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

#	Rule	Proof
1.	cb ⇒ bc	[5]
2.	b³ ⇒ c	[2]
3.	cd ⇒ 1	[24]
4.	dc ⇒ 1	[16]
5.	db ⇒ bd	[25]
6.	aba²c ⇒ caba²	[17]
7.	aba²bc ⇒ caba²b	[27]
8.	aba²b²c ⇒ caba²b²	[31]
9.	aba²d ⇒ daba²	[6]
10.	aba²bd ⇒ daba²b	[26]
11.	aba²b²d ⇒ daba²b²	[32]
12.	aba³b ⇒ bda²caba	[33]
13.	a²cabab² ⇒ b²aba³c	[35]
14.	a³ba²b² ⇒ b²dacaba³	[30]
15.	a²caba²b² ⇒ b²dacaba³c	[36]
16.	a²c²aba²b² ⇒ b²dacaba³c²	[38]
17.	acaba³c³ ⇒ ba²c³aba²b²	[41]
18.	acaba³d ⇒ ba²daba²b²	[39]
19.	a²caba³ ⇒ b²d	[28]

# ab:aabaabbbaba=1 reversed:cb/d/a bbb=c,abaaabaa=d magic:1 cb=bc bbb=c cd=1 dc=1 db=bd abaac=cabaa abaabc=cabaab abaabbc=cabaabb abaad=dabaa abaabd=dabaab abaabbd=dabaabb abaaab=bdaacaba aacababb=bbabaaac aaabaabb=bbdacabaaa aacabaabb=bbdacabaaac aaccabaabb=bbdacabaaacc acabaaaccc=baacccabaabb acabaaad=baadabaabb aacabaaa=bbd

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

Σ	#	Presentation	Mapping
11	3089	⟨a, b \| aababbbabba=1⟩	φ(a) = b, φ(b) = a
11	3143	⟨a, b \| aabbbabaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3089

⟨a, b | aababbbabba=1⟩

φ(a) = b, φ(b) = a

3143

⟨a, b | aabbbabaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3047 ⟨a, b \| aabaabbbaab=1⟩
Next:	#3050 ⟨a, b \| aabaabbbbab=1⟩

#3048 ⟨a, b | aabaabbbaba=1⟩

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Properties

Rewriting system

Isomorphic instances