by AProVE
l0 | 1 | l1: | x1 = _i2HAT0 ∧ x2 = _iHAT0 ∧ x3 = _rHAT0 ∧ x1 = _i2HATpost ∧ x2 = _iHATpost ∧ x3 = _rHATpost ∧ _rHAT0 = _rHATpost ∧ _i2HAT0 = _i2HATpost ∧ _iHATpost = 0 ∧ 1 ≤ _iHAT0 | |
l0 | 2 | l2: | x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x3 = _x1 ∧ 1 + _x1 ≤ 1 | |
l3 | 3 | l1: | x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x6 = _x9 ∧ _x10 = 1 + _x7 | |
l4 | 4 | l5: | x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x12 = _x15 ∧ _x13 = _x16 | |
l5 | 5 | l3: | x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x20 = _x23 ∧ _x18 = _x21 ∧ _x19 = _x22 | |
l6 | 6 | l0: | x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x26 = _x29 ∧ _x24 = _x27 ∧ _x25 = _x28 | |
l7 | 7 | l4: | x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x32 = _x35 ∧ _x30 = _x33 ∧ _x31 = _x34 | |
l7 | 8 | l5: | x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x38 = _x41 ∧ _x36 = _x39 ∧ _x37 = _x40 | |
l8 | 9 | l7: | x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x42 = _x45 ∧ _x43 = _x46 ∧ _x47 = _x47 | |
l9 | 10 | l8: | x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ _x50 = _x53 ∧ _x48 = _x51 ∧ _x49 = _x52 | |
l9 | 11 | l3: | x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ _x56 = _x59 ∧ _x54 = _x57 ∧ _x55 = _x58 | |
l10 | 12 | l11: | x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ _x62 = _x65 ∧ _x60 = _x63 ∧ _x61 = _x64 ∧ 1 ≤ _x61 | |
l10 | 13 | l9: | x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x1 = _x69 ∧ x2 = _x70 ∧ x3 = _x71 ∧ _x68 = _x71 ∧ _x66 = _x69 ∧ _x67 = _x70 ∧ 1 + _x67 ≤ 1 | |
l12 | 14 | l6: | x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x1 = _x75 ∧ x2 = _x76 ∧ x3 = _x77 ∧ _x74 = _x77 ∧ _x72 = _x75 ∧ _x76 = 1 + _x73 | |
l1 | 15 | l10: | x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x1 = _x81 ∧ x2 = _x82 ∧ x3 = _x83 ∧ _x80 = _x83 ∧ _x78 = _x81 ∧ _x79 = _x82 | |
l13 | 16 | l14: | x1 = _x84 ∧ x2 = _x85 ∧ x3 = _x86 ∧ x1 = _x87 ∧ x2 = _x88 ∧ x3 = _x89 ∧ _x86 = _x89 ∧ _x84 = _x87 ∧ _x85 = _x88 | |
l14 | 17 | l12: | x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x1 = _x93 ∧ x2 = _x94 ∧ x3 = _x95 ∧ _x92 = _x95 ∧ _x90 = _x93 ∧ _x91 = _x94 | |
l15 | 18 | l13: | x1 = _x96 ∧ x2 = _x97 ∧ x3 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ _x98 = _x101 ∧ _x96 = _x99 ∧ _x97 = _x100 | |
l15 | 19 | l14: | x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x1 = _x105 ∧ x2 = _x106 ∧ x3 = _x107 ∧ _x104 = _x107 ∧ _x102 = _x105 ∧ _x103 = _x106 | |
l16 | 20 | l15: | x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x1 = _x111 ∧ x2 = _x112 ∧ x3 = _x113 ∧ _x110 = _x113 ∧ _x108 = _x111 ∧ _x109 = _x112 | |
l2 | 21 | l16: | x1 = _x114 ∧ x2 = _x115 ∧ x3 = _x116 ∧ x1 = _x117 ∧ x2 = _x118 ∧ x3 = _x119 ∧ _x116 = _x119 ∧ _x114 = _x117 ∧ _x115 = _x118 | |
l2 | 22 | l12: | x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x1 = _x123 ∧ x2 = _x124 ∧ x3 = _x125 ∧ _x122 = _x125 ∧ _x120 = _x123 ∧ _x121 = _x124 | |
l17 | 23 | l6: | x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x1 = _x129 ∧ x2 = _x130 ∧ x3 = _x131 ∧ _x132 = 0 ∧ _x130 = 0 ∧ _x126 = _x129 ∧ _x128 = _x131 | |
l18 | 24 | l17: | x1 = _x133 ∧ x2 = _x134 ∧ x3 = _x135 ∧ x1 = _x136 ∧ x2 = _x137 ∧ x3 = _x138 ∧ _x135 = _x138 ∧ _x133 = _x136 ∧ _x134 = _x137 |
l5 | l5 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l7 | l7 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l1 | l1 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l3 | l3 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l13 | l13 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l18 | l18 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l17 | l17 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l2 | l2 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l9 | l9 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l14 | l14 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l4 | l4 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l6 | l6 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l10 | l10 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l8 | l8 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l15 | l15 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l16 | l16 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l0 | l0 | : | x1 = x1 ∧ x2 = x2 ∧ x3 = x3 |
l12 | l12 | : | 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 |
: | −1 − x2 |
: | − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
We remove transitions
, , , , , , , , using the following ranking functions, which are bounded by −6.: | −6 |
: | −7 |
: | −5 |
: | 0 |
: | −4 |
: | −2 |
: | −3 |
: | −1 |
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 |
: | − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
: | −1 − x2 |
We remove transitions
, , , , , , , , using the following ranking functions, which are bounded by 0.: | 0 |
: | −1 |
: | 1 |
: | 6 |
: | 2 |
: | 4 |
: | 3 |
: | 5 |
There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.