⟨a, b | aabba=abab⟩

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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

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

#	Rule	Proof
1.	(ab)² ⇒ ac	[3]
2.	ab²a ⇒ c	[2]
3.	abc ⇒ acba	[6]
4.	abac ⇒ acab	[7]
5.	cbab ⇒ c²	[5]
6.	(ac)²ba ⇒ ac²b	[10]
7.	ab²c ⇒ cb²a	[4]
8.	cbc ⇒ c²ba	[8]
9.	cbac ⇒ c²ab	[9]
10.	ac²b² ⇒ acac²	[12]
11.	ac³ba ⇒ acac²ab	[14]
12.	c²acba ⇒ c³b	[11]
13.	ac⁴a ⇒ acac³	[17]
14.	c³b² ⇒ c²ac²	[13]
15.	acac²ab² ⇒ ac⁴	[15]
16.	c⁴ba ⇒ (c²a)²b	[16]
17.	c⁵a ⇒ c²ac³	[18]
18.	aca(c²a)² ⇒ ac⁵	[19]
19.	(c²a)²b² ⇒ c⁵	[21]
20.	(c²a)³ ⇒ c⁶	[20]

# ab:aabba=abab reversed:a/bc abba=c morph:4/0 abab=ac abba=c abc=acba abac=acab cbab=cc acacba=accb abbc=cbba cbc=ccba cbac=ccab accbb=acacc acccba=acaccab ccacba=cccb acccca=acaccc cccbb=ccacc acaccabb=acccc ccccba=ccaccab ccccca=ccaccc acaccacca=accccc ccaccabb=ccccc ccaccacca=cccccc

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#1228 ⟨a, b | aabba=abab⟩

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