by AProVE
f169_0_createList_Return | 1 | f229_0_random_ArrayAccess: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg1P ≤ _arg2 | |
f1_0_main_Load | 2 | f229_0_random_ArrayAccess: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x1 = _x4 ∧ −1 ≤ _x3 − 1 ∧ 0 ≤ _x − 1 | |
f1_0_main_Load | 3 | f194_0_createList_LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 0 ≤ _x6 − 1 ∧ −1 ≤ _x9 − 1 ∧ −1 ≤ _x7 − 1 | |
f194_0_createList_LE | 4 | f194_0_createList_LE: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x12 − 1 = _x15 ∧ 0 ≤ _x12 − 1 | |
f229_0_random_ArrayAccess | 5 | f298_0_appE_NONNULL: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ −1 ≤ _x23 − 1 ∧ 0 ≤ _x21 − 1 ∧ 0 ≤ _x18 − 1 ∧ _x23 + 1 ≤ _x18 ∧ _x21 ≤ _x18 ∧ 1 ≤ _x19 − 1 ∧ −1 ≤ _x22 − 1 | |
f298_0_appE_NONNULL | 6 | f298_0_appE_NONNULL: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x25 = _x28 ∧ −1 ≤ _x29 − 1 ∧ 0 ≤ _x27 − 1 ∧ 0 ≤ _x26 − 1 ∧ 2 ≤ _x24 − 1 ∧ _x29 + 1 ≤ _x26 ∧ _x29 + 3 ≤ _x24 ∧ _x27 ≤ _x26 ∧ _x27 + 2 ≤ _x24 | |
f298_0_appE_NONNULL | 7 | f298_0_appE_NONNULL: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x31 − 1 = _x34 ∧ −1 ≤ _x35 − 1 ∧ 1 ≤ _x33 − 1 ∧ −1 ≤ _x32 − 1 ∧ 1 ≤ _x30 − 1 ∧ _x35 ≤ _x32 ∧ _x35 + 2 ≤ _x30 ∧ _x33 − 2 ≤ _x32 ∧ 0 ≤ _x31 − 1 ∧ _x33 ≤ _x30 | |
__init | 8 | f1_0_main_Load: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ 0 ≤ 0 |
f229_0_random_ArrayAccess | f229_0_random_ArrayAccess | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f194_0_createList_LE | f194_0_createList_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f169_0_createList_Return | f169_0_createList_Return | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f298_0_appE_NONNULL | f298_0_appE_NONNULL | : | 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 2 SCC(s) of the program graph.
Here we consider the SCC {
}.We remove transition
using the following ranking functions, which are bounded by 0.: | x1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.
Here we consider the SCC {
}.We remove transition
using the following ranking functions, which are bounded by 0.: | −1 + x2 |
We remove transition
using the following ranking functions, which are bounded by 0.: | −1 + x1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.