#2489 ⟨a, b | aabaab=baba⟩

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) = ab, φ(b) = b^-1a^-1a^-1

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

# ab:aabaab=baba a/cb baba=c magic:0
bac=cba
aabc=caab
aabaac=caba
baba=c
aabaab=c
babc=cabaab

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	2309	⟨a, b \| abaabab=baa⟩	Can Inf