by AProVE
l0 | 1 | l1: | x1 = ___const_5HAT0 ∧ x2 = _xHAT0 ∧ x1 = ___const_5HATpost ∧ x2 = _xHATpost ∧ ___const_5HAT0 = ___const_5HATpost ∧ _xHATpost = 1 ∧ _xHAT0 ≤ 0 | |
l0 | 2 | l1: | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x = _x2 ∧ _x3 = 1 + _x1 ∧ 1 ≤ _x1 | |
l2 | 3 | l3: | x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 = _x6 ∧ 4 ≤ _x5 | |
l2 | 4 | l0: | x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10 ∧ 1 + _x9 ≤ 4 | |
l1 | 5 | l2: | x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x13 = _x15 ∧ _x12 = _x14 | |
l4 | 6 | l1: | x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x20 = _x16 ∧ _x19 = _x19 ∧ _x16 = _x18 | |
l5 | 7 | l4: | x1 = _x21 ∧ x2 = _x22 ∧ x1 = _x23 ∧ x2 = _x24 ∧ _x22 = _x24 ∧ _x21 = _x23 |
l5 | l5 | : | x1 = x1 ∧ x2 = x2 |
l4 | l4 | : | x1 = x1 ∧ x2 = x2 |
l1 | l1 | : | 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 −7.: | −3⋅x2 + 1 |
: | −3⋅x2 + 3 |
: | −3⋅x2 + 2 |
We remove transitions
, , using the following ranking functions, which are bounded by −1.: | 0 |
: | −1 |
: | −2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.