WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, -arg1P0 == 0, cost: 1 1: f139_0_main_GE -> f169_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (arg1-arg1P1 == 0 /\ -10+arg1 < 0 /\ 3-arg2P1 == 0), cost: 1 2: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=arg1P2, (-11+arg2 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f169_0_main_GE -> f169_0_main_GE : arg2'=arg2P3, arg1'=arg1P3, (-12+arg2 < 0 /\ 1+arg2-arg2P3 == 0 /\ -arg1P3+arg1 == 0), cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, -arg1P0 == 0, cost: 1 New rule: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f139_0_main_GE -> f169_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (arg1-arg1P1 == 0 /\ -10+arg1 < 0 /\ 3-arg2P1 == 0), cost: 1 New rule: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 Applied preprocessing Original rule: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=arg1P2, (-11+arg2 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 Applied preprocessing Original rule: f169_0_main_GE -> f169_0_main_GE : arg2'=arg2P3, arg1'=arg1P3, (-12+arg2 < 0 /\ 1+arg2-arg2P3 == 0 /\ -arg1P3+arg1 == 0), cost: 1 New rule: f169_0_main_GE -> f169_0_main_GE : arg2'=1+arg2, 12-arg2 > 0, cost: 1 Simplified rules Start location: __init 5: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 1 6: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 7: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 8: f169_0_main_GE -> f169_0_main_GE : arg2'=1+arg2, 12-arg2 > 0, cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied acceleration Original rule: f169_0_main_GE -> f169_0_main_GE : arg2'=1+arg2, 12-arg2 > 0, cost: 1 New rule: f169_0_main_GE -> f169_0_main_GE : arg2'=arg2+n, (n >= 0 /\ 13-arg2-n > 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_iPfidF.txt Applied instantiation Original rule: f169_0_main_GE -> f169_0_main_GE : arg2'=arg2+n, (n >= 0 /\ 13-arg2-n > 0), cost: n New rule: f169_0_main_GE -> f169_0_main_GE : arg2'=12, (1 > 0 /\ 12-arg2 >= 0), cost: 12-arg2 Applied simplification Original rule: f169_0_main_GE -> f169_0_main_GE : arg2'=12, (1 > 0 /\ 12-arg2 >= 0), cost: 12-arg2 New rule: f169_0_main_GE -> f169_0_main_GE : arg2'=12, -12+arg2 <= 0, cost: 12-arg2 Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 1 6: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 7: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 10: f169_0_main_GE -> f169_0_main_GE : arg2'=12, -12+arg2 <= 0, cost: 12-arg2 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied chaining First rule: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 Second rule: f169_0_main_GE -> f169_0_main_GE : arg2'=12, -12+arg2 <= 0, cost: 12-arg2 New rule: f139_0_main_GE -> f169_0_main_GE : arg2'=12, 10-arg1 > 0, cost: 10 Applied deletion Removed the following rules: 10 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 1 6: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 11: f139_0_main_GE -> f169_0_main_GE : arg2'=12, 10-arg1 > 0, cost: 10 7: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 1 New rule: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: __init 6: f139_0_main_GE -> f169_0_main_GE : arg2'=3, 10-arg1 > 0, cost: 1 11: f139_0_main_GE -> f169_0_main_GE : arg2'=12, 10-arg1 > 0, cost: 10 7: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 12: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 Eliminating location f169_0_main_GE by chaining: Applied chaining First rule: f139_0_main_GE -> f169_0_main_GE : arg2'=12, 10-arg1 > 0, cost: 10 Second rule: f169_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, -11+arg2 > 0, cost: 1 New rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, (10-arg1 > 0 /\ 1 > 0), cost: 11 Applied simplification Original rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, (10-arg1 > 0 /\ 1 > 0), cost: 11 New rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, 10-arg1 > 0, cost: 11 Applied deletion Removed the following rules: 6 7 11 Eliminated locations on tree-shaped paths Start location: __init 13: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, 10-arg1 > 0, cost: 11 12: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 Applied acceleration Original rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=1+arg1, 10-arg1 > 0, cost: 11 New rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=n0+arg1, (11-n0-arg1 > 0 /\ -1+n0 >= 0), cost: 11*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_KApbhI.txt Applied instantiation Original rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=n0+arg1, (11-n0-arg1 > 0 /\ -1+n0 >= 0), cost: 11*n0 New rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, (1 > 0 /\ 9-arg1 >= 0), cost: 110-11*arg1 Applied simplification Original rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, (1 > 0 /\ 9-arg1 >= 0), cost: 110-11*arg1 New rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, -9+arg1 <= 0, cost: 110-11*arg1 Applied deletion Removed the following rules: 13 Accelerated simple loops Start location: __init 15: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, -9+arg1 <= 0, cost: 110-11*arg1 12: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 Applied chaining First rule: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 Second rule: f139_0_main_GE -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, -9+arg1 <= 0, cost: 110-11*arg1 New rule: __init -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, -9 <= 0, cost: 112 Applied deletion Removed the following rules: 15 Chained accelerated rules with incoming rules Start location: __init 12: __init -> f139_0_main_GE : arg2'=arg2P0, arg1'=0, TRUE, cost: 2 16: __init -> f139_0_main_GE : arg2'=arg2P2, arg1'=10, -9 <= 0, cost: 112 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