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

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[18]
5.	a⁵ ⇒ c	[2]
6.	cb² ⇒ ba²ba³	[24]
7.	dba²b ⇒ b²da²	[20]
8.	cab² ⇒ aba²ba³	[25]
9.	daba²b ⇒ ab²da²	[23]
10.	a²bcb ⇒ ba²bc	[27]
11.	ca²b² ⇒ (a²b)²a³	[29]
12.	d(a²b)² ⇒ a²b²da²	[22]
13.	a³b² ⇒ bcbda³	[32]
14.	a(a²b)² ⇒ (cb)²d	[30]
15.	b²a²b ⇒ d	[3]

# ab:aaaabbaaba=1 cda/b aaaaa=c,bbaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c cbb=baabaaa dbaab=bbdaa cabb=abaabaaa dabaab=abbdaa aabcb=baabc caabb=aabaabaaa daabaab=aabbdaa aaabb=bcbdaaa aaabaab=cbcbd bbaab=d

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

Σ	#	Presentation	Mapping
10	1368	⟨a, b \| aaabbaabaa=1⟩	φ(a) = a, φ(b) = b
10	1478	⟨a, b \| abaaaaabba=1⟩	φ(a) = a, φ(b) = b
10	1540	⟨a, b \| abbabbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

1368

⟨a, b | aaabbaabaa=1⟩

φ(a) = a, φ(b) = b

1478

⟨a, b | abaaaaabba=1⟩

φ(a) = a, φ(b) = b

1540

⟨a, b | abbabbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#1323 ⟨a, b \| aaaabbaaab=1⟩
Next:	#1325 ⟨a, b \| aaaabbaabb=1⟩

#1324 ⟨a, b | aaaabbaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances