NO Initial ITS Start location: __init 0: f1_0_main_Load -> f71_0_main_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f71_0_main_LE -> f47_0_f_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg1P1 == 0), cost: 1 2: f71_0_main_LE -> f71_0_main_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f47_0_f_LE -> f47_0_f_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-arg1P3 == 0 /\ -1 < 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f71_0_main_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f71_0_main_LE -> f47_0_f_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg1P1 == 0), cost: 1 New rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f71_0_main_LE -> f71_0_main_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f71_0_main_LE -> f71_0_main_LE : arg1'=1+arg1, arg2'=arg2P2, arg1 > 0, cost: 1 Applied preprocessing Original rule: f47_0_f_LE -> f47_0_f_LE : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg1-arg1P3 == 0 /\ -1 < 0), cost: 1 New rule: f47_0_f_LE -> f47_0_f_LE : arg1'=-1+arg1, arg2'=arg2P3, arg1 > 0, cost: 1 Simplified rules Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 7: f71_0_main_LE -> f71_0_main_LE : arg1'=1+arg1, arg2'=arg2P2, arg1 > 0, cost: 1 8: f47_0_f_LE -> f47_0_f_LE : arg1'=-1+arg1, arg2'=arg2P3, arg1 > 0, cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied nonterm Original rule: f71_0_main_LE -> f71_0_main_LE : arg1'=1+arg1, arg2'=arg2P2, arg1 > 0, cost: 1 New rule: f71_0_main_LE -> [4] : arg1 > 0, cost: NONTERM Applied acceleration Original rule: f71_0_main_LE -> f71_0_main_LE : arg1'=1+arg1, arg2'=arg2P2, arg1 > 0, cost: 1 New rule: f71_0_main_LE -> f71_0_main_LE : arg1'=arg1+n0, arg2'=arg2P2, arg1 > 0, cost: n0 Applied deletion Removed the following rules: 7 Applied acceleration Original rule: f47_0_f_LE -> f47_0_f_LE : arg1'=-1+arg1, arg2'=arg2P3, arg1 > 0, cost: 1 New rule: f47_0_f_LE -> f47_0_f_LE : arg1'=arg1-n3, arg2'=arg2P3, (1+arg1-n3 > 0 /\ -1+n3 >= 0), cost: n3 Applied instantiation Original rule: f47_0_f_LE -> f47_0_f_LE : arg1'=arg1-n3, arg2'=arg2P3, (1+arg1-n3 > 0 /\ -1+n3 >= 0), cost: n3 New rule: f47_0_f_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 Applied simplification Original rule: f47_0_f_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 New rule: f47_0_f_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, -1+arg1 >= 0, cost: arg1 Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 9: f71_0_main_LE -> [4] : arg1 > 0, cost: NONTERM 10: f71_0_main_LE -> f71_0_main_LE : arg1'=arg1+n0, arg2'=arg2P2, arg1 > 0, cost: n0 12: f47_0_f_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, -1+arg1 >= 0, cost: arg1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f71_0_main_LE -> [4] : arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [4] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f71_0_main_LE -> f71_0_main_LE : arg1'=arg1+n0, arg2'=arg2P2, arg1 > 0, cost: n0 New rule: f1_0_main_Load -> f71_0_main_LE : arg1'=n0+arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 1+n0 Applied deletion Removed the following rules: 9 10 Applied chaining First rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 Second rule: f47_0_f_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, -1+arg1 >= 0, cost: arg1 New rule: f71_0_main_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, -1+arg1 >= 0, cost: 1+arg1 Applied deletion Removed the following rules: 12 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 13: f1_0_main_Load -> [4] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 14: f1_0_main_Load -> f71_0_main_LE : arg1'=n0+arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 1+n0 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 15: f71_0_main_LE -> f47_0_f_LE : arg1'=0, arg2'=arg2P3, -1+arg1 >= 0, cost: 1+arg1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 13: f1_0_main_Load -> [4] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1 Second rule: f1_0_main_Load -> [4] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM New rule: __init -> [4] : (arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM Applied deletion Removed the following rules: 4 13 Eliminated locations on linear paths Start location: __init 16: __init -> [4] : (arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 16 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg2P4 > 0 /\ arg1P4 > 0)