WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x30 > 0 /\ -2+x30 < 0 /\ -1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 1: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg1P1 > 0 /\ 1+arg2 > 0 /\ -2+x70 > 0), cost: 1 2: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ arg1-x120 > 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P2 == 0), cost: 1 4: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x170 == 0 /\ arg1-x180 > 0 /\ arg1-arg1P4 == 0), cost: 1 3: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-2*x150 >= 0 /\ arg1-2*x150 == 0 /\ -2+arg1-2*arg1P3 < 0 /\ -2+arg1-2*x150 < 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-arg1P3 > 0), cost: 1 5: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ arg1-arg1P5 > 0 /\ -2+arg1-2*x210 < 0 /\ arg1-2*x210 >= 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0 /\ -2+arg1-2*arg1P5 < 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x30 > 0 /\ -2+x30 < 0 /\ -1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg1P1 > 0 /\ 1+arg2 > 0 /\ -2+x70 > 0), cost: 1 New rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg1P1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ arg1-x120 > 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P2 == 0), cost: 1 New rule: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x110 == 0), cost: 1 Applied preprocessing Original rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-2*x150 >= 0 /\ arg1-2*x150 == 0 /\ -2+arg1-2*arg1P3 < 0 /\ -2+arg1-2*x150 < 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-arg1P3 > 0), cost: 1 New rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 1 Applied preprocessing Original rule: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x170 == 0 /\ arg1-x180 > 0 /\ arg1-arg1P4 == 0), cost: 1 New rule: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x170 == 0), cost: 1 Applied preprocessing Original rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ arg1-arg1P5 > 0 /\ -2+arg1-2*x210 < 0 /\ arg1-2*x210 >= 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0 /\ -2+arg1-2*arg1P5 < 0), cost: 1 New rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 8: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg1P1 > 0 /\ 1+arg2 > 0), cost: 1 9: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x110 == 0), cost: 1 11: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x170 == 0), cost: 1 10: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 1 12: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 New rule: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg1P1 > 0 /\ 1+arg2 > 0), cost: 1 New rule: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Applied deletion Removed the following rules: 6 7 8 Eliminating location f274_0_power_LE\' by chaining: Applied chaining First rule: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x110 == 0), cost: 1 Second rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 1 New rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 Applied simplification Original rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 New rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 Applied chaining First rule: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x170 == 0), cost: 1 Second rule: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 1 New rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 Applied simplification Original rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 New rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 Applied deletion Removed the following rules: 9 10 11 12 Eliminated locations on tree-shaped paths Start location: __init 15: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 16: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 13: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 14: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Accelerated simple loops Start location: __init 15: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 16: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 13: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 14: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Applied chaining First rule: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 New rule: __init -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (-2*arg1P3+2*x110 >= 0 /\ -1+2*x110 > 0 /\ 2+2*arg1P3-2*x110 > 0), cost: 4 Applied chaining First rule: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1-2*x150 == 0 /\ arg1-2*arg1P3 >= 0 /\ arg1-2*x110 == 0 /\ arg1-arg1P3 > 0 /\ 2-arg1+2*arg1P3 > 0), cost: 2 New rule: __init -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (-2*arg1P3+2*x110 >= 0 /\ -1+2*x110 > 0 /\ 2+2*arg1P3-2*x110 > 0), cost: 4 Applied chaining First rule: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 New rule: __init -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (1+2*x170-2*arg1P5 >= 0 /\ 2*x170 > 0 /\ 1-2*x170+2*arg1P5 > 0), cost: 4 Applied chaining First rule: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1-arg1P5 > 0 /\ 2-arg1+2*arg1P5 > 0 /\ -1+arg1-2*x170 == 0 /\ -1+arg1-2*x210 == 0 /\ arg1-2*arg1P5 >= 0), cost: 2 New rule: __init -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (1+2*x170-2*arg1P5 >= 0 /\ 2*x170 > 0 /\ 1-2*x170+2*arg1P5 > 0), cost: 4 Applied deletion Removed the following rules: 15 16 Chained accelerated rules with incoming rules Start location: __init 13: __init -> f274_0_power_LE : arg1'=arg1P0, arg2'=arg2P0, (-1+arg1P0 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 14: __init -> f274_0_power_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1P1 > 0 /\ 1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 17: __init -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (-2*arg1P3+2*x110 >= 0 /\ -1+2*x110 > 0 /\ 2+2*arg1P3-2*x110 > 0), cost: 4 18: __init -> f274_0_power_LE : arg1'=arg1P3, arg2'=arg2P3, (-2*arg1P3+2*x110 >= 0 /\ -1+2*x110 > 0 /\ 2+2*arg1P3-2*x110 > 0), cost: 4 19: __init -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (1+2*x170-2*arg1P5 >= 0 /\ 2*x170 > 0 /\ 1-2*x170+2*arg1P5 > 0), cost: 4 20: __init -> f274_0_power_LE : arg1'=arg1P5, arg2'=arg2P5, (1+2*x170-2*arg1P5 >= 0 /\ 2*x170 > 0 /\ 1-2*x170+2*arg1P5 > 0), cost: 4 Removed unreachable locations and irrelevant leafs Start location: __init Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0