WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1-arg1P1 == 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -1-arg2P1+arg2 == 0 /\ -4+arg1 > 0), cost: 1 2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P2, arg2'=arg2P2, (-1-arg2P2+arg2 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 2+arg1-arg1P2 == 0 /\ -5+arg1 < 0), cost: 1 3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P3, arg2'=arg2P3, (1+arg1-arg1P3 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ arg2-arg2P3 == 0 /\ -4-arg1+arg2 > 0 /\ -5+arg1 < 0), cost: 1 4: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P4, arg2'=arg2P4, (1+arg1-arg1P4 == 0 /\ -1+arg1 > 0 /\ 1-2*arg1+arg2 >= 0 /\ 1-arg2P4+arg2 == 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1 5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P5, arg2'=arg2P5, (-1+arg1-arg1P5 == 0 /\ 1+arg2-arg2P5 == 0 /\ -1+arg1 > 0 /\ 1-2*arg1+arg2 < 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1-arg1P1 == 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -1-arg2P1+arg2 == 0 /\ -4+arg1 > 0), cost: 1 2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P2, arg2'=arg2P2, (-1-arg2P2+arg2 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 2+arg1-arg1P2 == 0 /\ -5+arg1 < 0), cost: 1 3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P3, arg2'=arg2P3, (1+arg1-arg1P3 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ arg2-arg2P3 == 0 /\ -4-arg1+arg2 > 0 /\ -5+arg1 < 0), cost: 1 5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P5, arg2'=arg2P5, (-1+arg1-arg1P5 == 0 /\ 1+arg2-arg2P5 == 0 /\ -1+arg1 > 0 /\ 1-2*arg1+arg2 < 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1-arg1P1 == 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -1-arg2P1+arg2 == 0 /\ -4+arg1 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=-1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 > 0), cost: 1 Applied preprocessing Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P2, arg2'=arg2P2, (-1-arg2P2+arg2 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 2+arg1-arg1P2 == 0 /\ -5+arg1 < 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2+arg1, arg2'=-1+arg2, (1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 5-arg1 > 0), cost: 1 Applied preprocessing Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P3, arg2'=arg2P3, (1+arg1-arg1P3 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ arg2-arg2P3 == 0 /\ -4-arg1+arg2 > 0 /\ -5+arg1 < 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=1+arg1, (1+arg1 > 0 /\ -4-arg1+arg2 > 0 /\ 5-arg1 > 0), cost: 1 Applied preprocessing Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P5, arg2'=arg2P5, (-1+arg1-arg1P5 == 0 /\ 1+arg2-arg2P5 == 0 /\ -1+arg1 > 0 /\ 1-2*arg1+arg2 < 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=1+arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 8: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=-1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 > 0), cost: 1 9: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2+arg1, arg2'=-1+arg2, (1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 5-arg1 > 0), cost: 1 10: f54_0_loop_LE -> f54_0_loop_LE : arg1'=1+arg1, (1+arg1 > 0 /\ -4-arg1+arg2 > 0 /\ 5-arg1 > 0), cost: 1 11: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=1+arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied acceleration Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=-1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1-n3, arg2'=-n3+arg2, (n3 >= 0 /\ -3+arg1-n3 > 0 /\ -arg1+arg2 >= 0), cost: n3 Applied instantiation Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1-n3, arg2'=-n3+arg2, (n3 >= 0 /\ -3+arg1-n3 > 0 /\ -arg1+arg2 >= 0), cost: n3 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4-arg1+arg2, (1 > 0 /\ -arg1+arg2 >= 0 /\ -4+arg1 >= 0), cost: -4+arg1 Applied acceleration Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2+arg1, arg2'=-1+arg2, (1+arg1 > 0 /\ -arg1+arg2 >= 0 /\ arg2 > 0 /\ -4-arg1+arg2 <= 0 /\ 5-arg1 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*n5, arg2'=arg2-n5, (3-arg1+arg2-3*n5 >= 0 /\ 4+arg1-arg2 >= 0 /\ 7-arg1-2*n5 > 0 /\ 1+arg1 > 0 /\ n5 >= 0 /\ 1+arg2-n5 > 0), cost: n5 Applied instantiation Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*n5, arg2'=arg2-n5, (3-arg1+arg2-3*n5 >= 0 /\ 4+arg1-arg2 >= 0 /\ 7-arg1-2*n5 > 0 /\ 1+arg1 > 0 /\ n5 >= 0 /\ 1+arg2-n5 > 0), cost: n5 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*arg2, arg2'=0, (1 > 0 /\ 7-arg1-2*arg2 > 0 /\ 4+arg1-arg2 >= 0 /\ 1+arg1 > 0 /\ arg2 >= 0 /\ 3-arg1-2*arg2 >= 0), cost: arg2 Applied acceleration Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=1+arg1, (1+arg1 > 0 /\ -4-arg1+arg2 > 0 /\ 5-arg1 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+n7, (n7 >= 0 /\ 6-arg1-n7 > 0 /\ 1+arg1 > 0 /\ -3-arg1-n7+arg2 > 0), cost: n7 Applied instantiation Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+n7, (n7 >= 0 /\ 6-arg1-n7 > 0 /\ 1+arg1 > 0 /\ -3-arg1-n7+arg2 > 0), cost: n7 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-4+arg2, (1 > 0 /\ 1+arg1 > 0 /\ 10-arg2 > 0 /\ -4-arg1+arg2 >= 0), cost: -4-arg1+arg2 Applied instantiation Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+n7, (n7 >= 0 /\ 6-arg1-n7 > 0 /\ 1+arg1 > 0 /\ -3-arg1-n7+arg2 > 0), cost: n7 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=5, (1 > 0 /\ -8+arg2 > 0 /\ 1+arg1 > 0 /\ 5-arg1 >= 0), cost: 5-arg1 Applied acceleration Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=1+arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1-n10, arg2'=n10+arg2, (n10 >= 0 /\ arg2 > 0 /\ 2+arg1-2*n10-arg2 > 0), cost: n10 Applied simplification Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4-arg1+arg2, (1 > 0 /\ -arg1+arg2 >= 0 /\ -4+arg1 >= 0), cost: -4+arg1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4-arg1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 >= 0), cost: -4+arg1 Applied simplification Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*arg2, arg2'=0, (1 > 0 /\ 7-arg1-2*arg2 > 0 /\ 4+arg1-arg2 >= 0 /\ 1+arg1 > 0 /\ arg2 >= 0 /\ 3-arg1-2*arg2 >= 0), cost: arg2 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*arg2, arg2'=0, (1+arg1 > 0 /\ arg2 >= 0 /\ 3-arg1-2*arg2 >= 0), cost: arg2 Applied simplification Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-4+arg2, (1 > 0 /\ 1+arg1 > 0 /\ 10-arg2 > 0 /\ -4-arg1+arg2 >= 0), cost: -4-arg1+arg2 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-4+arg2, (1+arg1 > 0 /\ 10-arg2 > 0 /\ -4-arg1+arg2 >= 0), cost: -4-arg1+arg2 Applied simplification Original rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=5, (1 > 0 /\ -8+arg2 > 0 /\ 1+arg1 > 0 /\ 5-arg1 >= 0), cost: 5-arg1 New rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=5, (-8+arg2 > 0 /\ 1+arg1 > 0 /\ -5+arg1 <= 0), cost: 5-arg1 Applied deletion Removed the following rules: 8 9 10 11 Accelerated simple loops Start location: __init 7: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 16: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1-n10, arg2'=n10+arg2, (n10 >= 0 /\ arg2 > 0 /\ 2+arg1-2*n10-arg2 > 0), cost: n10 17: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4-arg1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 >= 0), cost: -4+arg1 18: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*arg2, arg2'=0, (1+arg1 > 0 /\ arg2 >= 0 /\ 3-arg1-2*arg2 >= 0), cost: arg2 19: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-4+arg2, (1+arg1 > 0 /\ 10-arg2 > 0 /\ -4-arg1+arg2 >= 0), cost: -4-arg1+arg2 20: f54_0_loop_LE -> f54_0_loop_LE : arg1'=5, (-8+arg2 > 0 /\ 1+arg1 > 0 /\ -5+arg1 <= 0), cost: 5-arg1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1-n10, arg2'=n10+arg2, (n10 >= 0 /\ arg2 > 0 /\ 2+arg1-2*n10-arg2 > 0), cost: n10 New rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=-n10+arg2, arg2'=n10+arg2, (arg1 > 0 /\ n10 >= 0 /\ 2-2*n10 > 0 /\ arg2 > 0), cost: 1+n10 Applied chaining First rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4-arg1+arg2, (-arg1+arg2 >= 0 /\ -4+arg1 >= 0), cost: -4+arg1 New rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=4, arg2'=4, (arg1 > 0 /\ -4+arg2 >= 0), cost: -3+arg2 Applied chaining First rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1+2*arg2, arg2'=0, (1+arg1 > 0 /\ arg2 >= 0 /\ 3-arg1-2*arg2 >= 0), cost: arg2 New rule: f1_0_main_Load -> f54_0_loop_LE : arg1'=3*arg2, arg2'=0, (arg1 > 0 /\ -1+arg2 <= 0 /\ 1+arg2 > 0), cost: 1+arg2 Applied deletion Removed the following rules: 16 17 18 19 20 Chained accelerated rules with incoming rules Start location: __init 7: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 21: f1_0_main_Load -> f54_0_loop_LE : arg1'=-n10+arg2, arg2'=n10+arg2, (arg1 > 0 /\ n10 >= 0 /\ 2-2*n10 > 0 /\ arg2 > 0), cost: 1+n10 22: f1_0_main_Load -> f54_0_loop_LE : arg1'=4, arg2'=4, (arg1 > 0 /\ -4+arg2 >= 0), cost: -3+arg2 23: f1_0_main_Load -> f54_0_loop_LE : arg1'=3*arg2, arg2'=0, (arg1 > 0 /\ -1+arg2 <= 0 /\ 1+arg2 > 0), cost: 1+arg2 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, 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