by AProVE
l0 | 1 | l1: | x1 = _xHAT0 ∧ x2 = _yHAT0 ∧ x3 = _zHAT0 ∧ x1 = _xHATpost ∧ x2 = _yHATpost ∧ x3 = _zHATpost ∧ _zHAT0 = _zHATpost ∧ _yHAT0 = _yHATpost ∧ _xHATpost = −1 + _xHAT0 ∧ 1 ≤ _xHAT0 | |
l1 | 2 | l0: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x = _x3 | |
l2 | 3 | l0: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x7 = _x10 ∧ _x6 = _x9 ∧ _x7 ≤ 0 | |
l2 | 4 | l3: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x12 = _x15 ∧ _x16 = −1 + _x13 ∧ 1 ≤ _x13 | |
l3 | 5 | l2: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x20 = _x23 ∧ _x19 = _x22 ∧ _x18 = _x21 | |
l4 | 6 | l2: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x26 = _x29 ∧ _x25 = _x28 ∧ _x24 = _x27 ∧ _x26 ≤ _x24 | |
l4 | 7 | l5: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x32 = _x35 ∧ _x31 = _x34 ∧ _x33 = 1 + _x30 ∧ 1 + _x30 ≤ _x32 | |
l5 | 8 | l4: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x38 = _x41 ∧ _x37 = _x40 ∧ _x36 = _x39 | |
l6 | 9 | l4: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x44 = _x47 ∧ _x43 = _x46 ∧ _x42 = _x45 ∧ _x43 ≤ _x44 | |
l6 | 10 | l7: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ _x50 = _x53 ∧ _x48 = _x51 ∧ _x52 = −1 + _x49 ∧ 1 + _x50 ≤ _x49 | |
l7 | 11 | l6: | x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ _x56 = _x59 ∧ _x55 = _x58 ∧ _x54 = _x57 | |
l8 | 12 | l6: | x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ _x62 = _x65 ∧ _x61 = _x64 ∧ _x63 = 0 | |
l9 | 13 | l8: | x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x1 = _x69 ∧ x2 = _x70 ∧ x3 = _x71 ∧ _x68 = _x71 ∧ _x67 = _x70 ∧ _x66 = _x69 |
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 |
l1 | l1 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l8 | l8 | : | 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 |
l9 | l9 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
We consider subproblems for each of the 4 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⋅x2 |
: | 2⋅x2 − 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.
Here we consider the SCC {
, }.We remove transition
using the following ranking functions, which are bounded by 0.: | −2⋅x1 + 2⋅x3 |
: | −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.
Here we consider the SCC {
, }.We remove transition
using the following ranking functions, which are bounded by 0.: | 2⋅x2 |
: | 2⋅x2 + 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.
Here we consider the SCC {
, }.We remove transition
using the following ranking functions, which are bounded by 0.: | 2⋅x1 |
: | 2⋅x1 + 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.