〈a, b | aaabaaabba=1〉

Monoid presentation of length 10

Properties

Infinite non-Abelian group

Completion parameters

Reduction order: left-to-right cda/b
Auxiliary generator aaaa=c
Auxiliary generator baaabb=d

Inverses of generators

a^-1 = da³
b^-1 = bcba³
c^-1 = d
d^-1 = c

Complete rewriting system

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a⁴ ⇒ c
cba³b ⇒ bcba³
dbcb ⇒ ba³bda
abcb ⇒ cb²a
aba³b ⇒ b²c
a³b² ⇒ bcbda³
b²cb ⇒ da
cba²b² ⇒ (bc)²a²bd
cbca²b² ⇒ (bc)²a³bda³
aba²b² ⇒ b²ca³bd
abca²b² ⇒ b²c²bda³

Other isomorphic instances

3 total

Length:	Presentation:
10	〈a, b \| aaabbaaaab=1〉
10	〈a, b \| aabaaabbaa=1〉
10	〈a, b \| aabbaaaaba=1〉

Other anti-isomorphic instances

2 total

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