#4553 ⟨a, b | aaabbaba=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. aabbab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³c(ca)² ⇒ ca²	[16]
2.	a²(ac²)² ⇒ cac	[7]
3.	a³c²bc ⇒ c²	[12]
4.	a³c²acbc ⇒ cabc	[13]
5.	ba² ⇒ aca	[3]
6.	bac ⇒ ac²	[6]
7.	bc² ⇒ aca²c²bc	[14]
8.	bca² ⇒ aca²c(ca)²	[9]
9.	bcac ⇒ aca(ac²)²	[10]
10.	a³c²b²c ⇒ cbc	[20]
11.	a³c²acb²c ⇒ cab²c	[18]
12.	babc ⇒ acbc	[8]
13.	(bc)² ⇒ aca²c²b²c	[21]
14.	bcabc ⇒ aca²c²acbc	[15]
15.	a²b²ab ⇒ c	[2]
16.	acab²ab ⇒ bc	[5]
17.	ac²ab²ab ⇒ b²c	[11]
18.	b³c ⇒ ac³ab²ab	[19]
19.	bab²c ⇒ acb²c	[17]
20.	bcb²c ⇒ aca²c²ac³ab²ab	[23]
21.	bcab²c ⇒ aca²c²acb²c	[22]

# ab:aaabbaba=baa reversed:ac/b aabbab=c morph:6/2
aaaccaca=caa
aaaccacc=cac
aaaccbc=cc
aaaccacbc=cabc
baa=aca
bac=acc
bcc=acaaccbc
bcaa=acaaccaca
bcac=acaaccacc
aaaccbbc=cbc
aaaccacbbc=cabbc
babc=acbc
bcbc=acaaccbbc
bcabc=acaaccacbc
aabbab=c
acabbab=bc
accabbab=bbc
bbbc=acccabbab
babbc=acbbc
bcbbc=acaaccacccabbab
bcabbc=acaaccacbbc