#927 ⟨a, b | aabaaab=ba⟩

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Properties
Rewriting system
Other submonoids of same group

Properties

Presentation has sum-of-sides 9
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨a, b | aabba^-1b^-1⟩

Embedding: φ(a) = a, φ(b) = a^-1ba^-1a^-1

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Auxiliary generators:
1. c = aab
Reduction order:
- Right-to-left 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.

#	Rule	Proof
1.	a(ac)² ⇒ ca	[4]
2.	a²b ⇒ c	[2]
3.	ba ⇒ cac	[3]
4.	bc ⇒ (ca)²b	[5]

# ab:aabaaab=ba reversed:ac/b aab=c morph:3/1
aacac=ca
aab=c
ba=cac
bc=cacab

Other submonoids of same group

17 unique, 17 total

Σ	#	Presentation	Description	Related
6	107	⟨a, b \| aabb=ba⟩	Infinite cancellative non-commutative monoid
6	121	⟨a, b \| baa=abb⟩	Infinite cancellative non-commutative monoid
7	217	⟨a, b \| aabab=ba⟩	Infinite cancellative non-commutative monoid
7	262	⟨a, b \| abab=baa⟩	Infinite cancellative non-commutative monoid
8	445	⟨a, b \| aabaab=ba⟩	Infinite cancellative non-commutative monoid
8	541	⟨a, b \| abaab=baa⟩	Infinite cancellative non-commutative monoid
9	976	⟨a, b \| abaabab=ba⟩	Infinite cancellative non-commutative monoid
9	1107	⟨a, b \| abaaab=baa⟩	Infinite cancellative non-commutative monoid
9	1249	⟨a, b \| abaab=baba⟩	Infinite cancellative non-commutative monoid
10	1937	⟨a, b \| aabaaaab=ba⟩	Infinite cancellative non-commutative monoid
10	2295	⟨a, b \| abaaaab=baa⟩	Infinite cancellative non-commutative monoid
11	4063	⟨a, b \| aabaaaaab=ba⟩	Infinite cancellative non-commutative monoid
11	4242	⟨a, b \| abaaabaab=ba⟩	Infinite cancellative non-commutative monoid
11	4289	⟨a, b \| ababaabab=ba⟩	Infinite cancellative non-commutative monoid
11	4757	⟨a, b \| abaaaaab=baa⟩	Infinite cancellative non-commutative monoid
11	5349	⟨a, b \| ababaab=baba⟩	Infinite cancellative non-commutative monoid
11	5827	⟨a, b \| abaaab=baaba⟩	Infinite cancellative non-commutative monoid