〈a, b | aaaabaabba=1〉

Monoid presentation of length 10

Properties

Infinite non-Abelian group

Completion parameters

Reduction order: right-to-left cda/b
Auxiliary generator aaaaa=c
Auxiliary generator baabb=d

Inverses of generators

a^-1 = da⁴
b^-1 = ba²bc
c^-1 = d
d^-1 = c

Complete rewriting system

dc ⇒ 1
cd ⇒ 1
ca ⇒ ac
da ⇒ ad
a⁵ ⇒ c
b²c ⇒ a(a²b)²
ba²bd ⇒ a²db²
b²ac ⇒ a(a²b)²a
ba²bad ⇒ a²db²a
bcba² ⇒ cba²b
b²a²c ⇒ a³(ba²)²
(ba²)²d ⇒ a²db²a²
b²a³ ⇒ a³dbcb
ba²ba³ ⇒ d(bc)²
ba²b² ⇒ d

Other isomorphic instances

1 total

Length:	Presentation:
10	〈a, b \| aaabaabbaa=1〉

Other anti-isomorphic instances

3 total

Length:	Presentation:
10	〈a, b \| aaaabbaaba=1〉
10	〈a, b \| aaabbaabaa=1〉
10	〈a, b \| abbabbbbba=1〉