#2309 ⟨a, b | abaabab=baa⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababba^-1b^-1⟩
- Embedding: φ(a) = b^-1, φ(b) = bba

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = baa
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# ab:abaabab=baa bc/a baa=c magic:0
ccbab=bac
acbab=c
baa=c
caa=acbac

4 unique, 4 total

Σ	#	Presentation	Properties
8	453	⟨a, b \| aababb=ba⟩	Can Inf
8	527	⟨a, b \| aabab=bba⟩	Can Inf
10	1952	⟨a, b \| aabaabab=ba⟩	Can Inf
10	2489	⟨a, b \| aabaab=baba⟩	Can Inf