⟨a, b | abababbba=ab⟩

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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
2. d = cb
3. e = dbdb
Reduction order:
- Right-to-left recursive path with deg(d) = deg(c) = 0, d < c; deg(e) = deg(b) = 1, e < b; deg(a) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ed ⇒ (dc)²e	[23]
2.	ec ⇒ dc³e	[22]
3.	cb ⇒ d	[3]
4.	d²bd ⇒ c²dce	[25]
5.	dcdbd ⇒ c²e	[12]
6.	c²dbd ⇒ db	[8]
7.	d²bc ⇒ c⁴e	[24]
8.	dcdbc ⇒ db	[10]
9.	c²dbc ⇒ d	[7]
10.	eb ⇒ dbc²e	[19]
11.	db² ⇒ c²e	[17]
12.	(db)² ⇒ e	[4]
13.	dbcdbd ⇒ dce	[18]
14.	(dbc)² ⇒ c²e	[14]
15.	ea ⇒ dcdb	[21]
16.	d²ba ⇒ c²db	[20]
17.	dcdba ⇒ d	[9]
18.	c²dba ⇒ c	[6]
19.	dbcdba ⇒ db	[13]
20.	ab ⇒ c	[2]

# ab:abababbba=ab reversed:dc/eb/a ab=c,cb=d,dbdb=e morph:2/1,2/0,4/1 ed=dcdce ec=dccce cb=d ddbd=ccdce dcdbd=cce ccdbd=db ddbc=cccce dcdbc=db ccdbc=d eb=dbcce dbb=cce dbdb=e dbcdbd=dce dbcdbc=cce ea=dcdb ddba=ccdb dcdba=d ccdba=c dbcdba=db ab=c

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#4303 ⟨a, b | abababbba=ab⟩

Contents

Properties

Rewriting system