WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 2-arg3P0 == 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 1: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg3-arg3P1 == 0 /\ -1-arg2P1 == 0 /\ 1+arg1 > 0 /\ -1-arg2 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 2: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (1+arg3-arg3P2 == 0 /\ -1+arg2-arg2P2 == 0 /\ 1+arg2 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 2-arg3P0 == 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg3-arg3P1 == 0 /\ -1-arg2P1 == 0 /\ 1+arg1 > 0 /\ -1-arg2 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=-1+arg1, arg2'=-1, (1+arg1 > 0 /\ 1+arg2 == 0), cost: 1 Applied preprocessing Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (1+arg3-arg3P2 == 0 /\ -1+arg2-arg2P2 == 0 /\ 1+arg2 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3, arg2'=-1+arg2, (1+arg2 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 5: f339_0_main_LT -> f339_0_main_LT : arg1'=-1+arg1, arg2'=-1, (1+arg1 > 0 /\ 1+arg2 == 0), cost: 1 6: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3, arg2'=-1+arg2, (1+arg2 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, TRUE, cost: 1 Applied acceleration Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=-1+arg1, arg2'=-1, (1+arg1 > 0 /\ 1+arg2 == 0), cost: 1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1-n1, arg2'=-1, (2+arg1-n1 > 0 /\ 1+arg2 >= 0 /\ -1-arg2 >= 0 /\ -1+n1 >= 0), cost: n1 Applied instantiation Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1-n1, arg2'=-1, (2+arg1-n1 > 0 /\ 1+arg2 >= 0 /\ -1-arg2 >= 0 /\ -1+n1 >= 0), cost: n1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, (arg1 >= 0 /\ 1 > 0 /\ 1+arg2 >= 0 /\ -1-arg2 >= 0), cost: 1+arg1 Applied acceleration Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3, arg2'=-1+arg2, (1+arg2 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=arg3+n3, arg2'=arg2-n3, (-1+n3 >= 0 /\ 2+arg2-n3 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: n3 Applied instantiation Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=arg3+n3, arg2'=arg2-n3, (-1+n3 >= 0 /\ 2+arg2-n3 > 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: n3 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3+arg2, arg2'=-1, (1 > 0 /\ arg2 >= 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1+arg2 Applied simplification Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, (arg1 >= 0 /\ 1 > 0 /\ 1+arg2 >= 0 /\ -1-arg2 >= 0), cost: 1+arg1 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, (arg1 >= 0 /\ 1+arg2 <= 0 /\ 1+arg2 >= 0), cost: 1+arg1 Applied simplification Original rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3+arg2, arg2'=-1, (1 > 0 /\ arg2 >= 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1+arg2 New rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3+arg2, arg2'=-1, (arg2 >= 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1+arg2 Applied deletion Removed the following rules: 5 6 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 9: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, (arg1 >= 0 /\ 1+arg2 <= 0 /\ 1+arg2 >= 0), cost: 1+arg1 10: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3+arg2, arg2'=-1, (arg2 >= 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1+arg2 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P2, arg3'=1+arg3+arg2, arg2'=-1, (arg2 >= 0 /\ 1+arg1P2 > 0 /\ 1+arg3 > 0), cost: 1+arg2 New rule: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P2, arg3'=3+arg2P0, arg2'=-1, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0 /\ 1+arg1P2 > 0), cost: 2+arg2P0 Applied deletion Removed the following rules: 9 10 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P0, arg3'=2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0), cost: 1 11: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P2, arg3'=3+arg2P0, arg2'=-1, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg2 > 0 /\ 1+arg1P2 > 0), cost: 2+arg2P0 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, 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