⟨a, b | aabbbbaaab=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. aaa=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²b⁴cb ⇒ cb⁴cbc	[12]
2.	c²bcb⁴cb ⇒ c²b⁵cbc	[17]
3.	(cb)³b³cb ⇒ cbcb⁵cbc	[16]
4.	cb(bc)²b⁴cb ⇒ cb²cb⁵cbc	[15]
5.	cb³cbcb⁴cb ⇒ cb³cb⁵cbc	[13]
6.	(cb⁴cb)² ⇒ c(b⁴cb)²c	[10]
7.	c²b⁵cbcb⁴cb ⇒ cbcb⁵cbcb⁴c	[20]
8.	cbcb⁵cbcb⁴cb ⇒ cb²cb⁵cbcb⁴c	[19]
9.	cb²cb⁵cbcb⁴cb ⇒ cb³cb⁵cbcb⁴c	[18]
10.	cb³cb⁵cbcb⁴cb ⇒ c(b⁴cb)²cb⁴c	[14]
11.	c(b⁴cb)²cb⁴cb ⇒ c	[11]
12.	a ⇒ c(b⁴cb)²	[9]

# ab:aabbbbaaab=a bc/a aaa=c morph:3/0 ccbbbbcb=cbbbbcbc ccbcbbbbcb=ccbbbbbcbc cbcbcbbbbcb=cbcbbbbbcbc cbbcbcbbbbcb=cbbcbbbbbcbc cbbbcbcbbbbcb=cbbbcbbbbbcbc cbbbbcbcbbbbcb=cbbbbcbbbbbcbc ccbbbbbcbcbbbbcb=cbcbbbbbcbcbbbbc cbcbbbbbcbcbbbbcb=cbbcbbbbbcbcbbbbc cbbcbbbbbcbcbbbbcb=cbbbcbbbbbcbcbbbbc cbbbcbbbbbcbcbbbbcb=cbbbbcbbbbbcbcbbbbc cbbbbcbbbbbcbcbbbbcb=c a=cbbbbcbbbbbcb

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#3679 ⟨a, b | aabbbbaaab=a⟩

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Rewriting system