by AProVE
f1_0_main_Load | 1 | f117_0_createList_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ 0 ≤ _arg2 − 1 ∧ −1 ≤ _arg1P − 1 | |
f1_0_main_Load | 2 | f232_0_main_InvokeMethod: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ −1 ≤ _x6 − 1 ∧ 0 ≤ _x1 − 1 ∧ _x3 ≤ _x ∧ 0 ≤ _x − 1 ∧ 0 ≤ _x3 − 1 ∧ 3 ≤ _x4 − 1 ∧ 0 = _x5 | |
f1_0_main_Load | 3 | f232_0_main_InvokeMethod: | x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x1 = _x11 ∧ x2 = _x13 ∧ x3 = _x14 ∧ −1 ≤ _x16 − 1 ∧ 0 ≤ _x9 − 1 ∧ _x11 ≤ _x8 ∧ _x13 − 1 ≤ _x8 ∧ 0 ≤ _x8 − 1 ∧ 0 ≤ _x11 − 1 ∧ 1 ≤ _x13 − 1 ∧ 0 = _x14 | |
f117_0_createList_GE | 4 | f117_0_createList_GE: | x1 = _x17 ∧ x2 = _x18 ∧ x3 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ _x17 − 1 = _x20 ∧ _x17 − 1 ≤ _x17 − 1 ∧ −1 ≤ _x17 − 1 | |
f232_0_main_InvokeMethod | 5 | f389_0_dupList_NONNULL: | x1 = _x23 ∧ x2 = _x24 ∧ x3 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ _x26 ≤ _x24 ∧ 0 ≤ _x29 − 1 ∧ _x27 + 2 ≤ _x24 ∧ 0 ≤ _x23 − 1 ∧ 1 ≤ _x24 − 1 ∧ 1 ≤ _x26 − 1 ∧ −1 ≤ _x27 − 1 ∧ 0 = _x25 ∧ 0 = _x28 | |
f389_0_dupList_NONNULL | 6 | f389_0_dupList_NONNULL: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x35 + 2 ≤ _x31 ∧ _x32 + 2 ≤ _x30 ∧ _x35 + 4 ≤ _x30 ∧ −1 ≤ _x34 − 1 ∧ 0 ≤ _x33 − 1 ∧ 0 ≤ _x31 − 1 ∧ 2 ≤ _x30 − 1 ∧ _x34 + 1 ≤ _x31 ∧ _x34 + 3 ≤ _x30 ∧ _x33 ≤ _x31 ∧ _x32 ≤ −1 ∧ _x33 + 2 ≤ _x30 | |
f389_0_dupList_NONNULL | 7 | f389_0_dupList_NONNULL: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x41 + 2 ≤ _x37 ∧ _x38 + 2 ≤ _x36 ∧ _x41 + 4 ≤ _x36 ∧ −1 ≤ _x40 − 1 ∧ 0 ≤ _x39 − 1 ∧ 0 ≤ _x37 − 1 ∧ 2 ≤ _x36 − 1 ∧ _x40 + 1 ≤ _x37 ∧ _x40 + 3 ≤ _x36 ∧ _x39 ≤ _x37 ∧ 0 ≤ _x38 − 1 ∧ _x39 + 2 ≤ _x36 | |
f389_0_dupList_NONNULL | 8 | f389_0_dupList_NONNULL: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ 1 = _x47 ∧ 0 = _x44 ∧ 0 ≤ _x46 − 1 ∧ 2 ≤ _x45 − 1 ∧ 0 ≤ _x43 − 1 ∧ 2 ≤ _x42 − 1 ∧ _x46 ≤ _x43 ∧ _x46 + 2 ≤ _x42 ∧ _x45 − 2 ≤ _x43 ∧ _x45 ≤ _x42 | |
__init | 9 | f1_0_main_Load: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ 0 ≤ 0 |
f389_0_dupList_NONNULL | f389_0_dupList_NONNULL | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f117_0_createList_GE | f117_0_createList_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 |
f232_0_main_InvokeMethod | f232_0_main_InvokeMethod | : | 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 transitions
, using the following ranking functions, which are bounded by 0.: | −1 + x1 |
We remove transition
using the following ranking functions, which are bounded by 0.: | − x3 |
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.: | x1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.