by AProVE
| l0 | 1 | l1: | x1 = ___const_20HAT0 ∧ x2 = _iHAT0 ∧ x3 = _jHAT0 ∧ x1 = ___const_20HATpost ∧ x2 = _iHATpost ∧ x3 = _jHATpost ∧ _jHAT0 = _jHATpost ∧ _iHAT0 = _iHATpost ∧ ___const_20HAT0 = ___const_20HATpost ∧ ___const_20HAT0 ≤ _jHAT0 | |
| l0 | 2 | l2: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x = _x3 ∧ 1 + _x2 ≤ _x | |
| l2 | 3 | l0: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x6 = _x9 ∧ _x10 = 2 + _x11 ∧ _x11 = 2 + _x8 | |
| l3 | 4 | l2: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x13 = _x16 ∧ _x12 = _x15 ∧ _x17 = 0 | |
| l4 | 5 | l3: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x20 = _x23 ∧ _x19 = _x22 ∧ _x18 = _x21 |
| l4 | l4 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| l3 | l3 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| l0 | l0 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| l2 | l2 | : | 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.
| : | −2⋅x3 + 2⋅x1 |
| : | 2⋅x1 − 2⋅x3 − 1 |
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.