by AProVE
l0 | 1 | l1: | x1 = ___const_10HAT0 ∧ x2 = _i5HAT0 ∧ x3 = _length4HAT0 ∧ x4 = _sHAT0 ∧ x5 = _tmpHAT0 ∧ x6 = _tmp___08HAT0 ∧ x1 = ___const_10HATpost ∧ x2 = _i5HATpost ∧ x3 = _length4HATpost ∧ x4 = _sHATpost ∧ x5 = _tmpHATpost ∧ x6 = _tmp___08HATpost ∧ _tmp___08HAT0 = _tmp___08HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _sHAT0 = _sHATpost ∧ _length4HAT0 = _length4HATpost ∧ _i5HAT0 = _i5HATpost ∧ ___const_10HAT0 = ___const_10HATpost ∧ _length4HAT0 ≤ _i5HAT0 | |
l0 | 2 | l2: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x4 = _x9 ∧ x5 = _x10 ∧ x6 = _x11 ∧ _x4 = _x10 ∧ _x3 = _x9 ∧ _x2 = _x8 ∧ _x = _x6 ∧ _x7 = 1 + _x1 ∧ _x11 = _x11 ∧ 1 + _x1 ≤ _x2 | |
l2 | 3 | l0: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x4 = _x15 ∧ x5 = _x16 ∧ x6 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x4 = _x21 ∧ x5 = _x22 ∧ x6 = _x23 ∧ _x17 = _x23 ∧ _x16 = _x22 ∧ _x15 = _x21 ∧ _x14 = _x20 ∧ _x13 = _x19 ∧ _x12 = _x18 | |
l3 | 4 | l2: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x4 = _x27 ∧ x5 = _x28 ∧ x6 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x4 = _x33 ∧ x5 = _x34 ∧ x6 = _x35 ∧ _x29 = _x35 ∧ _x24 = _x30 ∧ _x31 = 0 ∧ _x32 = _x24 ∧ _x33 = _x34 ∧ _x34 = _x34 | |
l4 | 5 | l3: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x5 = _x40 ∧ x6 = _x41 ∧ x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ x5 = _x46 ∧ x6 = _x47 ∧ _x41 = _x47 ∧ _x40 = _x46 ∧ _x39 = _x45 ∧ _x38 = _x44 ∧ _x37 = _x43 ∧ _x36 = _x42 |
l4 | l4 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 |
l3 | l3 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 |
l0 | l0 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 |
l2 | l2 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 |
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.: | −1 − x2 + x3 |
: | −1 − x2 + x3 |
We remove transition
using the following ranking functions, which are bounded by 0.: | 0 |
: | −1 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.