⟨a, b | aababa=abaab⟩

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

#	Rule	Proof
1.	a²ca ⇒ ac	[13]
2.	ac²a ⇒ a²c²	[19]
3.	(ca)² ⇒ c²	[29]
4.	c³a ⇒ cac²	[24]
5.	acb ⇒ a²ba²c	[18]
6.	cab ⇒ ba²c	[11]
7.	c²b ⇒ b(ac)²	[25]
8.	ca²baca ⇒ ca²bc	[30]
9.	ca²bc²a ⇒ ca²bac²	[28]
10.	(aba)²ca ⇒ aba²bc	[15]
11.	aba²bc²a ⇒ (aba)²c²	[21]
12.	cba²b ⇒ ba²bac	[31]
13.	a²(ba)² ⇒ aba²b	[1]
14.	ca(ab)² ⇒ baba³c	[12]
15.	ca²bcb ⇒ (ba)²c²	[26]
16.	baba²b ⇒ c	[2]
17.	(aba)²b ⇒ a²c	[3]
18.	aba²bcb ⇒ (ac)²	[22]
19.	ca²b²a²b ⇒ baba³bac	[32]
20.	a(ba²b)² ⇒ a²bac	[4]

# ab:aababa=abaab ac/b babaab=c morph:6/3 aaca=ac acca=aacc caca=cc ccca=cacc acb=aabaac cab=baac ccb=bacac caabaca=caabc caabcca=caabacc abaabaca=abaabc abaabcca=abaabacc cbaab=baabac aababa=abaab caabab=babaaac caabcb=babacc babaab=c abaabab=aac abaabcb=acac caabbaab=babaaabac abaabbaab=aabac

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#5686 ⟨a, b | aababa=abaab⟩

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Rewriting system