⟨a, b | aabbbaaba=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. bbbaab=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.	aba²b ⇒ (cb)²d	[24]
7.	a²bcb ⇒ ba²bc	[20]
8.	cb³ ⇒ b²a²ba	[15]
9.	db²a²b ⇒ b³da²	[12]
10.	ab³ ⇒ bcb²da	[33]
11.	ab²a²b ⇒ cbcb²d	[27]
12.	(abc)²b ⇒ (cb)²da²bc	[34]
13.	b³a²b ⇒ d	[3]
14.	db²cabcb ⇒ b³abc	[23]
15.	ab²cabcb ⇒ cbcb²da²bc	[35]
16.	(ab)²cb² ⇒ (cb)²db²a²	[36]
17.	b³cabcb ⇒ da²bc	[22]
18.	db²abcb² ⇒ b³da²b²a²	[37]
19.	ab²abcb² ⇒ cbcb²db²a²	[39]
20.	b³abcb² ⇒ db²a²	[30]

# ab:aabbbaaba=1 cda/b aaa=c,bbbaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abaab=cbcbd aabcb=baabc cbbb=bbaaba dbbaab=bbbdaa abbb=bcbbda abbaab=cbcbbd abcabcb=cbcbdaabc bbbaab=d dbbcabcb=bbbabc abbcabcb=cbcbbdaabc ababcbb=cbcbdbbaa bbbcabcb=daabc dbbabcbb=bbbdaabbaa abbabcbb=cbcbbdbbaa bbbabcbb=dbbaa

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

Σ	#	Presentation	Mapping
9	702	⟨a, b \| abaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

702

⟨a, b | abaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#685 ⟨a, b \| aabbabbba=1⟩
Next:	#688 ⟨a, b \| aabbbabab=1⟩

#687 ⟨a, b | aabbbaaba=1⟩

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Properties

Rewriting system

Isomorphic instances