⟨a, b | aabbbaaaab=a⟩

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Monoids with two generators and one relation

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

#	Rule	Proof
1.	c²b³cb ⇒ cb³cbc	[9]
2.	c²bcb³cb ⇒ c²b⁴cbc	[21]
3.	(cb)³b²cb ⇒ cbcb⁴cbc	[20]
4.	cb(bc)²b³cb ⇒ cb²cb⁴cbc	[19]
5.	(cb³cb)² ⇒ c(b³cb)²c	[11]
6.	c²b⁴cbcb³cb ⇒ c²(b⁴c)²bc	[24]
7.	cbcb⁴cbcb³cb ⇒ cbc(b⁴c)²bc	[23]
8.	cb²cb⁴cbcb³cb ⇒ cb²c(b⁴c)²bc	[22]
9.	c(b³cb)²cb³cb ⇒ c(b³cb)³c	[17]
10.	c²(b⁴c)²bcb³cb ⇒ cbc(b⁴c)²bcb³c	[26]
11.	cbc(b⁴c)²bcb³cb ⇒ cb²c(b⁴c)²bcb³c	[25]
12.	cb²c(b⁴c)²bcb³cb ⇒ c(b³cb)³cb³c	[18]
13.	c(b³cb)³cb³cb ⇒ c	[16]
14.	a ⇒ c(b³cb)³	[14]

# ab:aabbbaaaab=a bc/a aaaa=c morph:4/0 ccbbbcb=cbbbcbc ccbcbbbcb=ccbbbbcbc cbcbcbbbcb=cbcbbbbcbc cbbcbcbbbcb=cbbcbbbbcbc cbbbcbcbbbcb=cbbbcbbbbcbc ccbbbbcbcbbbcb=ccbbbbcbbbbcbc cbcbbbbcbcbbbcb=cbcbbbbcbbbbcbc cbbcbbbbcbcbbbcb=cbbcbbbbcbbbbcbc cbbbcbbbbcbcbbbcb=cbbbcbbbbcbbbbcbc ccbbbbcbbbbcbcbbbcb=cbcbbbbcbbbbcbcbbbc cbcbbbbcbbbbcbcbbbcb=cbbcbbbbcbbbbcbcbbbc cbbcbbbbcbbbbcbcbbbcb=cbbbcbbbbcbbbbcbcbbbc cbbbcbbbbcbbbbcbcbbbcb=c a=cbbbcbbbbcbbbbcb

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#3662 ⟨a, b | aabbbaaaab=a⟩

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Rewriting system