#19818 ⟨a, b | aaa=a, abba=bab⟩

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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

Auxiliary generators:
1. c = ab
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.	a³ ⇒ a	[1]
2.	a²c ⇒ c	[6]
3.	ab ⇒ c	[3]
4.	c²a² ⇒ c²	[9]
5.	cba ⇒ ac²	[8]
6.	bc ⇒ ac²	[21]
7.	c²aca² ⇒ c²ac	[18]
8.	cac² ⇒ c(ca)²	[15]
9.	ac²ac ⇒ c(ca)²	[22]
10.	c²b ⇒ c²ac	[14]
11.	bac² ⇒ c²ac	[12]
12.	c²(ac)² ⇒ c⁴a	[20]
13.	ac⁴ ⇒ c³ac	[17]
14.	ac³ac ⇒ c⁴	[16]
15.	c²acb ⇒ c⁴a	[23]

# ab:aaa=a,abba=bab a/cb ab=c morph:2/0
aaa=a
aac=c
ab=c
ccaa=cc
cba=acc
bc=acc
ccacaa=ccac
cacc=ccaca
accac=ccaca
ccb=ccac
bacc=ccac
ccacac=cccca
acccc=cccac
acccac=cccc
ccacb=cccca