by AProVE
l0 | 1 | l1: | x1 = _ResultHAT0 ∧ x2 = _xHAT0 ∧ x3 = _yHAT0 ∧ x1 = _ResultHATpost ∧ x2 = _xHATpost ∧ x3 = _yHATpost ∧ _yHAT0 = _yHATpost ∧ _xHAT0 = _xHATpost ∧ _ResultHATpost = _ResultHATpost ∧ − _xHAT0 ≤ 0 | |
l0 | 2 | l3: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x = _x3 ∧ 0 ≤ −1 − _x1 | |
l3 | 3 | l4: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x7 = _x10 ∧ _x6 = _x9 ∧ 1 + _x8 ≤ −1 | |
l3 | 4 | l4: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x13 = _x16 ∧ _x12 = _x15 ∧ 0 ≤ _x14 | |
l4 | 5 | l2: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x18 = _x21 ∧ _x23 = 1 + _x20 ∧ _x22 = 1 + _x19 | |
l2 | 6 | l0: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x26 = _x29 ∧ _x25 = _x28 ∧ _x24 = _x27 | |
l0 | 7 | l5: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x30 = _x33 ∧ _x34 = −99 + _x31 ∧ _x35 = 1 + _x32 ∧ −1 ≤ _x32 ∧ _x32 ≤ −1 ∧ 0 ≤ −1 − _x31 | |
l5 | 8 | l0: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x38 = _x41 ∧ _x37 = _x40 ∧ _x36 = _x39 | |
l6 | 9 | l0: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x44 = _x47 ∧ _x43 = _x46 ∧ _x42 = _x45 | |
l7 | 10 | l6: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ _x50 = _x53 ∧ _x49 = _x52 ∧ _x48 = _x51 |
l5 | l5 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l4 | l4 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l7 | l7 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l6 | l6 | : | 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 transitions
, using the following ranking functions, which are bounded by 0.: | −4⋅x3 + 1 |
: | −4⋅x3 |
: | −4⋅x3 + 2 |
: | −4⋅x3 + 2 |
: | −4⋅x3 − 1 |
We remove transition
using the following ranking functions, which are bounded by 0.: | −4⋅x2 |
: | −4⋅x2 − 1 |
: | −4⋅x2 + 1 |
: | −4⋅x2 + 1 |
: | −4⋅x2 − 2 |
We remove transitions
, , , using the following ranking functions, which are bounded by −1.: | −1 |
: | −2 |
: | −1 |
: | 0 |
: | 1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.