#4849 ⟨a, b | ababbbba=baa⟩

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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(b) = deg(c) = 0, b < c; deg(a) = 1
Auxiliary generators:
1. baa=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	abab³c ⇒ ca	[5]
2.	abab⁴c ⇒ bac	[6]
3.	ba² ⇒ c	[2]
4.	(ba)²c ⇒ cbab⁴c	[9]
5.	baca ⇒ cbab³c	[7]
6.	cbab⁴a ⇒ bac	[13]
7.	cbab⁵ac ⇒ bacbab⁴c	[14]
8.	cbab⁴ca ⇒ bacbab³c	[12]
9.	c(bab³c)² ⇒ bac²a	[10]
10.	(cbab³)²bc ⇒ (bac)²	[11]
11.	abab⁴a ⇒ c	[3]
12.	abab⁵ac ⇒ cbab⁴c	[8]

# ab:ababbbba=baa bc/a baa=c magic:0
ababbbc=ca
ababbbbc=bac
baa=c
babac=cbabbbbc
baca=cbabbbc
cbabbbba=bac
cbabbbbbac=bacbabbbbc
cbabbbbca=bacbabbbc
cbabbbcbabbbc=bacca
cbabbbcbabbbbc=bacbac
ababbbba=c
ababbbbbac=cbabbbbc