WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f49_0_increase_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f49_0_increase_LE -> f49_0_increase_LE\' : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0 /\ arg1-arg1P1 == 0), cost: 1 3: f49_0_increase_LE -> f49_0_increase_LE\' : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0 /\ arg1-arg1P3 == 0), cost: 1 2: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -2+arg1-2*x70 < 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x70 == 0 /\ -1+arg1-arg1P2 == 0), cost: 1 4: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 3+arg1-arg1P4 == 0 /\ arg1-2*x110 >= 0 /\ -2+arg1-2*x110 < 0 /\ -1+arg1-2*x110 == 0), cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f49_0_increase_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f49_0_increase_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0 /\ arg1-arg1P1 == 0), cost: 1 New rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0), cost: 1 Applied preprocessing Original rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -2+arg1-2*x70 < 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x70 == 0 /\ -1+arg1-arg1P2 == 0), cost: 1 New rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0), cost: 1 Applied preprocessing Original rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0 /\ arg1-arg1P3 == 0), cost: 1 New rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0), cost: 1 Applied preprocessing Original rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 3+arg1-arg1P4 == 0 /\ arg1-2*x110 >= 0 /\ -2+arg1-2*x110 < 0 /\ -1+arg1-2*x110 == 0), cost: 1 New rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f49_0_increase_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 7: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0), cost: 1 9: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0), cost: 1 8: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0), cost: 1 10: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> f49_0_increase_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 New rule: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: __init 7: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0), cost: 1 9: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0), cost: 1 8: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0), cost: 1 10: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1 11: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Eliminating location f49_0_increase_LE\' by chaining: Applied chaining First rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P1, (arg1 > 0 /\ arg1-2*x50 == 0), cost: 1 Second rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0), cost: 1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0 /\ arg1-2*x50 == 0), cost: 2 Applied chaining First rule: f49_0_increase_LE -> f49_0_increase_LE\' : arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-2*x90 == 0), cost: 1 Second rule: f49_0_increase_LE\' -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x90 == 0 /\ -1+arg1-2*x110 == 0), cost: 2 Applied deletion Removed the following rules: 7 8 9 10 Eliminated locations on tree-shaped paths Start location: __init 12: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0 /\ arg1-2*x50 == 0), cost: 2 13: f49_0_increase_LE -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x90 == 0 /\ -1+arg1-2*x110 == 0), cost: 2 11: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied acceleration Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ arg1-2*x70 == 0 /\ arg1-2*x50 == 0), cost: 2 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1-n1, arg2'=arg2P2, (1+arg1-n1-2*x70 >= 0 /\ arg1-2*x70 >= 0 /\ 1+arg1-n1-2*x50 >= 0 /\ arg1-2*x50 >= 0 /\ -1+n1 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1+arg1-n1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*n1 Applied instantiation Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1-n1, arg2'=arg2P2, (1+arg1-n1-2*x70 >= 0 /\ arg1-2*x70 >= 0 /\ 1+arg1-n1-2*x50 >= 0 /\ arg1-2*x50 >= 0 /\ -1+n1 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1+arg1-n1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*n1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=0, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -1+arg1 >= 0 /\ arg1-2*x50 >= 0 /\ 1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 1-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 1 > 0)), cost: 2*arg1 Applied instantiation Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1-n1, arg2'=arg2P2, (1+arg1-n1-2*x70 >= 0 /\ arg1-2*x70 >= 0 /\ 1+arg1-n1-2*x50 >= 0 /\ arg1-2*x50 >= 0 /\ -1+n1 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1+arg1-n1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*n1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (0 >= 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ -arg1+2*x50 >= 0 /\ 2*x70-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 2*x70 > 0)), cost: 2+2*arg1-4*x70 Applied instantiation Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1-n1, arg2'=arg2P2, (1+arg1-n1-2*x70 >= 0 /\ arg1-2*x70 >= 0 /\ 1+arg1-n1-2*x50 >= 0 /\ arg1-2*x50 >= 0 /\ -1+n1 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1+arg1-n1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*n1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, (0 >= 0 /\ -2*x70+2*x50 >= 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 2*x50 > 0)), cost: 2+2*arg1-4*x50 Applied acceleration Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=3+arg1, arg2'=arg2P4, (arg1 > 0 /\ -1+arg1-2*x90 == 0 /\ -1+arg1-2*x110 == 0), cost: 2 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1+3*n5, arg2'=arg2P4, (arg1 > 0 /\ 4-arg1-3*n5+2*x90 >= 0 /\ -1+n5 >= 0 /\ 1-arg1+2*x90 >= 0 /\ -1+arg1-2*x90 >= 0 /\ 1-arg1+2*x110 >= 0 /\ -1+arg1-2*x110 >= 0 /\ 4-arg1-3*n5+2*x110 >= 0), cost: 2*n5 Applied simplification Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=0, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -1+arg1 >= 0 /\ arg1-2*x50 >= 0 /\ 1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 1-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 1 > 0)), cost: 2*arg1 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=0, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -1+arg1 >= 0 /\ arg1-2*x50 >= 0 /\ 1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 1-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*arg1 Applied simplification Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (0 >= 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ -arg1+2*x50 >= 0 /\ 2*x70-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 2*x70 > 0)), cost: 2+2*arg1-4*x70 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 2*x70 > 0 /\ 2*x70-2*x50 >= 0), cost: 2+2*arg1-4*x70 Applied simplification Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, (0 >= 0 /\ -2*x70+2*x50 >= 0 /\ arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ ((arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0) \/ 2*x50 > 0)), cost: 2+2*arg1-4*x50 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ 2*x50 > 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0), cost: 2+2*arg1-4*x50 Applied simplification Original rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1+3*n5, arg2'=arg2P4, (arg1 > 0 /\ 4-arg1-3*n5+2*x90 >= 0 /\ -1+n5 >= 0 /\ 1-arg1+2*x90 >= 0 /\ -1+arg1-2*x90 >= 0 /\ 1-arg1+2*x110 >= 0 /\ -1+arg1-2*x110 >= 0 /\ 4-arg1-3*n5+2*x110 >= 0), cost: 2*n5 New rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1+3*n5, arg2'=arg2P4, (arg1 > 0 /\ -1+n5 >= 0 /\ 1-arg1+2*x90 >= 0 /\ -1+arg1-2*x90 >= 0 /\ -1+arg1-2*x110 >= 0 /\ 4-arg1-3*n5+2*x110 >= 0), cost: 2*n5 Applied deletion Removed the following rules: 12 13 Accelerated simple loops Start location: __init 18: f49_0_increase_LE -> f49_0_increase_LE : arg1'=0, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -1+arg1 >= 0 /\ arg1-2*x50 >= 0 /\ 1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 1-2*x50 >= 0 /\ -arg1+2*x70 >= 0 /\ (1 > 0 \/ (arg1 > 0 /\ arg1-2*x70 >= 0 /\ -arg1+2*x70 >= 0))), cost: 2*arg1 19: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 2*x70 > 0 /\ 2*x70-2*x50 >= 0), cost: 2+2*arg1-4*x70 20: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ 2*x50 > 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0), cost: 2+2*arg1-4*x50 21: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1+3*n5, arg2'=arg2P4, (arg1 > 0 /\ -1+n5 >= 0 /\ 1-arg1+2*x90 >= 0 /\ -1+arg1-2*x90 >= 0 /\ -1+arg1-2*x110 >= 0 /\ 4-arg1-3*n5+2*x110 >= 0), cost: 2*n5 11: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied chaining First rule: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ -arg1+2*x50 >= 0 /\ 2*x70 > 0 /\ 2*x70-2*x50 >= 0), cost: 2+2*arg1-4*x70 New rule: __init -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (2*x50-arg2P5 >= 0 /\ -2*x70+arg2P5 >= 0 /\ 2*x70 > 0 /\ 2*x70-2*x50 >= 0), cost: 4-4*x70+2*arg2P5 Applied chaining First rule: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, (arg1-2*x70 >= 0 /\ arg1-2*x50 >= 0 /\ 2*x50 > 0 /\ -arg1+2*x50 >= 0 /\ -arg1+2*x70 >= 0), cost: 2+2*arg1-4*x50 New rule: __init -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, 2*x50 > 0, cost: 4 Applied chaining First rule: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f49_0_increase_LE -> f49_0_increase_LE : arg1'=arg1+3*n5, arg2'=arg2P4, (arg1 > 0 /\ -1+n5 >= 0 /\ 1-arg1+2*x90 >= 0 /\ -1+arg1-2*x90 >= 0 /\ -1+arg1-2*x110 >= 0 /\ 4-arg1-3*n5+2*x110 >= 0), cost: 2*n5 New rule: __init -> f49_0_increase_LE : arg1'=1+3*n5+2*x90, arg2'=arg2P4, (-2*x110+2*x90 >= 0 /\ -1+n5 >= 0 /\ 1+2*x90 > 0 /\ 3-3*n5+2*x110-2*x90 >= 0), cost: 2+2*n5 Applied deletion Removed the following rules: 18 19 20 21 Chained accelerated rules with incoming rules Start location: __init 11: __init -> f49_0_increase_LE : arg1'=arg2P5, arg2'=arg2P0, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 22: __init -> f49_0_increase_LE : arg1'=-1+2*x70, arg2'=arg2P2, (2*x50-arg2P5 >= 0 /\ -2*x70+arg2P5 >= 0 /\ 2*x70 > 0 /\ 2*x70-2*x50 >= 0), cost: 4-4*x70+2*arg2P5 23: __init -> f49_0_increase_LE : arg1'=-1+2*x50, arg2'=arg2P2, 2*x50 > 0, cost: 4 24: __init -> f49_0_increase_LE : arg1'=1+3*n5+2*x90, arg2'=arg2P4, (-2*x110+2*x90 >= 0 /\ -1+n5 >= 0 /\ 1+2*x90 > 0 /\ 3-3*n5+2*x110-2*x90 >= 0), cost: 2+2*n5 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