#5315 ⟨a, b | abaabab=baaa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababba^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a^-1, φ(b) = aab

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 = baa
Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = deg(c) = 1, a < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaabab=baaa b/ac baa=c morph:3/0
baa=c
acbab=ca
ccbab=baca
caaa=acbac

3 unique, 3 total

Σ	#	Presentation	Properties
9	911	⟨a, b \| aaababb=ba⟩	Can Inf
9	1221	⟨a, b \| aabab=bbba⟩	Can Inf
11	3973	⟨a, b \| aaabaabab=ba⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
10	2243	⟨a, b \| aababab=bba⟩	Can Inf