by AProVE
f1_0_main_Load | 1 | f135_0_f_LE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ _arg2 = _arg2P ∧ _arg2 = _arg1P ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 | |
f135_0_f_LE | 2 | f182_0_f_LE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x1 = _x5 ∧ 2 = _x4 ∧ _x = _x3 ∧ 0 ≤ _x − 1 | |
f182_0_f_LE | 3 | f135_0_f_LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 − 1 = _x10 ∧ _x6 − _x7 = _x9 ∧ 0 ≤ _x6 − 1 ∧ 0 ≤ _x7 − 1 | |
f182_0_f_LE | 4 | f182_0_f_LE: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 − 1 = _x17 ∧ _x13 − 1 = _x16 ∧ _x12 = _x15 ∧ 0 ≤ _x12 − 1 ∧ 0 ≤ _x13 − 1 | |
f182_0_f_LE | 5 | f182_0_f_LE: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x19 − 1 = _x22 ∧ _x18 = _x21 ∧ 0 ≤ _x18 − 1 ∧ 0 ≤ _x19 − 1 | |
__init | 6 | f1_0_main_Load: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ 0 ≤ 0 |
f182_0_f_LE | f182_0_f_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f135_0_f_LE | f135_0_f_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
__init | __init | : | 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.: | 3 + 3⋅x1 |
: | 3⋅x1 + x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.