#2303 ⟨a, b | abaaaba=bab⟩

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) = ab, φ(b) = b^-1a^-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 = bab
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.

# ab:abaaaba=bab ac/b bab=c magic:0
cb=abaaac
cab=bac
caaba=abaac
caaaba=bc
bab=c
abaaaba=c

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	1810	⟨a, b \| abbababba=b⟩	Can Inf