#4128 ⟨a, b | aabababba=ab⟩

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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(c) = deg(a) = 0, c < a; deg(b) = 1
Auxiliary generators:
1. bababba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ca(ca²)²c² ⇒ c²(aca)²ca	[12]
2.	(a²c)³c ⇒ (a(ca)²)²	[10]
3.	c(aca)³c² ⇒ c³(a²c)²aca	[16]
4.	c(aca)³ca ⇒ c²	[14]
5.	(a²c)³ac² ⇒ ac(ca²)²(ca)²	[11]
6.	(a²c)³aca ⇒ ac	[8]
7.	b(a²c)²c ⇒ c(aca)²ca	[7]
8.	b(a²c)²ac² ⇒ c(ca²)²(ca)²	[15]
9.	b(a²c)²aca ⇒ c	[13]
10.	cb ⇒ cac	[6]
11.	ab ⇒ a²c	[3]

# ab:aabababba=ab ca/b bababba=c morph:7/0
cacaacaacc=ccacaacaca
aacaacaacc=acacaacaca
cacaacaacacc=cccaacaacaca
cacaacaacaca=cc
aacaacaacacc=accaacaacaca
aacaacaacaca=ac
baacaacc=cacaacaca
baacaacacc=ccaacaacaca
baacaacaca=c
cb=cac
ab=aac