by AProVE
f1_0_main_ConstantStackPush | 1 | f458_0_sort_GE: | x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ 1 = _arg1P | |
f458_0_sort_GE | 2 | f543_0_sort_GE: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ 100 − _x = _x5 ∧ 0 = _x4 ∧ _x = _x3 ∧ _x ≤ 99 ∧ 0 ≤ _x − 1 | |
f543_0_sort_GE | 3 | f458_0_sort_GE: | x1 = _x6 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x1 = _x11 ∧ x2 = _x14 ∧ x3 = _x15 ∧ _x6 + 1 = _x11 ∧ _x10 ≤ _x9 | |
f543_0_sort_GE | 4 | f543_0_sort_GE: | x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x1 = _x19 ∧ x2 = _x20 ∧ x3 = _x21 ∧ _x17 ≤ 99 ∧ _x17 ≤ _x18 − 1 ∧ −1 ≤ _x17 − 1 ∧ _x17 ≤ 98 ∧ _x22 ≤ _x23 ∧ 0 ≤ _x16 − 1 ∧ _x16 = _x19 ∧ _x17 + 1 = _x20 ∧ 100 − _x16 = _x21 | |
f543_0_sort_GE | 5 | f543_0_sort_GE: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x25 ≤ 99 ∧ _x25 ≤ _x26 − 1 ∧ −1 ≤ _x25 − 1 ∧ _x25 ≤ 98 ∧ 0 ≤ _x24 − 1 ∧ _x30 ≤ _x31 − 1 ∧ _x24 = _x27 ∧ _x25 + 1 = _x28 ∧ 100 − _x24 = _x29 | |
__init | 6 | f1_0_main_ConstantStackPush: | x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ 0 ≤ 0 |
f1_0_main_ConstantStackPush | f1_0_main_ConstantStackPush | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f543_0_sort_GE | f543_0_sort_GE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
f458_0_sort_GE | f458_0_sort_GE | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
__init | __init | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
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 −196.: | −2⋅x1 + 2 |
: | −2⋅x1 + 1 |
We remove transition
using the following ranking functions, which are bounded by 0.: | 0 |
: | −1 |
We remove transitions
, using the following ranking functions, which are bounded by 0.: | 98 − x2 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.