⟨a, b | aabbbba=bbaa⟩

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

#	Rule	Proof
1.	ad ⇒ ea	[8]
2.	aed ⇒ da	[13]
3.	aca ⇒ e	[4]
4.	aeca ⇒ d	[11]
5.	ca² ⇒ d	[3]
6.	ace ⇒ eca	[6]
7.	aece ⇒ dca	[12]
8.	cae ⇒ dca	[7]
9.	cea ⇒ deca	[15]
10.	cd ⇒ dce	[17]
11.	ce² ⇒ dece	[18]
12.	ced ⇒ dedce	[19]
13.	cb ⇒ bc	[9]
14.	b²a² ⇒ ae	[5]
15.	b²ae ⇒ d	[10]
16.	b²ea ⇒ ae²ca	[16]
17.	b²d ⇒ dca	[14]
18.	b²e² ⇒ ae²ce	[20]
19.	b²ed ⇒ ae²dce	[21]
20.	b⁴ ⇒ c	[2]

# ab:aabbbba=bbaa reversed:a/ed/cb bbbb=c,caa=d,aca=e morph:4/0,3/0,3/0 ad=ea aed=da aca=e aeca=d caa=d ace=eca aece=dca cae=dca cea=deca cd=dce cee=dece ced=dedce cb=bc bbaa=ae bbae=d bbea=aeeca bbd=dca bbee=aeece bbed=aeedce bbbb=c

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#5277 ⟨a, b | aabbbba=bbaa⟩

Contents

Properties

Rewriting system