⟨a, b | aaaaabaabba=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. aaaaaa=c
2. baabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[15]
2.	cd ⇒ 1	[9]
3.	ca ⇒ ac	[6]
4.	da ⇒ ad	[13]
5.	a⁶ ⇒ c	[2]
6.	b²c ⇒ a⁴ba²b	[18]
7.	ba²bd ⇒ a²db²	[16]
8.	b²ac ⇒ a³(aba)²	[20]
9.	ba²bad ⇒ a²db²a	[14]
10.	bcba² ⇒ cba²b	[21]
11.	b²a²c ⇒ a⁴(ba²)²	[24]
12.	(ba²)²d ⇒ a²db²a²	[23]
13.	b²a³c ⇒ a⁴ba²ba³	[27]
14.	ba²ba³d ⇒ a²db²a³	[26]
15.	b²a⁴ ⇒ a⁴dbcb	[29]
16.	ba²ba⁴ ⇒ d(bc)²	[25]
17.	ba²b² ⇒ d	[3]

# ab:aaaaabaabba=1 reversed:cda/b aaaaaa=c,baabb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaaa=c bbc=aaaabaab baabd=aadbb bbac=aaaabaaba baabad=aadbba bcbaa=cbaab bbaac=aaaabaabaa baabaad=aadbbaa bbaaac=aaaabaabaaa baabaaad=aadbbaaa bbaaaa=aaaadbcb baabaaaa=dbcbc baabb=d

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

Σ	#	Presentation	Mapping
11	2851	⟨a, b \| aaaabaabbaa=1⟩	φ(a) = a, φ(b) = b
11	2920	⟨a, b \| aaabaabbaaa=1⟩	φ(a) = a, φ(b) = b
11	3095	⟨a, b \| aabbaaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2851

⟨a, b | aaaabaabbaa=1⟩

φ(a) = a, φ(b) = b

2920

⟨a, b | aaabaabbaaa=1⟩

φ(a) = a, φ(b) = b

3095

⟨a, b | aabbaaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2814 ⟨a, b \| aaaaabaabab=1⟩
Next:	#2816 ⟨a, b \| aaaaabaabbb=1⟩

#2815 ⟨a, b | aaaaabaabba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances