⟨a, b | aaabbaaaba=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. aaaa=c
2. bbaaab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[12]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[11]
5.	a⁴ ⇒ c	[2]
6.	ba³bc ⇒ a³bcb	[20]
7.	bcbd ⇒ adba³b	[30]
8.	bcba ⇒ ab²c	[27]
9.	ba³ba ⇒ cb²	[16]
10.	b²a³ ⇒ a³dbcb	[28]
11.	bcb² ⇒ ad	[25]
12.	b²a²bc ⇒ dba²(cb)²	[21]
13.	b²a²cbc ⇒ a³dba³(cb)²	[33]
14.	b²a²ba ⇒ dba³cb²	[17]
15.	b²a²cba ⇒ a³dbc²b²	[32]

# ab:aaabbaaaba=1 reversed:cda/b aaaa=c,bbaaab=d magic:0 dc=1 cd=1 ca=ac da=ad aaaa=c baaabc=aaabcb bcbd=adbaaab bcba=abbc baaaba=cbb bbaaa=aaadbcb bcbb=ad bbaabc=dbaacbcb bbaacbc=aaadbaaacbcb bbaaba=dbaaacbb bbaacba=aaadbccbb

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

Σ	#	Presentation	Mapping
10	1396	⟨a, b \| aabaaaabba=1⟩	φ(a) = a, φ(b) = b
10	1544	⟨a, b \| abbbabbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

1396

⟨a, b | aabaaaabba=1⟩

φ(a) = a, φ(b) = b

1544

⟨a, b | abbbabbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#1364 ⟨a, b \| aaababbbba=1⟩
Next:	#1367 ⟨a, b \| aaabbaaabb=1⟩

#1366 ⟨a, b | aaabbaaaba=1⟩

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Properties

Rewriting system

Isomorphic instances