⟨a, b | aaaa=1, abbbba=b⟩

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Monoids with two generators and two relations

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

Auxiliary generators:
1. c = bbba
2. d = accc
Reduction order:
- Left-to-right recursive path with deg(d) = deg(b) = 0, d < b; deg(c) = deg(a) = 1, c < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bd ⇒ db	[19]
2.	d²b³ ⇒ d	[28]
3.	db⁴ ⇒ b	[23]
4.	cdb³ ⇒ c	[39]
5.	b²c ⇒ dcb⁵	[33]
6.	d³c ⇒ bcd⁴b²	[51]
7.	d²bc ⇒ cd²b	[47]
8.	ad ⇒ dcd	[44]
9.	ab ⇒ dcb	[20]
10.	da ⇒ d²c	[30]
11.	ba ⇒ dbc	[36]
12.	cbc ⇒ b⁴	[8]
13.	bc² ⇒ (dc)²b	[25]
14.	bcdc ⇒ c²b⁴	[21]
15.	d²c² ⇒ cdcd³	[54]
16.	ca ⇒ cdc	[41]
17.	ac ⇒ dc²	[24]
18.	c³ ⇒ bcd²b²	[29]
19.	c(dc)² ⇒ d²cb⁹	[55]
20.	a⁴ ⇒ 1	[1]

# ab:aaaa=1,abbbba=b db/ca bbba=c,accc=d morph:4/0,4/0 bd=db ddbbb=d dbbbb=b cdbbb=c bbc=dcbbbbb dddc=bcddddbb ddbc=cddb ad=dcd ab=dcb da=ddc ba=dbc cbc=bbbb bcc=dcdcb bcdc=ccbbbb ddcc=cdcddd ca=cdc ac=dcc ccc=bcddbb cdcdc=ddcbbbbbbbbb aaaa=1

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#17137 ⟨a, b | aaaa=1, abbbba=b⟩

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