by AProVE
f1_0_main_Load | 1 | f213_0_main_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg3P − 1 ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 | |
f213_0_main_GE | 2 | f213_0_main_GE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x + 1 = _x3 ∧ _x ≤ _x1 ∧ _x1 ≤ _x2 − 1 | |
f213_0_main_GE | 3 | f213_0_main_GE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x7 + 1 = _x10 ∧ _x6 = _x9 ∧ _x7 ≤ _x6 − 1 ∧ _x7 ≤ _x8 − 1 | |
__init | 4 | f1_0_main_Load: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ 0 ≤ 0 |
f213_0_main_GE | f213_0_main_GE | : | 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 transition
using the following ranking functions, which are bounded by 0.: | −1 − x1 + x3 |
We remove transition
using the following ranking functions, which are bounded by 0.: | x1 − x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.