#4308 ⟨a, b | ababbaaab=ba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

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

#	Rule	Proof
1.	bc ⇒ cac³a²b	[10]
2.	abac ⇒ ba	[3]
3.	b²ac ⇒ cac²baca²b	[11]
4.	b²a²c ⇒ cacbaca²b	[12]
5.	b²a³c ⇒ cba³b	[4]
6.	b²a³b ⇒ c	[2]
7.	b³a ⇒ cac³	[8]
8.	b(ba)² ⇒ cac²	[6]
9.	b²a²ba ⇒ cac	[5]
10.	(b²a)² ⇒ cac²bac	[9]
11.	b²a²b²a ⇒ cacbac	[7]

# ab:ababbaaab=ba reversed:ac/b bbaaab=c morph:6/0
bc=cacccaab
abac=ba
bbac=caccbacaab
bbaac=cacbacaab
bbaaac=cbaaab
bbaaab=c
bbba=caccc
bbaba=cacc
bbaaba=cac
bbabba=caccbac
bbaabba=cacbac