#1868 ⟨a, b | aaaabbaa=ba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a⁴b²a ⋅ a = ba and b ⋅ a = ba, however a⁴b²a ≠ b
Enveloping group: ⟨a, b | aaaabab^-1b^-1⟩

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

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

#	Rule	Proof
1.	ba ⇒ ca²	[3]
2.	a⁴caca² ⇒ ca	[7]
3.	bc ⇒ cac	[5]
4.	a⁴b² ⇒ c	[2]
5.	a⁴cac²a ⇒ ca³caca²	[9]
6.	a³(ac)³ ⇒ c²	[6]
7.	ca³b² ⇒ a⁴cac²	[8]
8.	a⁴cac³ ⇒ ca²(ac)³	[10]
9.	(a⁴ca)²c² ⇒ ca²b²	[11]

# ab:aaaabbaa=ba a/cb aaaabb=c morph:6/0
ba=caa
aaaacacaa=ca
bc=cac
aaaabb=c
aaaacacca=caaacacaa
aaaacacac=cc
caaabb=aaaacacc
aaaacaccc=caaacacac
aaaacaaaaacacc=caabb