by AProVE
f1_0_main_New | 1 | f262_0_main_InvokeMethod: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 2 ≤ _arg1P − 1 | |
f1_0_main_New | 2 | f262_0_main_InvokeMethod: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ 1 ≤ _x3 − 1 | |
f1_0_main_New | 3 | f76_0__init__LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 5 = _x11 ∧ 5 = _x10 ∧ 5 = _x9 | |
f76_0__init__LE | 4 | f76_0__init__LE: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x13 − 1 = _x17 ∧ _x13 − 1 = _x16 ∧ _x13 − 1 = _x15 ∧ _x13 = _x14 ∧ 1 ≤ _x13 − 1 ∧ 0 ≤ _x12 − 1 ∧ _x13 − 1 ≤ _x13 − 1 | |
f76_0__init__LE | 5 | f288_0__init__InvokeMethod: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x19 − 1 = _x23 ∧ _x18 = _x21 ∧ _x19 = _x20 ∧ 0 ≤ _x18 − 1 ∧ 4 ≤ _x22 − 1 ∧ 1 ≤ _x19 − 1 ∧ _x19 − 1 ≤ _x19 − 1 | |
f76_0__init__LE | 6 | f288_0__init__InvokeMethod: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x25 − 1 = _x29 ∧ _x24 = _x27 ∧ _x25 = _x26 ∧ 0 ≤ _x24 − 1 ∧ 3 ≤ _x28 − 1 ∧ 1 ≤ _x25 − 1 ∧ _x25 − 1 ≤ _x25 − 1 | |
f288_0__init__InvokeMethod | 7 | f76_0__init__LE: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x32 = _x35 ∧ _x32 = _x34 ∧ _x32 = _x33 ∧ 2 ≤ _x31 − 1 ∧ 0 ≤ _x30 − 1 ∧ 0 ≤ _x32 − 1 | |
f262_0_main_InvokeMethod | 8 | f194_0_height_NONNULL: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ −1 ≤ _x40 − 1 ∧ 0 ≤ _x39 − 1 ∧ 0 ≤ _x36 − 1 ∧ _x40 + 1 ≤ _x36 ∧ _x39 ≤ _x36 | |
f194_0_height_NONNULL | 9 | f194_0_height_NONNULL: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ −1 ≤ _x46 − 1 ∧ 0 ≤ _x45 − 1 ∧ 0 ≤ _x43 − 1 ∧ 2 ≤ _x42 − 1 ∧ _x46 + 1 ≤ _x43 ∧ _x46 + 3 ≤ _x42 ∧ _x45 ≤ _x43 ∧ _x45 + 2 ≤ _x42 | |
f194_0_height_NONNULL | 10 | f194_0_height_NONNULL: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ −1 ≤ _x52 − 1 ∧ 0 ≤ _x51 − 1 ∧ −1 ≤ _x49 − 1 ∧ 2 ≤ _x48 − 1 ∧ _x52 + 3 ≤ _x48 ∧ _x51 + 2 ≤ _x48 | |
__init | 11 | f1_0_main_New: | x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ 0 ≤ 0 |
f1_0_main_New | f1_0_main_New | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f262_0_main_InvokeMethod | f262_0_main_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f288_0__init__InvokeMethod | f288_0__init__InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f76_0__init__LE | f76_0__init__LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f194_0_height_NONNULL | f194_0_height_NONNULL | : | 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 transitions
, , , using the following ranking functions, which are bounded by 0.: | 2⋅x2 |
: | 1 + 2⋅x3 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.
Here we consider the SCC {
}.We remove transitions
, 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.