WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 1: f256_0_log_LT -> f256_0_log_LT\' : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 > 0 /\ -1+arg2 > 0 /\ arg1-x80 > 0 /\ -arg1+arg2 <= 0 /\ -arg2P1+arg2 == 0 /\ arg1-arg1P1 == 0), cost: 1 2: f256_0_log_LT\' -> f256_0_log_LT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1 > 0 /\ -1+arg2 > 0 /\ arg2-arg2P2 == 0 /\ -arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f256_0_log_LT -> f256_0_log_LT\' : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 > 0 /\ -1+arg2 > 0 /\ arg1-x80 > 0 /\ -arg1+arg2 <= 0 /\ -arg2P1+arg2 == 0 /\ arg1-arg1P1 == 0), cost: 1 New rule: f256_0_log_LT -> f256_0_log_LT\' : (-1+arg2 > 0 /\ -arg1+arg2 <= 0), cost: 1 Applied preprocessing Original rule: f256_0_log_LT\' -> f256_0_log_LT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1 > 0 /\ -1+arg2 > 0 /\ arg2-arg2P2 == 0 /\ -arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 1 New rule: f256_0_log_LT\' -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 4: f256_0_log_LT -> f256_0_log_LT\' : (-1+arg2 > 0 /\ -arg1+arg2 <= 0), cost: 1 5: f256_0_log_LT\' -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 New rule: __init -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P0 > 0 /\ arg1P3 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P3 > 0), cost: 2 Applied deletion Removed the following rules: 0 3 Eliminating location f256_0_log_LT\' by chaining: Applied chaining First rule: f256_0_log_LT -> f256_0_log_LT\' : (-1+arg2 > 0 /\ -arg1+arg2 <= 0), cost: 1 Second rule: f256_0_log_LT\' -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 1 New rule: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-1+arg2 > 0 /\ -arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 Applied simplification Original rule: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-1+arg2 > 0 /\ -arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 New rule: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: __init 7: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 6: __init -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P0 > 0 /\ arg1P3 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P3 > 0), cost: 2 Accelerated simple loops Start location: __init 7: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 6: __init -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P0 > 0 /\ arg1P3 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P3 > 0), cost: 2 Applied chaining First rule: __init -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P0 > 0 /\ arg1P3 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P3 > 0), cost: 2 Second rule: f256_0_log_LT -> f256_0_log_LT : arg1'=arg1P2, (-arg1+arg2 <= 0 /\ arg1-arg1P2 > 0 /\ arg1-arg2*arg1P2 >= 0 /\ -arg1+arg2*arg1P2+arg2 > 0), cost: 2 New rule: __init -> f256_0_log_LT : arg1'=arg1P2, arg2'=arg2P0, (-1+arg1P2*arg2P0 >= 0 /\ 2-arg1P2*arg2P0+arg1P2-arg2P0 <= 0 /\ 1-arg2P0 <= 0), cost: 4 Applied deletion Removed the following rules: 7 Chained accelerated rules with incoming rules Start location: __init 6: __init -> f256_0_log_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P0 > 0 /\ arg1P3 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P3 > 0), cost: 2 8: __init -> f256_0_log_LT : arg1'=arg1P2, arg2'=arg2P0, (-1+arg1P2*arg2P0 >= 0 /\ 2-arg1P2*arg2P0+arg1P2-arg2P0 <= 0 /\ 1-arg2P0 <= 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