by AProVE
| l0 | 1 | l1: | x1 = _eHAT0 ∧ x2 = _nHAT0 ∧ x1 = _eHATpost ∧ x2 = _nHATpost ∧ _eHATpost = 1 + _eHAT0 ∧ _nHATpost = 11 + _nHAT0 ∧ _nHAT0 ≤ 100 ∧ 1 ≤ _eHAT0 | |
| l1 | 2 | l0: | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 = _x3 ∧ _x = _x2 | |
| l0 | 3 | l2: | x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x6 = −1 + _x4 ∧ _x7 = −10 + _x5 ∧ 101 ≤ _x5 ∧ 1 ≤ _x4 | |
| l2 | 4 | l0: | x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10 | |
| l3 | 5 | l0: | x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x14 = 1 ∧ _x15 = _x15 | |
| l4 | 6 | l3: | x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x17 = _x19 ∧ _x16 = _x18 |
| l4 | l4 | : | x1 = x1 ∧ x2 = x2 |
| l1 | l1 | : | x1 = x1 ∧ x2 = x2 |
| l3 | l3 | : | x1 = x1 ∧ x2 = x2 |
| l0 | l0 | : | x1 = x1 ∧ x2 = x2 |
| l2 | l2 | : | 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 −358.
| : | −4⋅x2 + 42⋅x1 |
| : | 42⋅x1 − 4⋅x2 + 1 |
| : | 42⋅x1 − 4⋅x2 + 1 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | −1 |
| : | −1 |
| : | 0 |
We remove transition using the following ranking functions, which are bounded by 0.
| : | −1 + x1 + x2 |
| : | −1 + x1 + x2 |
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.