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

#	Rule	Proof
1.	dc ⇒ 1	[13]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[12]
5.	a⁵ ⇒ c	[2]
6.	ba³bc ⇒ a³bcb	[19]
7.	bcbd ⇒ a²dba³b	[34]
8.	ba³bac ⇒ a³bcba	[28]
9.	bcbad ⇒ a²dba³ba	[35]
10.	bcba² ⇒ a²b²c	[27]
11.	ba³ba² ⇒ cb²	[30]
12.	b²a³ ⇒ a³dbcb	[22]
13.	bcb² ⇒ a²d	[25]
14.	b²abc ⇒ dba(cb)²	[36]
15.	b²acbc ⇒ a³dba³(cb)²	[41]
16.	b(ba)²c ⇒ dba(cb)²a	[38]
17.	b(bac)² ⇒ a³dba³(cb)²a	[42]
18.	b²aba² ⇒ dba³cb²	[40]
19.	b²acba² ⇒ a³dbc²b²	[39]

# ab:aaaabbaaaba=1 reversed:cda/b aaaaa=c,bbaaab=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaa=c baaabc=aaabcb bcbd=aadbaaab baaabac=aaabcba bcbad=aadbaaaba bcbaa=aabbc baaabaa=cbb bbaaa=aaadbcb bcbb=aad bbabc=dbacbcb bbacbc=aaadbaaacbcb bbabac=dbacbcba bbacbac=aaadbaaacbcba bbabaa=dbaaacbb bbacbaa=aaadbccbb

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

Σ	#	Presentation	Mapping
11	2957	⟨a, b \| aaabbaaabaa=1⟩	φ(a) = a, φ(b) = b
11	3010	⟨a, b \| aabaaaaabba=1⟩	φ(a) = a, φ(b) = b
11	3301	⟨a, b \| abbbabbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

2957

⟨a, b | aaabbaaabaa=1⟩

φ(a) = a, φ(b) = b

3010

⟨a, b | aabaaaaabba=1⟩

φ(a) = a, φ(b) = b

3301

⟨a, b | abbbabbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2870 ⟨a, b \| aaaabbaaaab=1⟩
Next:	#2872 ⟨a, b \| aaaabbaaabb=1⟩

#2871 ⟨a, b | aaaabbaaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances