by AProVE
f1_0_main_Load | 1 | f148_0_main_LE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ _arg1P + _arg2P = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg1P − 1 | |
f148_0_main_LE | 2 | f148_0_main_LE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x − 1 + _x1 = _x5 ∧ _x1 = _x4 ∧ _x − 1 = _x3 ∧ −1 ≤ _x1 − 1 ∧ 0 ≤ _x2 − 1 ∧ 0 ≤ _x − 1 | |
f148_0_main_LE | 3 | f148_0_main_LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 0 = _x11 ∧ 0 = _x10 ∧ 0 = _x9 ∧ 0 = _x7 ∧ 0 = _x6 ∧ 0 ≤ _x8 − 1 | |
f148_0_main_LE | 4 | f148_0_main_LE: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x13 − 1 = _x17 ∧ _x13 − 1 = _x16 ∧ 0 = _x15 ∧ 0 = _x12 ∧ 0 ≤ _x13 − 1 ∧ 0 ≤ _x14 − 1 | |
__init | 5 | f1_0_main_Load: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ 0 ≤ 0 |
f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f148_0_main_LE | f148_0_main_LE | : | 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.: | −1 + x1 + x2 |
We remove transition
using the following ranking functions, which are bounded by 0.: | 0⋅x1 + 0⋅x2 + x3 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.