NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1-arg1P0-arg2 == 0 /\ arg2 >= 0 /\ -2-arg2-arg2P0 == 0 /\ 1+arg2 > 0 /\ 2+arg2 > 0), cost: 1 1: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 < 0 /\ -1+arg2 < 0 /\ -arg1+arg2 < 0 /\ arg2 < 0 /\ -1-arg2P1+arg2 == 0 /\ -arg1P1+arg2 == 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1-arg1P0-arg2 == 0 /\ arg2 >= 0 /\ -2-arg2-arg2P0 == 0 /\ 1+arg2 > 0 /\ 2+arg2 > 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 < 0 /\ -1+arg2 < 0 /\ -arg1+arg2 < 0 /\ arg2 < 0 /\ -1-arg2P1+arg2 == 0 /\ -arg1P1+arg2 == 0), cost: 1 New rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg2, arg2'=-1+arg2, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: 1 Simplified rules Start location: __init 3: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 4: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg2, arg2'=-1+arg2, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied nonterm Original rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg2, arg2'=-1+arg2, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f40_0_sum_InvokeMethod -> [3] : (1-arg1 > 0 /\ arg1-arg2 > 0), cost: NONTERM Applied acceleration Original rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=arg2, arg2'=-1+arg2, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=1+arg2-n0, arg2'=arg2-n0, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: n0 Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f40_0_sum_InvokeMethod -> [3] : (1-arg1 > 0 /\ arg1-arg2 > 0), cost: NONTERM 6: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=1+arg2-n0, arg2'=arg2-n0, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: n0 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f40_0_sum_InvokeMethod -> [3] : (1-arg1 > 0 /\ arg1-arg2 > 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ 1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f40_0_sum_InvokeMethod -> f40_0_sum_InvokeMethod : arg1'=1+arg2-n0, arg2'=arg2-n0, (1-arg1 > 0 /\ arg1-arg2 > 0), cost: n0 New rule: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2-n0, arg2'=-2-arg2-n0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1+n0 Applied deletion Removed the following rules: 5 6 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2, arg2'=-2-arg2, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 7: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ 1+arg2 > 0), cost: NONTERM 8: f1_0_main_ConstantStackPush -> f40_0_sum_InvokeMethod : arg1'=-1-arg2-n0, arg2'=-2-arg2-n0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1+n0 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 7: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ 1+arg2 > 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : (arg1 > 0 /\ 1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (1+arg2P2 > 0 /\ arg1P2 > 0), cost: NONTERM Applied deletion Removed the following rules: 2 7 Eliminated locations on linear paths Start location: __init 9: __init -> [3] : (1+arg2P2 > 0 /\ arg1P2 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 9 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (1+arg2P2 > 0 /\ arg1P2 > 0)