⟨a, b | aaabbbaaaba=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. aaaa=c
2. bbbaaab=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.	aba³b ⇒ (cb)²d	[36]
7.	a³bcb ⇒ ba³bc	[31]
8.	cb³ ⇒ b²a³ba	[24]
9.	db²a³b ⇒ b³da³	[21]
10.	ab³ ⇒ bcb²da	[47]
11.	ab²a³b ⇒ cbcb²d	[39]
12.	abca²bcb ⇒ (cb)²da³bc	[49]
13.	b³a³b ⇒ d	[3]
14.	db²ca²bcb ⇒ b³a²bc	[35]
15.	ab²ca²bcb ⇒ cbcb²da³bc	[51]
16.	aba²bcb² ⇒ (cb)²db²a³	[48]
17.	b³ca²bcb ⇒ da³bc	[34]
18.	db²a²bcb² ⇒ b³da³b²a³	[52]
19.	ab²a²bcb² ⇒ cbcb²db²a³	[50]
20.	b³a²bcb² ⇒ db²a³	[32]

# ab:aaabbbaaaba=1 cda/b aaaa=c,bbbaaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c abaaab=cbcbd aaabcb=baaabc cbbb=bbaaaba dbbaaab=bbbdaaa abbb=bcbbda abbaaab=cbcbbd abcaabcb=cbcbdaaabc bbbaaab=d dbbcaabcb=bbbaabc abbcaabcb=cbcbbdaaabc abaabcbb=cbcbdbbaaa bbbcaabcb=daaabc dbbaabcbb=bbbdaaabbaaa abbaabcbb=cbcbbdbbaaa bbbaabcbb=dbbaaa

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

Σ	#	Presentation	Mapping
11	3016	⟨a, b \| aabaaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3016

⟨a, b | aabaaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2979 ⟨a, b \| aaabbabbbba=1⟩
Next:	#2982 ⟨a, b \| aaabbbaaabb=1⟩

#2981 ⟨a, b | aaabbbaaaba=1⟩

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Properties

Rewriting system

Isomorphic instances