WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0), cost: 1 2: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2P2, arg1'=arg1P2, (arg2-arg1 < 0 /\ arg1-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0), cost: 1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=1+arg1, arg2-arg1 > 0, cost: 1 Applied preprocessing Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2P2, arg1'=arg1P2, (arg2-arg1 < 0 /\ arg1-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=1+arg2, -arg2+arg1 > 0, cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 4: f145_0_main_EQ -> f145_0_main_EQ : arg1'=1+arg1, arg2-arg1 > 0, cost: 1 5: f145_0_main_EQ -> f145_0_main_EQ : arg2'=1+arg2, -arg2+arg1 > 0, cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=1+arg1, arg2-arg1 > 0, cost: 1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg1+n, (n >= 0 /\ 1+arg2-arg1-n > 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_DPaGiL.txt Applied instantiation Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg1+n, (n >= 0 /\ 1+arg2-arg1-n > 0), cost: n New rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg2, (1 > 0 /\ arg2-arg1 >= 0), cost: arg2-arg1 Applied acceleration Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=1+arg2, -arg2+arg1 > 0, cost: 1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2+n0, (n0 >= 0 /\ 1-arg2-n0+arg1 > 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_FGopFh.txt Applied instantiation Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg2+n0, (n0 >= 0 /\ 1-arg2-n0+arg1 > 0), cost: n0 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg1, (1 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 Applied simplification Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg2, (1 > 0 /\ arg2-arg1 >= 0), cost: arg2-arg1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg2, arg2-arg1 >= 0, cost: arg2-arg1 Applied simplification Original rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg1, (1 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 New rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg1, -arg2+arg1 >= 0, cost: -arg2+arg1 Applied deletion Removed the following rules: 4 5 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 8: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg2, arg2-arg1 >= 0, cost: arg2-arg1 9: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg1, -arg2+arg1 >= 0, cost: -arg2+arg1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f145_0_main_EQ -> f145_0_main_EQ : arg1'=arg2, arg2-arg1 >= 0, cost: arg2-arg1 New rule: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg2P0, (arg2P0-arg1P0 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1+arg2P0-arg1P0 Applied chaining First rule: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f145_0_main_EQ -> f145_0_main_EQ : arg2'=arg1, -arg2+arg1 >= 0, cost: -arg2+arg1 New rule: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg1P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ -arg2P0+arg1P0 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1-arg2P0+arg1P0 Applied deletion Removed the following rules: 8 9 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 10: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg2P0, arg1'=arg2P0, (arg2P0-arg1P0 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1+arg2P0-arg1P0 11: f1_0_main_Load -> f145_0_main_EQ : arg2'=arg1P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ -arg2P0+arg1P0 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1-arg2P0+arg1P0 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, 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