by AProVE
l0 | 1 | l1: | x1 = _xHAT0 ∧ x2 = _yHAT0 ∧ x1 = _xHATpost ∧ x2 = _yHATpost ∧ _yHATpost = 1 + _yHAT0 ∧ _xHATpost = −1 + _xHAT0 ∧ _yHAT0 ≤ 0 | |
l0 | 2 | l2: | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x = _x2 ∧ _x3 = −1 + _x1 ∧ 1 ≤ _x1 | |
l2 | 3 | l0: | x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 = _x6 | |
l3 | 4 | l1: | x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10 | |
l1 | 5 | l0: | x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x12 = _x14 ∧ _x15 = _x12 ∧ 1 ≤ _x12 | |
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 0.: | −1 + x1 |
: | x1 |
: | −1 + x1 |
We remove transition
using the following ranking functions, which are bounded by 0.: | 0 |
: | −1 |
: | 0 |
We remove transition
using the following ranking functions, which are bounded by 0.: | −1 + x2 |
: | −1 + 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.