by AProVE
| f1_0_main_ConstantStackPush | 1 | f139_0_main_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 = _arg1P | |
| f139_0_main_GE | 2 | f169_0_main_GE: | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ 3 = _x3 ∧ _x = _x2 ∧ _x ≤ 9 | |
| f169_0_main_GE | 3 | f139_0_main_GE: | x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x4 + 1 = _x6 ∧ 11 ≤ _x5 − 1 | |
| f169_0_main_GE | 4 | f169_0_main_GE: | x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 + 1 = _x11 ∧ _x8 = _x10 ∧ _x9 ≤ 11 | |
| __init | 5 | f1_0_main_ConstantStackPush: | x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ 0 ≤ 0 |
| f169_0_main_GE | f169_0_main_GE | : | x1 = x1 ∧ x2 = x2 |
| f139_0_main_GE | f139_0_main_GE | : | x1 = x1 ∧ x2 = x2 |
| f1_0_main_ConstantStackPush | f1_0_main_ConstantStackPush | : | x1 = x1 ∧ x2 = x2 |
| __init | __init | : | x1 = x1 ∧ x2 = x2 |
We consider subproblems for each of the 1 SCC(s) of the program graph.
Here we consider the SCC { , }.
We remove transition using the following ranking functions, which are bounded by 0.
| : | 9 − x1 |
| : | 8 − x1 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | 0 |
| : | −1 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | 11 − x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.