#4297 ⟨a, b | abababaab=ba⟩

Properties

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

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
2. d = ccac
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(d) = 1; deg(a) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abababaab=ba bc/d/a ab=c,ccac=d morph:2/0,4/0
cdb=bc
ddb=cccc
ddc=cd
cdcdcdc=bd
ab=c
acdcdc=d
ba=cd
ca=acd
da=adddddddd

9 unique, 9 total

Σ	#	Presentation	Properties
5	49	⟨a, b \| aab=ba⟩	Can Inf
6	110	⟨a, b \| abab=ba⟩	Can Inf
7	225	⟨a, b \| abaab=ba⟩	Can Inf
8	467	⟨a, b \| abaaab=ba⟩	Can Inf
9	969	⟨a, b \| abaaaab=ba⟩	Can Inf
9	984	⟨a, b \| ababaab=ba⟩	Can Inf
10	2021	⟨a, b \| abaaaaab=ba⟩	Can Inf
11	4227	⟨a, b \| abaaaaaab=ba⟩	Can Inf
11	4258	⟨a, b \| abaabaaab=ba⟩	Can Inf