#3646 ⟨a, b | aabbabaaba=b⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

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

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	a²bc²ac ⇒ b	[3]
3.	cabc(ca)² ⇒ bc	[5]
4.	b² ⇒ cabc²ac	[4]
5.	a²(bc)² ⇒ cbc(ca)⁴	[9]
6.	a²bc²abc ⇒ cbc(ca)²	[7]
7.	ca(bc)² ⇒ (bc)²(ca)⁴	[10]
8.	(cabc)² ⇒ (bc)²(ca)²	[8]
9.	cabc²acb ⇒ bcabc²ac	[6]

# ab:aabbabaaba=b ac/b ba=c morph:2/0
ba=c
aabccac=b
cabccaca=bc
bb=cabccac
aabcbc=cbccacacaca
aabccabc=cbccaca
cabcbc=bcbccacacaca
cabccabc=bcbccaca
cabccacb=bcabccac