#5663 ⟨a, b | aabaab=baaba⟩

Properties

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

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 = baaba
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aabaab=baaba a/cb baaba=c magic:0
aac=ca
bc=cab
baaba=c
aabaab=c

7 unique, 7 total

Σ	#	Presentation	Properties
7	258	⟨a, b \| aabb=baa⟩	Can Inf
8	525	⟨a, b \| aabab=baa⟩	Can Inf
9	1065	⟨a, b \| aabaab=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