In three phases of a helpmate twomover the roles of three thematic white pieces are cyclically changed: each one mates once and is captured twice. A true cycle occurs when each piece is once captured on the first, once on the second black move, and once survives and eventually mates. Further, for a pure cycle the first white move must be an active sacrifice of a thematic piece.
See also: Cyclic Zilahi.
Gurov, Valery
Probleemblad, 2001
1st Prize
1.Qxd2
b6
2.Sxa5
Sb5#
1.Qxa5
f5
2.Sxd4
Bf4#
1.Qxd4
a7
2.Sxd2
Ra6#
Feather, Christopher John
Schach-Report, 1993
3rd Prize
a) 1.exf3
Rxd4+
2.Kxd4
Qxd3#
b) 1.Bxf4
Qxe4+
2.Kxe4
Sh4#
c) 1.exf5
Sxe5
2.Kxe5
Rxf5#
Semenenko, Oleksandr
International Chess Composition Day, 2015
1st Prize
1.exd2
e4
2.Kc1
e5
3.d1=Q
e6
4.Qxc2
e7
5.Qb2
e8=Q
6.c2
Qxe1#
1.cxd2
c4
2.Sc2
c5
3.Sb4
c6
4.Sa6
c7
5.Sb8
cxb8=Q
6.dxe2
Qb1#
1.dxc2
d4
2.Kxe2
d5
3.Kf3
d6
4.Kf4
d7
5.Kg5
d8=Q+
6.Kh6
Qh4#