by AProVE
l0 | 1 | l1: | x1 = _iHAT0 ∧ x1 = _iHATpost ∧ _iHAT0 = _iHATpost ∧ 3 ≤ _iHAT0 | |
l0 | 2 | l2: | x1 = _x ∧ x1 = _x1 ∧ _x1 = 1 + _x ∧ 1 + _x ≤ 3 | |
l3 | 3 | l0: | x1 = _x2 ∧ x1 = _x3 ∧ _x2 = _x3 | |
l3 | 4 | l1: | x1 = _x4 ∧ x1 = _x5 ∧ _x4 = _x5 | |
l2 | 5 | l3: | x1 = _x6 ∧ x1 = _x7 ∧ _x6 = _x7 | |
l4 | 6 | l5: | x1 = _x8 ∧ x1 = _x9 ∧ _x8 = _x9 | |
l1 | 7 | l6: | x1 = _x10 ∧ x1 = _x11 ∧ _x10 = _x11 | |
l6 | 8 | l4: | x1 = _x12 ∧ x1 = _x13 ∧ _x12 = _x13 ∧ 1 + _x12 ≤ 2 | |
l6 | 9 | l4: | x1 = _x14 ∧ x1 = _x15 ∧ _x14 = _x15 ∧ 2 ≤ _x14 | |
l7 | 10 | l2: | x1 = _x16 ∧ x1 = _x17 ∧ _x17 = 0 | |
l8 | 11 | l7: | x1 = _x18 ∧ x1 = _x19 ∧ _x18 = _x19 |
l4 | l4 | : | x1 = x1 |
l7 | l7 | : | x1 = x1 |
l6 | l6 | : | x1 = x1 |
l1 | l1 | : | x1 = x1 |
l8 | l8 | : | x1 = x1 |
l3 | l3 | : | x1 = x1 |
l0 | l0 | : | x1 = x1 |
l2 | l2 | : | x1 = x1 |
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 − x1 |
: | 2 − x1 |
: | 2 − x1 |
We remove transitions
, using the following ranking functions, which are bounded by 0.: | 0 |
: | −1 |
: | 1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.