#5291 ⟨a, b | abaaaab=baba⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabab^-1b^-1a^-1b⟩
- Embedding: φ(a) = a, φ(b) = a^-1b^-1a^-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 = baba
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:abaaaab=baba ac/b baba=c magic:0
cba=bac
caba=abaaaac
caaab=bc
caaaab=abaaac
baba=c
abaaaab=c

3 unique, 3 total

Σ	#	Presentation	Properties
9	1109	⟨a, b \| abaaab=bba⟩	Can Inf
10	1994	⟨a, b \| aabbabab=ba⟩	Can Inf
10	2044	⟨a, b \| abaabbab=ba⟩	Can Inf