#20217 ⟨a, b | aba=a, abba=abb⟩

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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

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

#	Rule	Proof
1.	ca ⇒ c	[13]
2.	aba ⇒ a	[1]
3.	abc ⇒ c	[7]
4.	cba ⇒ c	[15]
5.	cbc ⇒ c²	[16]
6.	ab²a ⇒ ab²	[2]
7.	cb² ⇒ ab²c	[8]
8.	ab³a ⇒ ab²	[4]
9.	ab³c ⇒ ab²c	[9]
10.	ab⁴a ⇒ ab⁴	[5]
11.	ab⁵a ⇒ ab⁴	[6]
12.	ab⁵c ⇒ ab⁴c	[10]
13.	ab⁶a ⇒ ab⁶	[11]
14.	ab⁷a ⇒ ab⁶	[12]
15.	ab⁷c ⇒ ab⁶c	[14]
16.	ab⁸ ⇒ c	[3]

# ab:aba=a,abba=abb ac/b abbbbbbbb=c morph:9/0
ca=c
aba=a
abc=c
cba=c
cbc=cc
abba=abb
cbb=abbc
abbba=abb
abbbc=abbc
abbbba=abbbb
abbbbba=abbbb
abbbbbc=abbbbc
abbbbbba=abbbbbb
abbbbbbba=abbbbbb
abbbbbbbc=abbbbbbc
abbbbbbbb=c