#3929 ⟨a, b | aaaabbaaa=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:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. aabb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a⁴c²a ⇒ ca²ca³	[8]
2.	a⁴c³ ⇒ c(a²c)²	[10]
3.	(a⁴c)²a³ ⇒ ca	[4]
4.	(a⁴c)²aca ⇒ ca²(aca³)²	[9]
5.	(a⁴c)²a²c ⇒ c²	[6]
6.	(a⁴c)²ac² ⇒ c(a³ca)²ac	[11]
7.	ba ⇒ a²ca³	[3]
8.	bc ⇒ (a²c)²	[5]
9.	a²b² ⇒ c	[2]
10.	cab² ⇒ (a⁴c)²ac	[7]

# ab:aaaabbaaa=ba reversed:ac/b aabb=c morph:4/0
aaaacca=caacaaa
aaaaccc=caacaac
aaaacaaaacaaa=ca
aaaacaaaacaca=caaacaaaacaaa
aaaacaaaacaac=cc
aaaacaaaacacc=caaacaaaacaac
ba=aacaaa
bc=aacaac
aabb=c
cabb=aaaacaaaacac