〈a, b | aaaa=1, aabbb=ba〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 148 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁹ ⇒ b
bab⁸ ⇒ ba
a²b ⇒ bab⁶
ba² ⇒ b²ab⁵
(ba)² ⇒ b⁷ab
bab²a ⇒ b⁵ab⁴
bab³a ⇒ b⁸ab²
bab⁴a ⇒ b⁴ab⁷
bab⁵a ⇒ b⁶ab⁶
bab⁶a ⇒ b³
bab⁷a ⇒ b³ab³
a⁴ ⇒ 1

Idempotents

3 elements

1
b⁸
(ab⁶)²

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 4 total

Length:	Presentation:	Description:	Related:
11	〈a, b \| aaab=bba, bbbb=1〉	Finite non-commutative monoid with 148 elements	1 isomorphic
11	〈a, b \| babb=aaa, bbbb=1〉	Finite non-commutative monoid with 148 elements
11	〈a, b \| aaaa=a, abbba=b〉	Finite non-commutative monoid with 148 elements