#2612 ⟨a, b | ababba=bbab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababbab^-1⟩
- Embedding: φ(a) = babab^-1, φ(b) = ba^-1b^-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 = bbab
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:ababba=bbab a/cb bbab=c magic:0
abac=cb
bbc=cabba
bbac=cbab
bbab=c
ababba=c

4 unique, 9 total

Σ	#	Presentation	Properties	φ
8	382	⟨a, b \| aababba=b⟩	Can Inf
8	592	⟨a, b \| babb=abaa⟩	Can Inf
10	1408	⟨a, b \| aabaababba=1⟩	Grp Inf	5
10	1678	⟨a, b \| aabaababa=b⟩	Can Inf