#4316 ⟨a, b | ababbbaab=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(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbbaab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bc ⇒ cac²ab	[8]
2.	abac ⇒ ba	[3]
3.	b³ac ⇒ cac(bac)²ab	[10]
4.	b³a²c ⇒ cb²a²b	[4]
5.	b³a²b ⇒ c	[2]
6.	b⁴a ⇒ cac²	[6]
7.	b³aba ⇒ cac	[5]
8.	b(b²a)² ⇒ cacbac	[7]
9.	(b³a)² ⇒ cac(bac)²	[9]

# ab:ababbbaab=ba reversed:ac/b bbbaab=c morph:6/0
bc=caccab
abac=ba
bbbac=cacbacbacab
bbbaac=cbbaab
bbbaab=c
bbbba=cacc
bbbaba=cac
bbbabba=cacbac
bbbabbba=cacbacbac