#1810 ⟨a, b | abbababba=b⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbabb⟩
- Embedding: φ(a) = aab, φ(b) = a^-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 = abba
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abbababba=b ac/b abba=c morph:4/0
cbc=b
abba=c
abbc=bbca
cbb=bbc
abbb=bbcabc

3 unique, 5 total

Σ	#	Presentation	Properties	φ
8	315	⟨a, b \| aabbabba=1⟩	Grp Inf	2
8	471	⟨a, b \| abaaba=bb⟩	Can Inf
10	2303	⟨a, b \| abaaaba=bab⟩	Can Inf