⟨a, b | abaabbabbba=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:
- Right-to-left recursive path with deg(b) = deg(d) = 0, b < d; deg(c) = 1; deg(a) = 2
Auxiliary generators:
1. baa=c
2. ccbba=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	bd ⇒ db	[25]
2.	db² ⇒ 1	[19]
3.	c²bcd ⇒ d²bcb²c²	[39]
4.	cb²c²b² ⇒ b³c²bc	[44]
5.	c²b⁴c²b ⇒ b²c²bcb²c	[55]
6.	cb⁴c(cb)² ⇒ b²c²b⁴c²	[52]
7.	c²b⁴c²d ⇒ dcbcb²c²b	[48]
8.	c²bcb²cd ⇒ d²cb⁴c²bc	[41]
9.	c²bcb²c² ⇒ d²	[38]
10.	c²bc³b² ⇒ d²bcb²cb³c²bc	[50]
11.	c²bcb²cb³c²b ⇒ dc²b⁶c²bcb²c	[60]
12.	c²bcb²cb³c²d ⇒ dc²b(bc)²b²c²b	[59]
13.	c²(bcb)²c²b² ⇒ dc²b⁴cb³c²bc	[51]
14.	c²bc(b²c)²(cb)² ⇒ d²cb(b³c²)²b⁴c²	[61]
15.	a ⇒ b²c²bc	[28]

# ab:abaabbabbba=1 reversed:bd/c/a baa=c,ccbba=d morph:3/0,5/0 bd=db dbb=1 ccbcd=ddbcbbcc cbbccbb=bbbccbc ccbbbbccb=bbccbcbbc cbbbbccbcb=bbccbbbbcc ccbbbbccd=dcbcbbccb ccbcbbcd=ddcbbbbccbc ccbcbbcc=dd ccbcccbb=ddbcbbcbbbccbc ccbcbbcbbbccb=dccbbbbbbccbcbbc ccbcbbcbbbccd=dccbbcbcbbccb ccbcbbcbccbb=dccbbbbcbbbccbc ccbcbbcbbccbcb=ddcbbbbccbbbccbbbbcc a=bbccbc

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#3219 ⟨a, b | abaabbabbba=1⟩

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