WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f161_0_createList_Return -> f227_0_isCyclic_NONNULL : arg1'=arg1P0, arg2'=arg2P0, (-arg1+arg1P0 <= 0 /\ 1+arg1P0 > 0 /\ 1+arg1 > 0), cost: 1 2: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 1: f1_0_main_Load -> f227_0_isCyclic_NONNULL : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 3: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ 1+arg1P3 > 0 /\ -2+arg2 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 5: f201_0_createList_LE -> f201_0_createList_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1-arg1P5 == 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Removed unreachable rules and leafs Start location: __init 2: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 1: f1_0_main_Load -> f227_0_isCyclic_NONNULL : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 3: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ 1+arg1P3 > 0 /\ -2+arg2 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 5: f201_0_createList_LE -> f201_0_createList_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1-arg1P5 == 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied preprocessing Original rule: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 New rule: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 Applied preprocessing Original rule: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ 1+arg1P3 > 0 /\ -2+arg2 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 New rule: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1+arg1P3 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 Applied preprocessing Original rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1-arg1P5 == 0), cost: 1 New rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 Simplified rules Start location: __init 7: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 1: f1_0_main_Load -> f227_0_isCyclic_NONNULL : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 8: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1+arg1P3 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 9: f201_0_createList_LE -> f201_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied acceleration Original rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 New rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=arg1-n2, arg2'=arg2P5, (1+arg1-n2 > 0 /\ -1+n2 >= 0), cost: n2 Applied instantiation Original rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=arg1-n2, arg2'=arg2P5, (1+arg1-n2 > 0 /\ -1+n2 >= 0), cost: n2 New rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 Applied simplification Original rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 New rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 Applied deletion Removed the following rules: 9 Accelerated simple loops Start location: __init 7: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 1: f1_0_main_Load -> f227_0_isCyclic_NONNULL : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 8: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1+arg1P3 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 11: f201_0_createList_LE -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied chaining First rule: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 Second rule: f331_0_isCyclic_NULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1+arg1P3 > 0 /\ -1+arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -3+arg2-arg2P3 >= 0), cost: 1 New rule: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1-arg1+arg1P3 <= 0 /\ 1+arg1P3 > 0 /\ 4-arg1+arg2P3 <= 0 /\ 1+arg2P3 > 0), cost: 2 Applied deletion Removed the following rules: 8 Applied chaining First rule: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f201_0_createList_LE -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 New rule: f1_0_main_Load -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1P4 >= 0 /\ 1+arg2 > 0), cost: 1+arg1P4 Applied deletion Removed the following rules: 11 Chained accelerated rules with incoming rules Start location: __init 7: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P2, arg2'=arg2P2, (1+arg2P2 > 0 /\ arg1P2 > 0 /\ 1-arg1+arg2P2 <= 0 /\ -arg1+arg1P2 <= 0), cost: 1 12: f227_0_isCyclic_NONNULL -> f331_0_isCyclic_NULL : arg1'=arg1P3, arg2'=arg2P3, (1-arg1+arg1P3 <= 0 /\ 1+arg1P3 > 0 /\ 4-arg1+arg2P3 <= 0 /\ 1+arg2P3 > 0), cost: 2 1: f1_0_main_Load -> f227_0_isCyclic_NONNULL : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f201_0_createList_LE : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+arg1P4 > 0 /\ 1+arg2 > 0), cost: 1 13: f1_0_main_Load -> f201_0_createList_LE : arg1'=0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1P4 >= 0 /\ 1+arg2 > 0), cost: 1+arg1P4 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