by AProVE
f1_0_main_Load | 1 | f127_0_times_NE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ 1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 | |
f127_0_times_NE | 2 | f127_0_times_NE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x1 − 1 = _x4 ∧ _x = _x3 ∧ _x1 − 1 ≤ _x1 − 1 ∧ 0 ≤ _x1 − 1 | |
f127_0_times_NE | 3 | f469_0_times_InvokeMethod: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x6 = _x11 ∧ 0 = _x10 ∧ 1 = _x9 ∧ 1 = _x7 | |
f127_0_times_NE | 4 | f469_0_times_InvokeMethod: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ 0 = _x17 ∧ 0 = _x16 ∧ _x13 = _x15 ∧ 0 = _x12 ∧ _x13 − 1 ≤ _x13 − 1 ∧ 0 ≤ _x13 − 1 | |
f127_0_times_NE | 5 | f469_0_times_InvokeMethod: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x18 = _x23 ∧ _x19 = _x21 ∧ _x19 − 1 ≤ _x19 − 1 ∧ 0 ≤ _x19 − 1 | |
f127_0_times_NE | 6 | f469_0_times_InvokeMethod: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ 0 = _x29 ∧ _x25 = _x27 ∧ 0 = _x24 ∧ _x25 − 1 ≤ _x25 − 1 ∧ 0 ≤ _x25 − 1 | |
f218_0_times_Return | 7 | f469_0_times_InvokeMethod: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x31 = _x35 ∧ _x32 = _x34 ∧ _x30 = _x33 | |
f469_0_times_InvokeMethod | 8 | f484_0_plus_LE: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x38 = _x40 ∧ _x37 = _x39 ∧ 0 ≤ _x36 − 1 | |
f484_0_plus_LE | 9 | f484_0_plus_LE: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x43 − 1 = _x46 ∧ _x42 = _x45 ∧ _x43 − 1 ≤ _x43 − 1 ∧ 0 ≤ _x43 − 1 | |
f484_0_plus_LE | 10 | f484_0_plus_LE: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ _x49 = _x52 ∧ _x48 − 1 = _x51 ∧ 0 ≤ _x48 − 1 ∧ _x48 − 1 ≤ _x48 − 1 ∧ _x49 ≤ 0 | |
__init | 11 | f1_0_main_Load: | x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ 0 ≤ 0 |
f218_0_times_Return | f218_0_times_Return | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f469_0_times_InvokeMethod | f469_0_times_InvokeMethod | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f484_0_plus_LE | f484_0_plus_LE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f127_0_times_NE | f127_0_times_NE | : | 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.: | x2 |
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 + x1 |
We remove transition
using the following ranking functions, which are bounded by 0.: | x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.