⟨a, b | aabbaababba=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(b) = deg(c) = 0, b < c; deg(a) = 1
Auxiliary generators:
1. abbaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cb ⇒ bc	[8]
2.	bc² ⇒ 1	[9]
3.	cab²a ⇒ ba²bc	[13]
4.	cabca ⇒ ab²ac⁴	[20]
5.	b²a² ⇒ abcab²c	[16]
6.	b²ca² ⇒ ab²ac	[10]
7.	a²bca ⇒ c⁴	[18]
8.	cabab²a ⇒ ab²ac³ab²	[26]
9.	a²bab²a ⇒ c³ab²	[24]

# ab:aabbaababba=1 bc/a abbaa=c morph:5/0 cb=bc bcc=1 cabba=baabc cabca=abbacccc bbaa=abcabbc bbcaa=abbac aabca=cccc cababba=abbacccabb aababba=cccabb

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

Σ	#	Presentation	Mapping
11	3275	⟨a, b \| abbaaabbaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3275

⟨a, b | abbaaabbaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3108 ⟨a, b \| aabbaababab=1⟩
Next:	#3111 ⟨a, b \| aabbaabbaba=1⟩

#3109 ⟨a, b | aabbaababba=1⟩

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Properties

Rewriting system

Isomorphic instances