NO Initial ITS Start location: __init 0: f1_0_main_Load -> f31_0_f_NE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f31_0_f_NE -> f31_0_f_NE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg1P1 == 0), cost: 1 2: f31_0_f_NE -> f31_0_f_NE : arg1'=arg1P2, arg2'=arg2P2, (1-arg1P2 == 0 /\ -arg1 == 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg1P1 == 0), cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=arg1P2, arg2'=arg2P2, (1-arg1P2 == 0 /\ -arg1 == 0), cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 6: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2 Applied nonterm Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2 New rule: f31_0_f_NE -> [3] : arg1 > 0, cost: NONTERM Applied acceleration Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2*n3 Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 Second rule: f31_0_f_NE -> [3] : arg1 > 0, cost: NONTERM New rule: f31_0_f_NE -> [3] : (arg1 == 0 /\ 1 > 0), cost: NONTERM Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2*n3 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 == 0 /\ 1 > 0), cost: 1+2*n3 Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 == 0, cost: 2 Applied nonterm Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 == 0, cost: 2 New rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0), cost: NONTERM Applied acceleration Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 == 0, cost: 2 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, (arg1 >= 0 /\ -arg1 >= 0), cost: 2*n5 Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 Second rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (0 >= 0 /\ arg1 > 0), cost: NONTERM Heuristically decided not to add the following rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, (arg1 >= 0 /\ -arg1 >= 0), cost: 2*n5 Applied simplification Original rule: f31_0_f_NE -> [3] : (arg1 == 0 /\ 1 > 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : arg1 == 0, cost: NONTERM Applied simplification Original rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 == 0 /\ 1 > 0), cost: 1+2*n3 New rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1+2*n3 Applied simplification Original rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0), cost: NONTERM Applied simplification Original rule: f31_0_f_NE -> [3] : (0 >= 0 /\ arg1 > 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : arg1 > 0, cost: NONTERM Applied deletion Removed the following rules: 7 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 6: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 9: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2*n3 13: f31_0_f_NE -> [3] : arg1 == 0, cost: NONTERM 14: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1+2*n3 15: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0), cost: NONTERM 16: f31_0_f_NE -> [3] : arg1 > 0, cost: NONTERM 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 > 0, cost: 2*n3 New rule: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 1+2*n3 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : arg1 == 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, arg1 == 0, cost: 1+2*n3 New rule: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 2+2*n3 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 6 9 13 14 15 16 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 17: f1_0_main_Load -> f31_0_f_NE : arg1'=0, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 2 18: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 2 19: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 1+2*n3 20: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 21: f1_0_main_Load -> f31_0_f_NE : arg1'=1, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 2+2*n3 22: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 23: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 20: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 22: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 23: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 20 22 23 Eliminated locations on tree-shaped paths Start location: __init 24: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM 25: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM 26: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Removed duplicate rules (ignoring updates) Start location: __init 25: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM 26: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 25 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ arg2P3 == 0)