NO Initial ITS Start location: __init 0: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1-arg1P1 == 0 /\ -4+arg1 > 0), cost: 1 2: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -5+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_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1-arg1P1 == 0 /\ -4+arg1 > 0), cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: 1 Applied preprocessing Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -5+arg1 < 0), cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ 5-arg1 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: 1 6: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ 5-arg1 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied nonterm Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: 1 New rule: f31_0_loop_EQ -> [3] : -4+arg1 > 0, cost: NONTERM Applied acceleration Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: n1 Applied acceleration Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=-1+arg1, arg2'=arg2P2, (arg1 > 0 /\ 5-arg1 > 0), cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1-n3, arg2'=arg2P2, (1+arg1-n3 > 0 /\ -1+n3 >= 0 /\ 5-arg1 > 0), cost: n3 Applied instantiation Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=arg1-n3, arg2'=arg2P2, (1+arg1-n3 > 0 /\ -1+n3 >= 0 /\ 5-arg1 > 0), cost: n3 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (1 > 0 /\ -1+arg1 >= 0 /\ 5-arg1 > 0), cost: arg1 Applied simplification Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (1 > 0 /\ -1+arg1 >= 0 /\ 5-arg1 > 0), cost: arg1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (-1+arg1 >= 0 /\ 5-arg1 > 0), cost: arg1 Applied deletion Removed the following rules: 5 6 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 7: f31_0_loop_EQ -> [3] : -4+arg1 > 0, cost: NONTERM 8: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: n1 10: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (-1+arg1 >= 0 /\ 5-arg1 > 0), cost: arg1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_loop_EQ -> [3] : -4+arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -4+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, -4+arg1 > 0, cost: n1 New rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P1, (arg1 > 0 /\ -4+arg2 > 0), cost: 1+n1 Applied chaining First rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (-1+arg1 >= 0 /\ 5-arg1 > 0), cost: arg1 New rule: f1_0_main_Load -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (arg1 > 0 /\ -1+arg2 >= 0 /\ 5-arg2 > 0), cost: 1+arg2 Applied deletion Removed the following rules: 7 8 10 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 11: f1_0_main_Load -> [3] : (arg1 > 0 /\ -4+arg2 > 0), cost: NONTERM 12: f1_0_main_Load -> f31_0_loop_EQ : arg1'=arg2, arg2'=arg2P1, (arg1 > 0 /\ -4+arg2 > 0), cost: 1+n1 13: f1_0_main_Load -> f31_0_loop_EQ : arg1'=0, arg2'=arg2P2, (arg1 > 0 /\ -1+arg2 >= 0 /\ 5-arg2 > 0), cost: 1+arg2 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 11: f1_0_main_Load -> [3] : (arg1 > 0 /\ -4+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 /\ -4+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ -4+arg2P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 11 Eliminated locations on linear paths Start location: __init 14: __init -> [3] : (arg1P3 > 0 /\ -4+arg2P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 14 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ -4+arg2P3 > 0)