#4443 ⟨a, b | aaaababa=baa⟩

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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. aaaabab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a⁴c²a ⇒ ca²	[17]
2.	a⁴c³ ⇒ cac	[7]
3.	a⁴cbc ⇒ c²	[11]
4.	a⁴c²bc ⇒ cabc	[12]
5.	ba² ⇒ ca	[3]
6.	bac ⇒ c²	[6]
7.	bc² ⇒ ca³cbc	[13]
8.	bca² ⇒ ca³c²a	[8]
9.	bcac ⇒ ca³c³	[9]
10.	a⁴bab ⇒ c	[2]
11.	ca³bab ⇒ bc	[5]
12.	b²c ⇒ ca³c²a(ab)²	[16]
13.	babc ⇒ cbc	[10]
14.	(bc)² ⇒ c(a³c²)²a(ab)²	[15]
15.	bcabc ⇒ ca³c²bc	[14]

# ab:aaaababa=baa reversed:ac/b aaaabab=c morph:7/0
aaaacca=caa
aaaaccc=cac
aaaacbc=cc
aaaaccbc=cabc
baa=ca
bac=cc
bcc=caaacbc
bcaa=caaacca
bcac=caaaccc
aaaabab=c
caaabab=bc
bbc=caaaccaabab
babc=cbc
bcbc=caaaccaaaccaabab
bcabc=caaaccbc