by AProVE
| f1_0_main_ConstantStackPush | 1 | f66_0_main_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ _arg2 = _arg3P ∧ 0 = _arg2P ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1 | |
| f66_0_main_GE | 2 | f66_0_main_GE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 + 1 = _x4 ∧ 0 ≤ _x3 − 1 ∧ 0 ≤ _x − 1 ∧ _x3 ≤ _x ∧ −1 ≤ _x2 − 1 ∧ _x1 ≤ _x2 − 1 | |
| __init | 3 | f1_0_main_ConstantStackPush: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 0 ≤ 0 |
| f66_0_main_GE | f66_0_main_GE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| f1_0_main_ConstantStackPush | f1_0_main_ConstantStackPush | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| __init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
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.
| : | − x2 + x3 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.