by AProVE
| f1_0_main_Load | 1 | f213_0_main_LE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg3P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 | |
| f213_0_main_LE | 2 | f227_0_main_LE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x = _x4 ∧ _x1 = _x3 ∧ _x2 ≤ _x1 − 1 | |
| f227_0_main_LE | 3 | f213_0_main_LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x6 − 1 = _x10 ∧ _x7 = _x9 ∧ _x7 ≤ _x8 | |
| f227_0_main_LE | 4 | f227_0_main_LE: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x13 − 1 = _x16 ∧ _x12 = _x15 ∧ _x14 ≤ _x13 − 1 | |
| __init | 5 | f1_0_main_Load: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ 0 ≤ 0 |
| f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| f227_0_main_LE | f227_0_main_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| f213_0_main_LE | f213_0_main_LE | : | 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.
| : | −1 + x1 − x3 |
| : | −1 + x2 − x3 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | x2 − x3 |
| : | −1 + x1 − x3 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | 0 |
| : | −1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.