by AProVE
f1_0_main_Load | 1 | f145_0_main_LE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 | |
f145_0_main_LE | 2 | f145_0_main_LE': | x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 + 1 − 2⋅_x4 = 0 ∧ −1 ≤ _x1 − 1 ∧ _x1 ≤ _x − 1 ∧ _x = _x2 ∧ _x1 = _x3 | |
f145_0_main_LE' | 3 | f145_0_main_LE: | x1 = _x5 ∧ x2 = _x6 ∧ x1 = _x7 ∧ x2 = _x8 ∧ _x6 + 1 − 2⋅_x9 = 0 ∧ _x6 ≤ _x5 − 1 ∧ −1 ≤ _x6 − 1 ∧ _x6 + 1 − 2⋅_x9 ≤ 1 ∧ 0 ≤ _x6 + 1 − 2⋅_x9 ∧ _x5 = _x7 ∧ _x6 + 1 = _x8 | |
f145_0_main_LE | 4 | f145_0_main_LE': | x1 = _x11 ∧ x2 = _x12 ∧ x1 = _x14 ∧ x2 = _x15 ∧ −1 ≤ _x12 − 1 ∧ _x12 + 1 − 2⋅_x17 = 1 ∧ _x12 ≤ _x11 − 1 ∧ _x11 = _x14 ∧ _x12 = _x15 | |
f145_0_main_LE' | 5 | f145_0_main_LE: | x1 = _x18 ∧ x2 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ −1 ≤ _x20 − 1 ∧ _x20 ≤ _x18 − 1 ∧ _x20 + 1 − 2⋅_x23 = 1 ∧ _x20 + 1 − 2⋅_x23 ≤ 1 ∧ 0 ≤ _x20 + 1 − 2⋅_x23 ∧ _x18 = _x21 ∧ _x20 + 2 = _x22 | |
__init | 6 | f1_0_main_Load: | x1 = _x24 ∧ x2 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ 0 ≤ 0 |
f145_0_main_LE' | f145_0_main_LE' | : | x1 = x1 ∧ x2 = x2 |
f145_0_main_LE | f145_0_main_LE | : | x1 = x1 ∧ x2 = x2 |
f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 |
__init | __init | : | 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 transitions
, , , using the following ranking functions, which are bounded by 0.: | −2⋅x2 + 2⋅x1 |
: | 2⋅x1 − 2⋅x2 − 1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.