⟨a, b | aabbba=baa⟩

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

#	Rule	Proof
1.	a²ed ⇒ ea	[17]
2.	aea(ed)² ⇒ da	[25]
3.	ace ⇒ eca	[10]
4.	cd ⇒ dce	[8]
5.	ca² ⇒ aeca	[11]
6.	cea ⇒ aedeca	[28]
7.	cae ⇒ aece	[14]
8.	ce² ⇒ aedece	[29]
9.	cad ⇒ aedce	[21]
10.	ced ⇒ a(ed)²ce	[30]
11.	a(ca)² ⇒ e	[4]
12.	a(ec)²a ⇒ d	[15]
13.	ae(ce)² ⇒ d(ca)²	[16]
14.	bd ⇒ dca	[7]
15.	ba² ⇒ a²ca	[5]
16.	bea ⇒ a²deca	[27]
17.	bae ⇒ aeca	[12]
18.	be² ⇒ a²dece	[31]
19.	bad ⇒ a²dce	[20]
20.	bed ⇒ a²dedce	[32]
21.	bc ⇒ cb	[6]
22.	b³ ⇒ c	[2]

# ab:aabbba=baa reversed:aed/c/b bbb=c,ccaa=d,acaca=e morph:3/0,4/0,5/0 aaed=ea aeaeded=da ace=eca cd=dce caa=aeca cea=aedeca cae=aece cee=aedece cad=aedce ced=aededce acaca=e aececa=d aecece=dcaca bd=dca baa=aaca bea=aadeca bae=aeca bee=aadece bad=aadce bed=aadedce bc=cb bbb=c

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#1099 ⟨a, b | aabbba=baa⟩

Contents

Properties

Rewriting system