#4808 ⟨a, b | abaabbba=bab⟩

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

#	Rule	Proof
1.	a²b(ac)³ ⇒ cb	[5]
2.	bab ⇒ abac	[3]
3.	abacab ⇒ ba²bac	[7]
4.	b²cb ⇒ (ab(ac)²)²	[14]
5.	b²a²bac ⇒ aba(ca)²b	[10]
6.	ab³c ⇒ cb³a	[4]
7.	ab³a ⇒ c	[2]
8.	abacb²a ⇒ bc	[6]
9.	aba(cb)² ⇒ ba(ab(ac)²)²	[20]
10.	abacba²bac ⇒ ba²ba(ca)²b	[12]
11.	ab(ac)²b²a ⇒ b²c	[8]
12.	ab(a(ca)²b)² ⇒ b²cabac	[15]
13.	ab(ac)³b²a ⇒ b³c	[13]
14.	b⁴c ⇒ ab(ac)⁴b²a	[17]
15.	b³cabac ⇒ abac(a(ca)²b)²	[19]
16.	bcb³a ⇒ abacb²c	[9]
17.	abacb³c ⇒ bcbacb²a	[18]
18.	abacb²cabac ⇒ bcaba(ca)³b	[16]
19.	abac²b³a ⇒ ba²bacb²c	[11]
20.	ab(ac)²b²cabac ⇒ b²caba(ca)³b	[25]
21.	(ab(ac)²)²bcb ⇒ b²c(ab(ac)²)²	[23]
22.	(ab(ac)²)²ba²bac ⇒ b²caba(ca)²b	[22]
23.	(ab(ac)²)²b³c ⇒ b²cab(ac)⁴b²a	[24]
24.	(ab(ac)²)²cb³a ⇒ b²cabacb²c	[21]

# ab:abaabbba=bab ca/b abbba=c morph:5/0
aabacacac=cb
bab=abac
abacab=baabac
bbcb=abacacabacac
bbaabac=abacacab
abbbc=cbbba
abbba=c
abacbba=bc
abacbcb=baabacacabacac
abacbaabac=baabacacab
abacacbba=bbc
abacacabacacab=bbcabac
abacacacbba=bbbc
bbbbc=abacacacacbba
bbbcabac=abacacacabacacab
bcbbba=abacbbc
abacbbbc=bcbacbba
abacbbcabac=bcabacacacab
abaccbbba=baabacbbc
abacacbbcabac=bbcabacacacab
abacacabacacbcb=bbcabacacabacac
abacacabacacbaabac=bbcabacacab
abacacabacacbbbc=bbcabacacacacbba
abacacabacaccbbba=bbcabacbbc