#4780 ⟨a, b | abaaabba=bab⟩

Contents

Properties
Rewriting system
Other submonoids of same group

Properties

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

Rewriting system

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

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	aca²cbc ⇒ c²b	[6]
3.	ca²cba ⇒ bc	[4]
4.	c²b² ⇒ a(ca²c)²bc	[9]
5.	bcb ⇒ ca²cbc	[5]
6.	c²bca²cbc ⇒ a(ca²c)²bc²b	[10]
7.	bc²a²cbc ⇒ ca²cbc²b	[7]
8.	c²ba²cba ⇒ aca²cb²c	[8]

# ab:abaaabba=bab reversed:ca/b ab=c morph:2/0
ab=c
acaacbc=ccb
caacba=bc
ccbb=acaaccaacbc
bcb=caacbc
ccbcaacbc=acaaccaacbccb
bccaacbc=caacbccb
ccbaacba=acaacbbc

Other submonoids of same group

1 unique, 1 total

Σ	#	Presentation	Properties
11	4808	⟨a, b \| abaabbba=bab⟩	Can Inf