#4822 ⟨a, b | abababab=baa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabba^-1b^-1⟩
- Embedding: φ(a) = b^-1, φ(b) = ab

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 = ba
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.

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	ca ⇒ ac³b	[4]

# ab:abababab=baa bc/a ba=c morph:2/0
ba=c
ca=acccb

5 unique, 5 total

Σ	#	Presentation	Properties
8	426	⟨a, b \| aaaabb=ba⟩	Can Inf
9	888	⟨a, b \| aaaabab=ba⟩	Can Inf
10	1856	⟨a, b \| aaaabaab=ba⟩	Can Inf
10	2737	⟨a, b \| baaaa=abaab⟩	Can Inf
11	3901	⟨a, b \| aaaabaaab=ba⟩	Can Inf

4 unique, 4 total

Σ	#	Presentation	Properties
8	497	⟨a, b \| aaaab=bba⟩	Can Inf
9	1159	⟨a, b \| aaaab=baba⟩	Can Inf
11	4125	⟨a, b \| aabababab=ba⟩	Can Inf
11	5825	⟨a, b \| abaaab=baaaa⟩	Can Inf