#4153 ⟨a, b | aabbaaaab=ba⟩

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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(c) = deg(d) = 0, c < d; deg(a) = 1; deg(b) = 2
Auxiliary generators:
1. aaab=c
2. abba=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cadc²dc ⇒ d	[10]
2.	cadc²d² ⇒ dadc²dc	[11]
3.	a²d ⇒ cadc	[9]
4.	a²cadc² ⇒ ca	[12]
5.	a²cadcd ⇒ c²adc³dc	[13]
6.	a³b ⇒ c	[2]
7.	bc ⇒ adca²b	[7]
8.	bd ⇒ (adc)²dc	[8]
9.	ba ⇒ adc	[4]

# ab:aabbaaaab=ba reversed:cd/a/b aaab=c,abba=d morph:4/0,4/0
cadccdc=d
cadccdd=dadccdc
aad=cadc
aacadcc=ca
aacadcd=ccadcccdc
aaab=c
bc=adcaab
bd=adcadcdc
ba=adc