〈a, b | babb=aaa, bbbb=1〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 148 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁹ ⇒ a
a⁸ba ⇒ ba
b²a ⇒ a⁵ba²
(ba)² ⇒ aba⁷
ba²ba ⇒ a⁴ba⁵
ba³ba ⇒ a²ba⁸
ba⁴ba ⇒ a⁷ba⁴
ba⁵ba ⇒ a⁶ba⁶
ba⁶ba ⇒ a³
ba⁷ba ⇒ a³ba³
ab² ⇒ a⁶ba
b⁴ ⇒ 1

Idempotents

3 elements

1
a⁸
(a⁶b)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 \| aaaa=a, abbba=b〉	Finite non-commutative monoid with 148 elements
11	〈a, b \| aaaa=1, aabbb=ba〉	Finite non-commutative monoid with 148 elements