#23326 ⟨a, b | aaa=1, bbbb=abba⟩

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

#	Rule	Proof
1.	b¹⁴ ⇒ b²	[17]
2.	cb¹² ⇒ c	[20]
3.	b⁶c ⇒ cb⁶	[14]
4.	ab² ⇒ b⁴cb⁸	[18]
5.	b²a ⇒ c	[3]
6.	c² ⇒ b⁶	[7]
7.	cb²c ⇒ b⁴cb⁴	[21]
8.	cb⁴c ⇒ b²cb²	[22]
9.	ca ⇒ b²cb⁸	[11]
10.	cba ⇒ cb⁵cb⁶	[16]
11.	ac ⇒ b⁴	[4]
12.	abc ⇒ b⁴cbcb⁶	[23]
13.	a³ ⇒ 1	[1]

# ab:aaa=1,bbbb=abba b/ca bba=c morph:3/0
bbbbbbbbbbbbbb=bb
cbbbbbbbbbbbb=c
bbbbbbc=cbbbbbb
abb=bbbbcbbbbbbbb
bba=c
cc=bbbbbb
cbbc=bbbbcbbbb
cbbbbc=bbcbb
ca=bbcbbbbbbbb
cba=cbbbbbcbbbbbb
ac=bbbb
abc=bbbbcbcbbbbbb
aaa=1