⟨a, b | aababbabbba=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:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. babbabbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	b³c ⇒ a²dbcbab	[21]
7.	bcbabd ⇒ ab³	[16]
8.	b³ac ⇒ a²dbc(ba)²	[22]
9.	bc(ba)²d ⇒ ab³a	[18]
10.	b³a²c ⇒ a²dbcbaba²	[24]
11.	bcbaba²d ⇒ ab³a²	[23]
12.	bcbab²a ⇒ c(bab)²	[26]
13.	(bab)²a² ⇒ dbcbab²c	[28]
14.	b(ab²)²d ⇒ adb²ab³	[11]
15.	ba(b²a)²d ⇒ adb²ab³a	[12]
16.	b²ab³a² ⇒ a²db²cbab²	[33]
17.	b(ab²)²a² ⇒ db²cbab²c	[31]
18.	bab²ab³ ⇒ d	[3]

# ab:aababbabbba=1 reversed:cda/b aaa=c,babbabbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bbbc=aadbcbab bcbabd=abbb bbbac=aadbcbaba bcbabad=abbba bbbaac=aadbcbabaa bcbabaad=abbbaa bcbabba=cbabbab babbabaa=dbcbabbc babbabbd=adbbabbb babbabbad=adbbabbba bbabbbaa=aadbbcbabb babbabbaa=dbbcbabbc babbabbb=d

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

Σ	#	Presentation	Mapping
11	3144	⟨a, b \| aabbbabaaba=1⟩	φ(a) = b, φ(b) = a
11	3198	⟨a, b \| abaaabbbaba=1⟩	φ(a) = b, φ(b) = a
11	3292	⟨a, b \| abbabbbaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3144

⟨a, b | aabbbabaaba=1⟩

φ(a) = b, φ(b) = a

3198

⟨a, b | abaaabbbaba=1⟩

φ(a) = b, φ(b) = a

3292

⟨a, b | abbabbbaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3082 ⟨a, b \| aababbabbab=1⟩
Next:	#3085 ⟨a, b \| aababbbaaba=1⟩

#3083 ⟨a, b | aababbabbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances