by AProVE
| f1_0_main_Load | 1 | f172_0_appendNewList_LE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 0 = _arg2P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ 0 ≤ _arg2 − 1 | |
| f172_0_appendNewList_LE | 2 | f172_0_appendNewList_LE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x − 1 = _x3 ∧ 0 ≤ _x1 − 1 ∧ 1 ≤ _x − 1 ∧ _x1 ≤ _x4 − 1 | |
| f172_0_appendNewList_LE | 3 | f172_0_appendNewList_LE: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ 1 = _x10 ∧ _x6 − 1 = _x9 ∧ 1 ≤ _x6 − 1 | |
| f172_0_appendNewList_LE | 4 | f282_0_copy_NULL: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ 0 = _x17 ∧ _x12 ≤ 1 ∧ 3 ≤ _x16 − 1 ∧ 1 ≤ _x15 − 1 | |
| f282_0_copy_NULL | 5 | f282_0_copy_NULL: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x23 + 2 ≤ _x19 ∧ _x20 + 2 ≤ _x18 ∧ −1 ≤ _x22 − 1 ∧ 1 ≤ _x21 − 1 ∧ 0 ≤ _x19 − 1 ∧ 1 ≤ _x18 − 1 ∧ _x22 + 1 ≤ _x19 ∧ _x21 − 1 ≤ _x19 | |
| __init | 6 | f1_0_main_Load: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ 0 ≤ 0 |
| f282_0_copy_NULL | f282_0_copy_NULL | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
| f172_0_appendNewList_LE | f172_0_appendNewList_LE | : | 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 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.
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.