⟨a, b | aababbbbaba=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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. babbbbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	abcbab ⇒ babcba	[22]
7.	a(ab)²cb ⇒ (cb)²abda²	[32]
8.	cbab³ ⇒ b³abc	[15]
9.	db³ab ⇒ bab³d	[12]
10.	cabab³ ⇒ ab³abc	[16]
11.	dab³ab ⇒ abab³d	[14]
12.	a²b²abcb ⇒ (cb)²ab²da²	[35]
13.	ca²bab³ ⇒ a²b³abc	[20]
14.	da²b³ab ⇒ a²bab³d	[21]
15.	ab⁴ab ⇒ b³abcbda	[19]
16.	abcb²abcb ⇒ ba(bc)²(ab)²da²	[38]
17.	a²b³abcb ⇒ cb⁴aba²	[34]
18.	a²bab⁴ ⇒ b⁴aba²	[29]
19.	b⁴abcb ⇒ da²	[28]
20.	abcb³abcb ⇒ ba(bc)²abab²da²	[40]

# ab:aababbbbaba=1 cda/b aaa=c,babbbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abcbab=babcba aababcb=cbcbabdaa cbabbb=bbbabc dbbbab=babbbd cababbb=abbbabc dabbbab=ababbbd aabbabcb=cbcbabbdaa caababbb=aabbbabc daabbbab=aababbbd abbbbab=bbbabcbda abcbbabcb=babcbcababdaa aabbbabcb=cbbbbabaa aababbbb=bbbbabaa bbbbabcb=daa abcbbbabcb=babcbcababbdaa

Up:	Monoids with two generators and one relation
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#3091 ⟨a, b | aababbbbaba=1⟩

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