WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg2 == 0 /\ arg1-arg1P1 == 0 /\ -1+arg1-arg2P1 == 0), cost: 1 2: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -arg2P2+arg2 == 0 /\ -arg1+arg2 > 0 /\ arg2 > 0 /\ arg2-arg1P2 == 0), cost: 1 3: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 < 0 /\ arg2 > 0 /\ arg1-arg2P3 == 0 /\ -arg1P3+arg2 == 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied preprocessing Original rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg2 == 0 /\ arg1-arg1P1 == 0 /\ -1+arg1-arg2P1 == 0), cost: 1 New rule: f116_0_flip_LE -> f116_0_flip_LE : arg2'=-1+arg1, (arg1 > 0 /\ arg1-arg2 == 0), cost: 1 Applied preprocessing Original rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -arg2P2+arg2 == 0 /\ -arg1+arg2 > 0 /\ arg2 > 0 /\ arg2-arg1P2 == 0), cost: 1 New rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 < 0 /\ arg2 > 0 /\ arg1-arg2P3 == 0 /\ -arg1P3+arg2 == 0), cost: 1 New rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, arg2'=arg1, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 5: f116_0_flip_LE -> f116_0_flip_LE : arg2'=-1+arg1, (arg1 > 0 /\ arg1-arg2 == 0), cost: 1 6: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1 7: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, arg2'=arg1, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 5: f116_0_flip_LE -> f116_0_flip_LE : arg2'=-1+arg1, (arg1 > 0 /\ arg1-arg2 == 0), cost: 1 6: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1 7: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, arg2'=arg1, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f116_0_flip_LE -> f116_0_flip_LE : arg2'=-1+arg1, (arg1 > 0 /\ arg1-arg2 == 0), cost: 1 New rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=-1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg2P0 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=arg2P0, (arg1 > 0 /\ -2+arg2P0 >= 0 /\ -1+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f116_0_flip_LE -> f116_0_flip_LE : arg1'=arg2, arg2'=arg1, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=arg1P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0-arg2P0 > 0 /\ arg2P0 > 0), cost: 2 Applied deletion Removed the following rules: 5 6 7 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 8: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=-1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg2P0 > 0), cost: 2 9: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=arg2P0, (arg1 > 0 /\ -2+arg2P0 >= 0 /\ -1+arg2 > 0), cost: 2 10: f1_0_main_Load -> f116_0_flip_LE : arg1'=arg2P0, arg2'=arg1P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0-arg2P0 > 0 /\ arg2P0 > 0), cost: 2 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 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