⟨a, b | aabbaa=abaab⟩

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Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

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

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	acbac ⇒ cacb	[5]
3.	c²acb² ⇒ cac²bac	[7]
4.	acba² ⇒ cac	[4]
5.	cac²ba² ⇒ c²acb	[6]
6.	(cacb)² ⇒ cac²b(ac)²	[11]
7.	cacb²ac ⇒ acbcacb	[9]
8.	cac²baca² ⇒ cacbcac	[13]
9.	cac²b(ac)³ ⇒ cacbc²acb	[15]
10.	cac²b(ac)²b ⇒ c²a(cb)²ac	[12]
11.	cacb²a² ⇒ acbcac	[8]
12.	c²a(cb)²a² ⇒ cac²b(ac)²	[19]
13.	c²a(cb)²(ac)² ⇒ cac²bac²acb	[16]
14.	cac²b(ac)²a² ⇒ cacbc²ac	[17]
15.	cacbcac²b(ac)² ⇒ cac²ba(cac)²b	[18]
16.	c²a(cb)²aca² ⇒ cac²bac²ac	[14]
17.	cac(cb(ac)²)² ⇒ c²a(cb)²ac²acb	[20]

# ab:aabbaa=abaab c/ab ab=c morph:2/0 ab=c acbac=cacb ccacbb=caccbac acbaa=cac caccbaa=ccacb cacbcacb=caccbacac cacbbac=acbcacb caccbacaa=cacbcac caccbacacac=cacbccacb caccbacacb=ccacbcbac cacbbaa=acbcac ccacbcbaa=caccbacac ccacbcbacac=caccbaccacb caccbacacaa=cacbccac cacbcaccbacac=caccbacaccacb ccacbcbacaa=caccbaccac caccbacaccbacac=ccacbcbaccacb

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#5733 ⟨a, b | aabbaa=abaab⟩

Contents

Properties

Rewriting system