WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=arg3P0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (arg1 > 0 /\ 1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0 /\ -arg3P0 == 0), cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg3P1, arg5'=arg5P1, arg2'=arg2P1, arg4'=arg4P1, (arg1 > 0 /\ 1+arg4 > 0 /\ -arg5P1+arg5 == 0 /\ 2-arg1+arg4 <= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2 > 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ 1-arg4P1+arg4 == 0 /\ 1-arg3P1+arg3 == 0 /\ arg3-arg5 < 0), cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg3'=arg3P2, arg5'=arg5P2, arg2'=arg2P2, arg4'=arg4P2, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=arg3P0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (arg1 > 0 /\ 1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0 /\ -arg3P0 == 0), cost: 1 New rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 Applied preprocessing Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg3P1, arg5'=arg5P1, arg2'=arg2P1, arg4'=arg4P1, (arg1 > 0 /\ 1+arg4 > 0 /\ -arg5P1+arg5 == 0 /\ 2-arg1+arg4 <= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2 > 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ 1-arg4P1+arg4 == 0 /\ 1-arg3P1+arg3 == 0 /\ arg3-arg5 < 0), cost: 1 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=1+arg3, arg2'=arg2P1, arg4'=1+arg4, (1+arg4 > 0 /\ 2-arg1+arg4 <= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ -arg3+arg5 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: 1 Simplified rules Start location: __init 3: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 4: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=1+arg3, arg2'=arg2P1, arg4'=1+arg4, (1+arg4 > 0 /\ 2-arg1+arg4 <= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ -arg3+arg5 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg3'=arg3P2, arg5'=arg5P2, arg2'=arg2P2, arg4'=arg4P2, TRUE, cost: 1 Applied acceleration Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=1+arg3, arg2'=arg2P1, arg4'=1+arg4, (1+arg4 > 0 /\ 2-arg1+arg4 <= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ -arg3+arg5 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: 1 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg3+n0, arg2'=arg2P1, arg4'=n0+arg4, (-1+n0 >= 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ 1-arg3+arg5-n0 > 0 /\ ((-1-n0+arg1P1-arg4 >= 0 /\ -2+arg1-arg4 >= 0) \/ (-1-n0+arg1P1-arg4 >= 0 /\ 1+arg1-arg1P1 >= 0))), cost: n0 Applied instantiation Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg3+n0, arg2'=arg2P1, arg4'=n0+arg4, (-1+n0 >= 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ 1-arg3+arg5-n0 > 0 /\ ((-1-n0+arg1P1-arg4 >= 0 /\ -2+arg1-arg4 >= 0) \/ (-1-n0+arg1P1-arg4 >= 0 /\ 1+arg1-arg1P1 >= 0))), cost: n0 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1+arg3+arg1P1-arg4, arg2'=arg2P1, arg4'=-1+arg1P1, (2-arg3+arg5-arg1P1+arg4 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ -2+arg1P1-arg4 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ ((0 >= 0 /\ -2+arg1-arg4 >= 0) \/ (0 >= 0 /\ 1+arg1-arg1P1 >= 0))), cost: -1+arg1P1-arg4 Applied instantiation Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg3+n0, arg2'=arg2P1, arg4'=n0+arg4, (-1+n0 >= 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ 1-arg3+arg5-n0 > 0 /\ ((-1-n0+arg1P1-arg4 >= 0 /\ -2+arg1-arg4 >= 0) \/ (-1-n0+arg1P1-arg4 >= 0 /\ 1+arg1-arg1P1 >= 0))), cost: n0 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5, arg2'=arg2P1, arg4'=-arg3+arg5+arg4, (1 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ -1-arg3+arg5 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ ((1+arg1-arg1P1 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0) \/ (-2+arg1-arg4 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0))), cost: -arg3+arg5 Applied simplification Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1+arg3+arg1P1-arg4, arg2'=arg2P1, arg4'=-1+arg1P1, (2-arg3+arg5-arg1P1+arg4 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ -2+arg1P1-arg4 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ ((0 >= 0 /\ -2+arg1-arg4 >= 0) \/ (0 >= 0 /\ 1+arg1-arg1P1 >= 0))), cost: -1+arg1P1-arg4 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1+arg3+arg1P1-arg4, arg2'=arg2P1, arg4'=-1+arg1P1, (2-arg3+arg5-arg1P1+arg4 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ -2+arg1P1-arg4 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: -1+arg1P1-arg4 Applied simplification Original rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5, arg2'=arg2P1, arg4'=-arg3+arg5+arg4, (1 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ -1-arg3+arg5 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ ((1+arg1-arg1P1 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0) \/ (-2+arg1-arg4 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0))), cost: -arg3+arg5 New rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5, arg2'=arg2P1, arg4'=-arg3+arg5+arg4, (1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ -1-arg3+arg5 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0), cost: -arg3+arg5 Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 7: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1+arg3+arg1P1-arg4, arg2'=arg2P1, arg4'=-1+arg1P1, (2-arg3+arg5-arg1P1+arg4 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ -2+arg1P1-arg4 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: -1+arg1P1-arg4 8: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5, arg2'=arg2P1, arg4'=-arg3+arg5+arg4, (1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ -1-arg3+arg5 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0), cost: -arg3+arg5 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg3'=arg3P2, arg5'=arg5P2, arg2'=arg2P2, arg4'=arg4P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 Second rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1+arg3+arg1P1-arg4, arg2'=arg2P1, arg4'=-1+arg1P1, (2-arg3+arg5-arg1P1+arg4 > 0 /\ 1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ -2+arg1P1-arg4 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0), cost: -1+arg1P1-arg4 New rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1-arg4P0+arg1P1, arg5'=arg5P0, arg2'=arg2P1, arg4'=-1+arg1P1, (-2-arg4P0+arg1P1 >= 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 2+arg4P0-arg1P1+arg5P0 > 0 /\ arg2P1 > 0 /\ -arg1+arg2P1 <= 0), cost: -arg4P0+arg1P1 Applied chaining First rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 Second rule: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5, arg2'=arg2P1, arg4'=-arg3+arg5+arg4, (1+arg4 > 0 /\ -arg2P1+arg1P1 >= 0 /\ -1-arg3+arg5 >= 0 /\ 1+arg1-arg1P1 >= 0 /\ arg2P1 > 0 /\ arg1-arg2P1 >= 0 /\ arg2-arg2P1 >= 0 /\ -1+arg3-arg5+arg1P1-arg4 >= 0), cost: -arg3+arg5 New rule: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5P0, arg5'=arg5P0, arg2'=arg2P1, arg4'=arg4P0+arg5P0, (1+arg4P0 > 0 /\ -1-arg4P0+arg1P1-arg5P0 >= 0 /\ -1+arg2 > 0 /\ -arg2P1+arg1P1 >= 0 /\ arg2P1 > 0 /\ -1+arg5P0 >= 0 /\ -arg1+arg2P1 <= 0), cost: 1+arg5P0 Applied deletion Removed the following rules: 7 8 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P0, arg3'=0, arg5'=arg5P0, arg2'=arg2P0, arg4'=arg4P0, (1+arg5P0 > 0 /\ arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg1+arg2P0 <= 0), cost: 1 9: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P1, arg3'=-1-arg4P0+arg1P1, arg5'=arg5P0, arg2'=arg2P1, arg4'=-1+arg1P1, (-2-arg4P0+arg1P1 >= 0 /\ 1+arg4P0 > 0 /\ -1+arg2 > 0 /\ -arg2P1+arg1P1 >= 0 /\ 2+arg4P0-arg1P1+arg5P0 > 0 /\ arg2P1 > 0 /\ -arg1+arg2P1 <= 0), cost: -arg4P0+arg1P1 10: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P1, arg3'=arg5P0, arg5'=arg5P0, arg2'=arg2P1, arg4'=arg4P0+arg5P0, (1+arg4P0 > 0 /\ -1-arg4P0+arg1P1-arg5P0 >= 0 /\ -1+arg2 > 0 /\ -arg2P1+arg1P1 >= 0 /\ arg2P1 > 0 /\ -1+arg5P0 >= 0 /\ -arg1+arg2P1 <= 0), cost: 1+arg5P0 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg3'=arg3P2, arg5'=arg5P2, arg2'=arg2P2, arg4'=arg4P2, 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