#2597 ⟨a, b | ababab=baba⟩

Properties

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

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 = ab
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.
Morphocompletion: how the auxiliary generators were found.

# ab:ababab=baba bc/a ab=c morph:2/0
cccb=bcc
ab=c
bca=ccc
cca=accc

1 unique, 1 total

Σ	#	Presentation	Properties
7	243	⟨a, b \| aaab=baa⟩	Can Inf