /\ -2+b_16^0 >= 0) \/ (b_16^0 <= 0 /\ 1+x_14^0 <= 0)), cost: 2 Applied merging first rule: l7 -> l9 : ((b_16^0 <= 0 /\ -1+x_14^0 >= 0) \/ (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0)), cost: 2 second rule: l7 -> l9 : ((1+x_14^0 <= 0 /\ -2+b_16^0 >= 0) \/ (b_16^0 <= 0 /\ 1+x_14^0 <= 0)), cost: 2 new rule: l7 -> l9 : ((b_16^0 <= 0 /\ -1+x_14^0 >= 0) \/ (b_16^0 <= 0 /\ 1+x_14^0 <= 0) \/ (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0)), cost: 2 Merged rules Start location: l11 36: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, ((-1+b_16^0 == 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -1+b_16^0 == 0)), cost: 3 39: l7 -> l9 : ((b_16^0 <= 0 /\ -1+x_14^0 >= 0) \/ (b_16^0 <= 0 /\ 1+x_14^0 <= 0) \/ (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0)), cost: 2 25: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Eliminating location l7 by chaining: Applied chaining First rule: l1 -> l7 : b_16^0'=0, x_14^0'=1-x_14^0, ((-1+b_16^0 == 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -1+b_16^0 == 0)), cost: 3 Second rule: l7 -> l9 : ((b_16^0 <= 0 /\ -1+x_14^0 >= 0) \/ (b_16^0 <= 0 /\ 1+x_14^0 <= 0) \/ (-2+b_16^0 >= 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -2+b_16^0 >= 0)), cost: 2 New rule: l1 -> l9 : b_16^0'=0, x_14^0'=1-x_14^0, (((-1+b_16^0 == 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -1+b_16^0 == 0)) /\ ((0 <= 0 /\ 2-x_14^0 <= 0) \/ (-2 >= 0 /\ 2-x_14^0 <= 0) \/ (0 <= 0 /\ -x_14^0 >= 0) \/ (-2 >= 0 /\ -x_14^0 >= 0))), cost: 5 Applied simplification Original rule: l1 -> l9 : b_16^0'=0, x_14^0'=1-x_14^0, (((-1+b_16^0 == 0 /\ -1+x_14^0 >= 0) \/ (1+x_14^0 <= 0 /\ -1+b_16^0 == 0)) /\ ((0 <= 0 /\ 2-x_14^0 <= 0) \/ (-2 >= 0 /\ 2-x_14^0 <= 0) \/ (0 <= 0 /\ -x_14^0 >= 0) \/ (-2 >= 0 /\ -x_14^0 >= 0))), cost: 5 New rule: l1 -> l9 : b_16^0'=0, x_14^0'=1-x_14^0, (((0 <= 0 /\ -x_14^0 >= 0) \/ -2+x_14^0 >= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 5 Applied deletion Removed the following rules: 36 39 Eliminating location l9 by chaining: Applied chaining First rule: l1 -> l9 : b_16^0'=0, x_14^0'=1-x_14^0, (((0 <= 0 /\ -x_14^0 >= 0) \/ -2+x_14^0 >= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 5 Second rule: l9 -> l1 : b_16^0'=1, x_14^0'=-1-x_14^0, TRUE, cost: 1 New rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, (((0 <= 0 /\ -x_14^0 >= 0) \/ -2+x_14^0 >= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 Applied simplification Original rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, (((0 <= 0 /\ -x_14^0 >= 0) \/ -2+x_14^0 >= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 New rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, ((-2+x_14^0 >= 0 \/ x_14^0 <= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 Applied deletion Removed the following rules: 25 40 Eliminated locations on linear paths Start location: l11 41: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, ((-2+x_14^0 >= 0 \/ x_14^0 <= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Applied nonterm Original rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, ((-2+x_14^0 >= 0 \/ x_14^0 <= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 New rule: l1 -> [12] : (-1-x_14^0 >= 0 /\ -x_14^0 >= 0 /\ ((1-b_16^0 >= 0 /\ -1+b_16^0 >= 0 /\ FALSE) \/ (-1-x_14^0 >= 0 /\ 1-b_16^0 >= 0 /\ -1+b_16^0 >= 0))), cost: NONTERM Applied acceleration Original rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2+x_14^0, ((-2+x_14^0 >= 0 \/ x_14^0 <= 0) /\ ((1+x_14^0 <= 0 /\ -1+b_16^0 == 0) \/ (-1+b_16^0 == 0 /\ -1+x_14^0 >= 0))), cost: 6 New rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-1+n0 >= 0 /\ ((1-b_16^0 >= 0 /\ -1+b_16^0 >= 0 /\ ((1-2*n0+x_14^0 >= 0 /\ -1+x_14^0 >= 0) \/ (-2+x_14^0 >= 0 /\ 1-2*n0+x_14^0 >= 0))) \/ (-1-x_14^0 >= 0 /\ 1-b_16^0 >= 0 /\ -1+b_16^0 >= 0)) /\ ((-1-x_14^0 >= 0 /\ -x_14^0 >= 0) \/ -2*n0+x_14^0 >= 0)), cost: 6*n0 Applied simplification Original rule: l1 -> [12] : (-1-x_14^0 >= 0 /\ -x_14^0 >= 0 /\ ((1-b_16^0 >= 0 /\ -1+b_16^0 >= 0 /\ FALSE) \/ (-1-x_14^0 >= 0 /\ 1-b_16^0 >= 0 /\ -1+b_16^0 >= 0))), cost: NONTERM New rule: l1 -> [12] : (-1-x_14^0 >= 0 /\ -1+b_16^0 <= 0 /\ -1+b_16^0 >= 0), cost: NONTERM Applied simplification Original rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-1+n0 >= 0 /\ ((1-b_16^0 >= 0 /\ -1+b_16^0 >= 0 /\ ((1-2*n0+x_14^0 >= 0 /\ -1+x_14^0 >= 0) \/ (-2+x_14^0 >= 0 /\ 1-2*n0+x_14^0 >= 0))) \/ (-1-x_14^0 >= 0 /\ 1-b_16^0 >= 0 /\ -1+b_16^0 >= 0)) /\ ((-1-x_14^0 >= 0 /\ -x_14^0 >= 0) \/ -2*n0+x_14^0 >= 0)), cost: 6*n0 New rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-1+b_16^0 <= 0 /\ -1+b_16^0 >= 0 /\ -1+n0 >= 0 /\ (1+x_14^0 <= 0 \/ -2*n0+x_14^0 >= 0)), cost: 6*n0 Applied deletion Removed the following rules: 41 Accelerated simple loops Start location: l11 44: l1 -> [12] : (-1-x_14^0 >= 0 /\ -1+b_16^0 <= 0 /\ -1+b_16^0 >= 0), cost: NONTERM 45: l1 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-1+b_16^0 <= 0 /\ -1+b_16^0 >= 0 /\ -1+n0 >= 0 /\ (1+x_14^0 <= 0 \/ -2*n0+x_14^0 >= 0)), cost: 6*n0 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Applied chaining First rule: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 Second rule: l1 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-1+b_16^0 <= 0 /\ -1+b_16^0 >= 0 /\ -1+n0 >= 0 /\ (1+x_14^0 <= 0 \/ -2*n0+x_14^0 >= 0)), cost: 6*n0 New rule: l11 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-2*n0+x_14^0 >= 0 /\ -1+n0 >= 0 /\ -1+x_14^0 >= 0), cost: 2+6*n0 Applied deletion Removed the following rules: 44 45 Chained accelerated rules with incoming rules Start location: l11 28: l11 -> l1 : b_16^0'=1, -1+x_14^0 >= 0, cost: 2 46: l11 -> l1 : b_16^0'=1, x_14^0'=-2*n0+x_14^0, (-2*n0+x_14^0 >= 0 /\ -1+n0 >= 0 /\ -1+x_14^0 >= 0), cost: 2+6*n0 Removed unreachable locations and irrelevant leafs Start location: l11 Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0