#4098 ⟨a, b | aabaabbaa=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. aabaabb=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.	bc ⇒ cac	[5]
3.	(a²ca)²ca² ⇒ ca	[6]
4.	a²ca³b² ⇒ c	[4]
5.	(a²ca)²c²a ⇒ caca³caca²	[9]
6.	a²ca²(ac)³ ⇒ c²	[7]
7.	caca³b² ⇒ (a²ca)²c²	[8]
8.	(a²ca)²c³ ⇒ caca²(ac)³	[10]
9.	(a²ca³)²cac² ⇒ ca²b²	[11]
10.	(a²ca)⁴c² ⇒ c²a³b²	[12]

# ab:aabaabbaa=ba a/cb aabaabb=c morph:7/0
ba=caa
bc=cac
aacaaacacaa=ca
aacaaabb=c
aacaaacacca=cacaaacacaa
aacaaacacac=cc
cacaaabb=aacaaacacc
aacaaacaccc=cacaaacacac
aacaaaaacaaacacc=caabb
aacaaacaaacaaacacc=ccaaabb