⟨a, b | aaabbababa=1⟩

Up:

Monoids with two generators and one relation

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:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaa=c
2. bbabab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[16]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[20]
5.	a⁴ ⇒ c	[2]
6.	abcb ⇒ cb²a	[27]
7.	a³b² ⇒ bcbda³	[32]
8.	cb²ab ⇒ (ba)³a²	[24]
9.	db(ab)² ⇒ b²abda	[21]
10.	cab²ab ⇒ (ab)³a³	[25]
11.	d(ab)³ ⇒ ab²abda	[23]
12.	ca²b²ab ⇒ a(ab)³a³	[34]
13.	da(ab)³ ⇒ a²b²abda	[33]
14.	a²(ab)³ ⇒ cbcb²da	[36]
15.	b²(ab)² ⇒ d	[3]
16.	(cb²)² ⇒ b(ab)²ca³bda³	[38]
17.	cab²cb² ⇒ (ab)³ca³bda³	[39]
18.	ca²b²cb² ⇒ a(ab)³ca³bda³	[40]

# ab:aaabbababa=1 cda/b aaaa=c,bbabab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c abcb=cbba aaabb=bcbdaaa cbbab=bababaaa dbabab=bbabda cabbab=abababaaa dababab=abbabda caabbab=aabababaaa daababab=aabbabda aaababab=cbcbbda bbabab=d cbbcbb=bababcaaabdaaa cabbcbb=abababcaaabdaaa caabbcbb=aabababcaaabdaaa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
10	1516	⟨a, b \| abababbbba=1⟩	φ(a) = b, φ(b) = a
10	1524	⟨a, b \| ababbbbaab=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

1516

⟨a, b | abababbbba=1⟩

φ(a) = b, φ(b) = a

1524

⟨a, b | ababbbbaab=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#1372 ⟨a, b \| aaabbabaab=1⟩
Next:	#1374 ⟨a, b \| aaabbababb=1⟩

#1373 ⟨a, b | aaabbababa=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances