⟨a, b | aabbaba=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. aaa=c
2. bbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[10]
2.	dc ⇒ 1	[12]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[11]
5.	a³ ⇒ c	[2]
6.	cb² ⇒ baba²	[16]
7.	dbab ⇒ b²da	[13]
8.	abcb ⇒ babc	[19]
9.	cab² ⇒ (ab)²a²	[17]
10.	d(ab)² ⇒ ab²da	[15]
11.	a²b² ⇒ bcbda²	[24]
12.	a(ab)² ⇒ (cb)²d	[22]
13.	b²ab ⇒ d	[3]

# ab:aabbaba=1 cda/b aaa=c,bbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c cbb=babaa dbab=bbda abcb=babc cabb=ababaa dabab=abbda aabb=bcbdaa aabab=cbcbd bbab=d

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

Σ	#	Presentation	Mapping
7	157	⟨a, b \| ababbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

157

⟨a, b | ababbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#146 ⟨a, b \| aabbaab=1⟩
Next:	#149 ⟨a, b \| aabbbab=1⟩

#147 ⟨a, b | aabbaba=1⟩

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Properties

Rewriting system

Isomorphic instances