⟨a, b | aabbbabbaab=1⟩

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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(d) = 0, b < d; deg(c) = 1; deg(a) = 2
Auxiliary generators:
1. baa=c
2. abccb=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	db ⇒ bd	[17]
2.	b²d ⇒ 1	[12]
3.	dcbc² ⇒ c²b²cbd²	[33]
4.	b²c²b²c ⇒ cbc²b³	[27]
5.	bc²b⁴c² ⇒ cb²cbc²b²	[41]
6.	bcbc²b⁴c ⇒ c²b⁴c²b²	[44]
7.	dc²b⁴c² ⇒ bc²b(bc)²d	[36]
8.	dcb²cbc² ⇒ cbc²b⁴cd²	[37]
9.	c²b²cbc² ⇒ d²	[32]
10.	b²c³bc² ⇒ cbc²b(b²c)²bd²	[47]
11.	bc²b(b²c)²bc² ⇒ cb²cbc²b⁶c²d	[50]
12.	dc²b(b²c)²bc² ⇒ bc²b(bc)²b²c²d	[49]
13.	b²c²(bcb)²c² ⇒ cbc²b³cb⁴c²d	[48]
14.	bcbc²(b²c)²bc² ⇒ c²b(b³c²)²b⁴cd²	[52]
15.	a ⇒ bc²b²c	[24]

# ab:aabbbabbaab=1 bd/c/a baa=c,abccb=d morph:3/1,5/1 db=bd bbd=1 dcbcc=ccbbcbdd bbccbbc=cbccbbb bccbbbbcc=cbbcbccbb bcbccbbbbc=ccbbbbccbb dccbbbbcc=bccbbcbcd dcbbcbcc=cbccbbbbcdd ccbbcbcc=dd bbcccbcc=cbccbbbcbbcbdd bccbbbcbbcbcc=cbbcbccbbbbbbccd dccbbbcbbcbcc=bccbbcbcbbccd bbccbcbbcbcc=cbccbbbcbbbbccd bcbccbbcbbcbcc=ccbbbbccbbbccbbbbcdd a=bccbbc

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#3147 ⟨a, b | aabbbabbaab=1⟩

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