#2586 ⟨a, b | abaaba=baab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabb⟩
- Embedding: φ(a) = aab, φ(b) = b^-1a^-1a^-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 = 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:abaaba=baab a/cb baab=c magic:0
aca=c
acc=cca
bc=caabaa
bac=caaba
baac=caab
baab=c

8 unique, 28 total

Σ	#	Presentation	Properties	φ
6	60	⟨a, b \| aaabba=1⟩	Grp Inf	19
6	93	⟨a, b \| abbba=b⟩	Can Inf
6	96	⟨a, b \| aaaa=bb⟩	Can Inf
6	113	⟨a, b \| abba=bb⟩	Can Inf
6	122	⟨a, b \| bab=aaa⟩	Can Inf
8	404	⟨a, b \| abababa=b⟩	Can Inf	1
8	549	⟨a, b \| ababa=bab⟩	Can Inf
10	2355	⟨a, b \| abbabba=bab⟩	Can Inf