#1065 ⟨a, b | aabaab=baa⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabba^-1a^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = a^-1a^-1b

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:aabaab=baa bc/a baa=c magic:0
ccb=bc
cacb=bac
aacb=c
baa=c
caa=aacc

7 unique, 7 total

Σ	#	Presentation	Properties
7	258	⟨a, b \| aabb=baa⟩	Can Inf
8	525	⟨a, b \| aabab=baa⟩	Can Inf
9	1217	⟨a, b \| aabab=baba⟩	Can Inf
10	2211	⟨a, b \| aabaaab=baa⟩	Can Inf
11	4593	⟨a, b \| aabaaaab=baa⟩	Can Inf
11	5317	⟨a, b \| abaabab=baba⟩	Can Inf
11	5663	⟨a, b \| aabaab=baaba⟩	Can Inf