by AProVE
| f1_0_main_Load | 1 | f278_0_main_NE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg3P − 1 ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 | |
| f278_0_main_NE | 2 | f322_0_main_LE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x1 = _x4 ∧ x2 = _x5 ∧ x3 = _x6 ∧ x4 = _x7 ∧ _x = _x7 ∧ _x1 = _x6 ∧ _x1 = _x5 ∧ _x1 = _x4 ∧ _x1 = _x2 ∧ _x ≤ _x1 − 1 | |
| f322_0_main_LE | 3 | f278_0_main_NE: | x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x4 = _x11 ∧ x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x4 = _x15 ∧ _x9 = _x14 ∧ _x8 = _x13 ∧ _x11 = _x12 ∧ _x9 = _x10 ∧ _x9 ≤ _x11 | |
| f322_0_main_LE | 4 | f322_0_main_LE: | x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x4 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ _x19 = _x23 ∧ _x17 − 1 = _x22 ∧ _x17 − 1 = _x21 ∧ _x16 − 1 = _x20 ∧ _x17 = _x18 ∧ _x19 ≤ _x17 − 1 | |
| __init | 5 | f1_0_main_Load: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x4 = _x27 ∧ x1 = _x28 ∧ x2 = _x29 ∧ x3 = _x30 ∧ x4 = _x31 ∧ 0 ≤ 0 |
| f278_0_main_NE | f278_0_main_NE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
| f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
| f322_0_main_LE | f322_0_main_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
| __init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 |
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 + x3 − x4 |
We remove transitions , using the following ranking functions, which are bounded by 0.
| : | 0 |
| : | −2⋅x3 + 2⋅x4 + 1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.