⟨a, b | aabaababbba=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(b) = 0, c < d < b; deg(a) = 1
Auxiliary generators:
1. bbb=c
2. aaabaaba=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[25]
2.	dc ⇒ 1	[11]
3.	bc ⇒ cb	[5]
4.	bd ⇒ db	[24]
5.	b³ ⇒ c	[2]
6.	ca³ ⇒ abacadb²	[31]
7.	dabaca ⇒ a³b	[8]
8.	cba³ ⇒ (ba)²cadb²	[32]
9.	d(ba)²ca ⇒ ba³b	[27]
10.	cb²a³ ⇒ b(ba)²cadb²	[35]
11.	db(ba)²ca ⇒ b²a³b	[34]
12.	ba²baca ⇒ (aba)²c	[29]
13.	b²(aba)² ⇒ ca²bacad	[37]
14.	d(a²b)²a ⇒ a³ba²db	[33]
15.	db(a²b)²a ⇒ ba³ba²db	[26]
16.	b²a³ba² ⇒ a²baca²db²	[42]
17.	b²(a²b)²a ⇒ ca²baca²d	[40]
18.	a(a²b)²a ⇒ d	[3]

# ab:aabaababbba=1 cdb/a bbb=c,aaabaaba=d magic:1 cd=1 dc=1 bc=cb bd=db bbb=c caaa=abacadbb dabaca=aaab cbaaa=babacadbb dbabaca=baaab cbbaaa=bbabacadbb dbbabaca=bbaaab baabaca=abaabac bbabaaba=caabacad daabaaba=aaabaadb dbaabaaba=baaabaadb bbaaabaa=aabacaadbb bbaabaaba=caabacaad aaabaaba=d

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

Σ	#	Presentation	Mapping
11	3084	⟨a, b \| aababbbaaab=1⟩	φ(a) = a, φ(b) = b
11	3148	⟨a, b \| aabbbabbaba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3084

⟨a, b | aababbbaaab=1⟩

φ(a) = a, φ(b) = b

3148

⟨a, b | aabbbabbaba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3039 ⟨a, b \| aabaababbab=1⟩
Next:	#3042 ⟨a, b \| aabaabbaaba=1⟩

#3040 ⟨a, b | aabaababbba=1⟩

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Properties

Rewriting system

Isomorphic instances