⟨a, b | abaabbbabba=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) = 0; deg(d) = 1; deg(c) = 2; deg(a) = 3
Auxiliary generators:
1. baa=c
2. abcc=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	db³ ⇒ 1	[42]
2.	bd ⇒ db	[44]
3.	b²c²b²c ⇒ cbc²b³	[43]
4.	dbcbc² ⇒ c²b²cd	[45]
5.	db²cbc² ⇒ bc²b²cd	[22]
6.	bc²b⁴c² ⇒ cb²cbc²b²	[60]
7.	bcbc²b⁴c ⇒ c²b⁴c²b²	[61]
8.	dc²b⁴c² ⇒ c²b(bc)²db	[48]
9.	dcb²cbc² ⇒ bc²b(bc)²d²b²	[54]
10.	d(bcb)²c² ⇒ cbc²b⁴cd²b²	[49]
11.	d(b²c)²bc² ⇒ c²b⁴c²db	[57]
12.	c²b²cbc² ⇒ d²b²	[53]
13.	b²c³bc² ⇒ cbc²b(b²c)²d	[63]
14.	bc²b(b²c)²bc² ⇒ cb²cbc²b⁶c²db	[56]
15.	b²c²(bcb)²c² ⇒ cbc²b³cb⁴c²db	[58]
16.	dc²b(b²c)²bc² ⇒ c²b(bc)²b²c²db	[59]
17.	bcbc²(b²c)²bc² ⇒ c²b(b³c²)²b⁴cd²b²	[66]
18.	a ⇒ bc²b²c	[20]

# ab:abaabbbabba=1 b/d/c/a baa=c,abcc=d morph:3/2,4/0 dbbb=1 bd=db bbccbbc=cbccbbb dbcbcc=ccbbcd dbbcbcc=bccbbcd bccbbbbcc=cbbcbccbb bcbccbbbbc=ccbbbbccbb dccbbbbcc=ccbbcbcdb dcbbcbcc=bccbbcbcddbb dbcbbcbcc=cbccbbbbcddbb dbbcbbcbcc=ccbbbbccdb ccbbcbcc=ddbb bbcccbcc=cbccbbbcbbcd bccbbbcbbcbcc=cbbcbccbbbbbbccdb bbccbcbbcbcc=cbccbbbcbbbbccdb dccbbbcbbcbcc=ccbbcbcbbccdb bcbccbbcbbcbcc=ccbbbbccbbbccbbbbcddbb a=bccbbc

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#3223 ⟨a, b | abaabbbabba=1⟩

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