#3936 ⟨a, b | aaaabbaba=ab⟩

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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:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. ab=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	a³cbca ⇒ c	[4]
3.	ca²cbca ⇒ cb	[6]
4.	a³cbc² ⇒ cb	[5]
5.	cb² ⇒ ca²cbc²	[8]
6.	a³(cb)² ⇒ cacbca	[7]
7.	cbacbca ⇒ ca²(cb)²	[10]
8.	cba²cbca ⇒ ca²cbc²	[9]
9.	cba²cbc² ⇒ ca²cbc²b	[11]
10.	cba²(cb)² ⇒ ca²cbc²acbca	[12]

# ab:aaaabbaba=ab reversed:ac/b ab=c magic:0
ab=c
aaacbca=c
caacbca=cb
aaacbcc=cb
cbb=caacbcc
aaacbcb=cacbca
cbacbca=caacbcb
cbaacbca=caacbcc
cbaacbcc=caacbccb
cbaacbcb=caacbccacbca