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

#	Rule	Proof
1.	c²aba² ⇒ c	[18]
2.	cac²b ⇒ c²abc	[23]
3.	(ca)²b ⇒ c²aba	[16]
4.	cb² ⇒ c²abac	[7]
5.	cbaba²c ⇒ cb	[9]
6.	cbaba³ ⇒ ab	[15]
7.	cbcaba² ⇒ cb	[19]
8.	cbac²b ⇒ cbcabc	[24]
9.	cbacab ⇒ cbcaba	[20]
10.	ab² ⇒ c	[2]
11.	abc²b ⇒ cbabc	[12]
12.	abcab ⇒ c(ba)²	[8]
13.	abac²b ⇒ c(ba)²c	[27]
14.	abacab ⇒ cbaba²	[14]
15.	c²abcb ⇒ cac³abac	[25]
16.	c²(ab)² ⇒ cac²	[21]
17.	c²abacb ⇒ cbcabac	[11]
18.	cbabcb ⇒ abc³abac	[13]
19.	cb(ab)² ⇒ abc²	[10]
20.	c(ba)²cb ⇒ abac³abac	[28]
21.	cbaba²b ⇒ abac²	[17]
22.	cbcabcb ⇒ cbac³abac	[26]
23.	cbc(ab)² ⇒ cbac²	[22]
24.	cbcabacb ⇒ (c²aba)²c	[29]

# ab:abaabbaba=ab ca/b abb=c morph:3/0 ccabaa=c caccb=ccabc cacab=ccaba cbb=ccabac cbabaac=cb cbabaaa=ab cbcabaa=cb cbaccb=cbcabc cbacab=cbcaba abb=c abccb=cbabc abcab=cbaba abaccb=cbabac abacab=cbabaa ccabcb=cacccabac ccabab=cacc ccabacb=cbcabac cbabcb=abcccabac cbabab=abcc cbabacb=abacccabac cbabaab=abacc cbcabcb=cbacccabac cbcabab=cbacc cbcabacb=ccabaccabac

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#4276 ⟨a, b | abaabbaba=ab⟩

Contents

Properties

Rewriting system