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