⟨a, b | aababbababa=1⟩

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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. aaa=c
2. babbabab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	cbab² ⇒ (ba)³a	[15]
7.	db(ab)² ⇒ bab²da	[12]
8.	abcbab ⇒ b(ab)²c	[19]
9.	cabab² ⇒ (ab)³a²	[16]
10.	d(ab)³ ⇒ abab²da	[14]
11.	a²bab² ⇒ bcbabda²	[27]
12.	a(ab)³ ⇒ (cb)²abd	[23]
13.	ab²(ab)² ⇒ b(ab)²cbda	[18]
14.	b²(ab)²cb ⇒ da²	[25]
15.	abcb²(ab)² ⇒ b(ab)²c²babd	[28]

# ab:aababbababa=1 cda/b aaa=c,babbabab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c cbabb=bababaa dbabab=babbda abcbab=bababc cababb=abababaa dababab=ababbda aababb=bcbabdaa aababab=cbcbabd abbabab=bababcbda bbababcb=daa abcbbabab=bababccbabd

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

Σ	#	Presentation	Mapping
11	3248	⟨a, b \| abababbbaba=1⟩	φ(a) = b, φ(b) = a
11	3262	⟨a, b \| ababbbabaab=1⟩	φ(a) = b, φ(b) = a
11	3287	⟨a, b \| abbababaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3248

⟨a, b | abababbbaba=1⟩

φ(a) = b, φ(b) = a

3262

⟨a, b | ababbbabaab=1⟩

φ(a) = b, φ(b) = a

3287

⟨a, b | abbababaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3079 ⟨a, b \| aababbabaab=1⟩
Next:	#3082 ⟨a, b \| aababbabbab=1⟩

#3080 ⟨a, b | aababbababa=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances