#5415 ⟨a, b | abbbbba=babb⟩

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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. abbbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²ba ⇒ bc	[5]
2.	bab² ⇒ cba	[3]
3.	bcb² ⇒ cbc	[7]
4.	cbabcba ⇒ bcab²	[12]
5.	cba(bc)² ⇒ bc²b²	[13]
6.	cba²b² ⇒ babcba	[6]
7.	cbacb² ⇒ ba(bc)²	[9]
8.	cbcab² ⇒ b(cb)²a	[10]
9.	cbc²b² ⇒ (bc)³	[11]
10.	c²b²cba ⇒ ab²cbc²	[14]
11.	ab⁴ ⇒ c	[2]
12.	ab³cba ⇒ cab²	[4]
13.	ab³cbc ⇒ c²b²	[8]
14.	c²b⁴ ⇒ ab³c²bc	[15]
15.	c²b³abcba ⇒ ab²cbc²ab²	[16]
16.	c²b³a(bc)² ⇒ ab²cbc³b²	[17]
17.	c²b³a²b² ⇒ ab(bc)²abcba	[18]
18.	c²b³acb² ⇒ ab(bc)²a(bc)²	[19]
19.	c²b³cab² ⇒ ab²(cbc)²ba	[20]
20.	c²b³c²b² ⇒ ab²(cbc)²bc	[21]

# ab:abbbbba=babb ac/b abbbb=c morph:5/1
ccba=bc
babb=cba
bcbb=cbc
cbabcba=bcabb
cbabcbc=bccbb
cbaabb=babcba
cbacbb=babcbc
cbcabb=bcbcba
cbccbb=bcbcbc
ccbbcba=abbcbcc
abbbb=c
abbbcba=cabb
abbbcbc=ccbb
ccbbbb=abbbccbc
ccbbbabcba=abbcbccabb
ccbbbabcbc=abbcbcccbb
ccbbbaabb=abbcbcabcba
ccbbbacbb=abbcbcabcbc
ccbbbcabb=abbcbccbcba
ccbbbccbb=abbcbccbcbc