#3882 ⟨a, b | aaaaabbaa=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) = 0; deg(c) = deg(b) = 1, c < b
Auxiliary generators:
1. aaaaabb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ba ⇒ ca²	[3]
2.	a⁵caca² ⇒ ca	[7]
3.	bc ⇒ cac	[5]
4.	a⁵b² ⇒ c	[2]
5.	a⁵cac²a ⇒ ca⁴caca²	[9]
6.	a⁴(ac)³ ⇒ c²	[6]
7.	ca⁴b² ⇒ a⁵cac²	[8]
8.	a⁵cac³ ⇒ ca³(ac)³	[10]
9.	(a⁵ca)²c² ⇒ ca³b²	[11]

# ab:aaaaabbaa=ba a/cb aaaaabb=c morph:7/0
ba=caa
aaaaacacaa=ca
bc=cac
aaaaabb=c
aaaaacacca=caaaacacaa
aaaaacacac=cc
caaaabb=aaaaacacc
aaaaacaccc=caaaacacac
aaaaacaaaaaacacc=caaabb