#2325 ⟨a, b | ababaab=baa⟩

Properties

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

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:ababaab=baa bc/a baa=c magic:0
cacbb=abc
cbacb=bac
abacb=c
baa=c
caa=abacc
cbabac=bacacb
ababac=cacb

5 unique, 5 total

Σ	#	Presentation	Properties
8	459	⟨a, b \| aabbab=ba⟩	Can Inf
8	543	⟨a, b \| abaab=bba⟩	Can Inf
10	1960	⟨a, b \| aababaab=ba⟩	Can Inf
10	2028	⟨a, b \| abaaabab=ba⟩	Can Inf
10	2573	⟨a, b \| abaaab=baba⟩	Can Inf