by AProVE
l0 | 1 | l1: | x1 = ___const_42HAT0 ∧ x2 = _i1HAT0 ∧ x1 = ___const_42HATpost ∧ x2 = _i1HATpost ∧ ___const_42HAT0 = ___const_42HATpost ∧ _i1HATpost = 1 + _i1HAT0 | |
l2 | 2 | l0: | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 = _x3 ∧ _x = _x2 | |
l3 | 3 | l2: | x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 = _x6 | |
l3 | 4 | l0: | x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10 | |
l4 | 5 | l5: | x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x13 = _x15 ∧ _x12 = _x14 ∧ _x12 ≤ _x13 | |
l4 | 6 | l3: | x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x17 = _x19 ∧ _x16 = _x18 ∧ 1 + _x17 ≤ _x16 | |
l1 | 7 | l4: | x1 = _x20 ∧ x2 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ _x21 = _x23 ∧ _x20 = _x22 | |
l6 | 8 | l1: | x1 = _x24 ∧ x2 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ _x24 = _x26 ∧ _x27 = 0 | |
l7 | 9 | l6: | x1 = _x28 ∧ x2 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ _x29 = _x31 ∧ _x28 = _x30 |
l4 | l4 | : | x1 = x1 ∧ x2 = x2 |
l7 | l7 | : | x1 = x1 ∧ x2 = x2 |
l6 | l6 | : | 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.: | −2 + x1 − x2 |
: | −1 + x1 − x2 |
: | −2 + x1 − x2 |
: | −2 + x1 − x2 |
: | −1 + x1 − x2 |
We remove transitions
, , , , using the following ranking functions, which are bounded by 0.: | 2 |
: | 1 |
: | 4 |
: | 3 |
: | 0 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.