#5142 ⟨a, b | aabaaba=baab⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabbab^-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 = baab
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:aabaaba=baab a/cb baab=c magic:0
aaca=c
aacc=caca
bc=caaba
baac=caab
baab=c

5 unique, 10 total

Σ	#	Presentation	Properties	φ
7	222	⟨a, b \| aabba=bb⟩	Can Inf
8	406	⟨a, b \| ababbba=b⟩	Can Inf
9	631	⟨a, b \| aaabaabba=1⟩	Grp Inf	5
9	1074	⟨a, b \| aababa=bab⟩	Can Inf
11	3737	⟨a, b \| abaabababa=b⟩	Can Inf