#4212 ⟨a, b | aabbbbaba=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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²bc² ⇒ c	[7]
2.	a²bcba ⇒ ba	[3]
3.	a²(bc)² ⇒ bc	[9]
4.	cabcba ⇒ bc	[4]
5.	ca(bc)² ⇒ bcabc²	[10]
6.	b³a ⇒ c	[2]
7.	b³c ⇒ cabc²	[8]
8.	a²bcb²a ⇒ b²a	[5]
9.	a²bcb²c ⇒ b²c	[11]
10.	cabcb²a ⇒ b²c	[6]
11.	cabcb²c ⇒ b²cabc²	[12]

# ab:aabbbbaba=ba ac/b bbba=c morph:4/1
aabcc=c
aabcba=ba
aabcbc=bc
cabcba=bc
cabcbc=bcabcc
bbba=c
bbbc=cabcc
aabcbba=bba
aabcbbc=bbc
cabcbba=bbc
cabcbbc=bbcabcc