Rooster and Dog compatibility
Rooster (You, 酉) and Dog (Xu, 戌): a harm (Hai, 害).
These are fixed relations among the twelve branches of the Chinese calendar, set out in the classic San Ming Tong Hui (三命通会), written in 1578, quoted below. They describe the signs, not two people: no classic gives a method for matching two people by their signs, so there is no score here.
What the book says
Harm (Hai, 害)
Why it is called harm: one befriends the other’s opponent. The Rooster clashes with the Rabbit, and the Dog is in a six harmony with the Rabbit.
The six harms are where the twelve branches override and fight one another.
六害者，十二支凌战之辰也。
Rooster and Dog harm each other because the Dog’s dead Fire harms the Rooster, Metal at its height. This is the harm of envy. So a Rooster person who meets a Dog has misfortune, and a Dog person who meets a Rooster comes to no harm.
酉戌相害者，谓戌以死火害酉旺金，此嫉妒相害，故酉人见戌则凶，戌人见酉无灾
Six: the six kinds of kin. Harm: loss. Having it means loss and friction among one’s closest family; hence the six harms.
六，六亲；害，损也。犯之主六亲上有损克，故谓六害。
San Ming Tong Hui, volume 2: On the six harms (论六害) · source text
Their elements
The Rooster is Metal and the Dog is Earth: Earth feeds Metal.
How much it counts
A sign is one character of the eight in a BaZi chart, the year’s branch. The book reads these relations between the pillars of one chart, and tells the reader to look at the whole chart’s elements first:
Clash and break, three harmony and six harmony: where a chart has them, ask next how its five elements get on. Misfortune may give rise to blessing, and blessing to misfortune.
相冲相破，三合六合，命中有之，即求五行相得何如。或祸中生福，福中生祸
San Ming Tong Hui, volume 3: On the symbolic stars as a whole (总论诸神煞) · source text
Birth years, and 2027
- Rooster: 1933, 1945, 1957, 1969, 1981, 1993, 2005, 2017. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Rooster has no clash with the year.
- Dog: 1934, 1946, 1958, 1970, 1982, 1994, 2006, 2018. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Dog is punished by the year (Xing Tai Sui, 刑太岁) and breaks with the year (Po Tai Sui, 破太岁).
A sign’s year is usually counted from Chinese New Year, between late January and mid-February; BaZi counts it from the Start of Spring, about 4 February. Born in January or early February? You may be the sign before: the sign pages check your date.
Two real people?
Each person’s chart has eight characters, and the same relations run between all of them, not only the two signs. The two-chart page sets both charts side by side, branch by branch, and gives what each chart says about marriage on its own. No score there either.
Rooster with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Monkey · Rooster · Pig.
Dog with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Monkey · Dog · Pig.