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

#	Rule	Proof
1.	db ⇒ 1	[12]
2.	bd ⇒ 1	[14]
3.	b²a ⇒ a(bc)²d	[23]
4.	cbac ⇒ bab	[6]
5.	bcba ⇒ abcb	[21]
6.	dabc ⇒ cbad	[17]
7.	c(ba)² ⇒ ba²bcb(cd)²	[39]
8.	c²ba² ⇒ a²b²	[26]
9.	da²bc ⇒ cba²d	[18]
10.	cda² ⇒ adcbad	[32]
11.	a³bc ⇒ d	[3]
12.	cba³ ⇒ d	[16]
13.	cba²dcba ⇒ ba³b	[34]
14.	daba² ⇒ cbadcba²d²	[28]
15.	dabadcba ⇒ cbad²a²b	[37]
16.	da²ba² ⇒ ba³bad²	[36]
17.	da²badcba ⇒ cba²d²a²b	[38]
18.	a³ba² ⇒ dcba²d²	[27]
19.	a³badcba ⇒ d²a²b	[35]

# ab:aabbabbaaab=1 bc/d/a aabbab=c,aaabc=d morph:6/1,5/0 db=1 bd=1 bba=abcbcd cbac=bab bcba=abcb dabc=cbad cbaba=baabcbcdcd ccbaa=aabb daabc=cbaad cdaa=adcbad aaabc=d cbaaa=d cbaadcba=baaab dabaa=cbadcbaadd dabadcba=cbaddaab daabaa=baaabadd daabadcba=cbaaddaab aaabaa=dcbaadd aaabadcba=ddaab

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#3125 ⟨a, b | aabbabbaaab=1⟩

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Rewriting system