by AProVE
| f1_0_main_Load | 1 | f262_0_take_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ 0 = _arg3P ∧ 0 ≤ _arg2P − 1 ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg2P ≤ _arg1 ∧ −1 ≤ _arg4P − 1 ∧ 1 ≤ _arg2 − 1 ∧ −1 ≤ _arg5P − 1 | |
| f262_0_take_GE | 2 | f262_0_take_GE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x1 = _x5 ∧ x2 = _x6 ∧ x3 = _x7 ∧ x4 = _x8 ∧ x5 = _x9 ∧ _x4 = _x9 ∧ _x3 + 1 = _x8 ∧ _x2 + 1 = _x7 ∧ _x3 + 2 ≤ _x ∧ 0 ≤ _x6 − 1 ∧ 0 ≤ _x5 − 1 ∧ 0 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x6 ≤ _x1 ∧ _x6 ≤ _x ∧ _x5 − 1 ≤ _x ∧ _x2 ≤ _x4 − 1 ∧ −1 ≤ _x3 − 1 | |
| __init | 3 | f1_0_main_Load: | x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ x4 = _x18 ∧ x5 = _x19 ∧ 0 ≤ 0 |
| f262_0_take_GE | f262_0_take_GE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 |
| f1_0_main_Load | f1_0_main_Load | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 |
| __init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 |
We consider subproblems for each of the 1 SCC(s) of the program graph.
Here we consider the SCC { }.
We remove transition using the following ranking functions, which are bounded by 0.
| : | − x3 + x5 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.