#4188 ⟨a, b | aabbabbba=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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	b³a ⇒ a²b²ac	[6]
2.	b³c ⇒ cab²ac	[8]
3.	a²b²abc ⇒ ba²b²ac	[7]
4.	cab²abc ⇒ bcab²ac	[11]
5.	b²a²b²ac ⇒ c	[14]
6.	a(ab²)²c ⇒ c	[9]
7.	(a²b²a)²c ⇒ ba	[15]
8.	a(ab²ac)² ⇒ bc	[10]
9.	c(ab²)²c ⇒ b²cab²ac	[13]
10.	cab²a³b²ac ⇒ bc	[17]
11.	a²b²aba²b²ac ⇒ b²a	[16]
12.	cab²aba²b²ac ⇒ b²c	[12]

# ab:aabbabbba=ba ac/b bbbbba=c morph:6/2
bbba=aabbac
bbbc=cabbac
aabbabc=baabbac
cabbabc=bcabbac
bbaabbac=c
aabbabbc=c
aabbaaabbac=ba
aabbacabbac=bc
cabbabbc=bbcabbac
cabbaaabbac=bc
aabbabaabbac=bba
cabbabaabbac=bbc