⟨a, b | abbaaab=babb⟩

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

#	Rule	Proof
1.	bc ⇒ ca³b	[6]
2.	b²ac ⇒ cab²	[3]
3.	ab²a³c ⇒ baca³b	[7]
4.	ab²a³b ⇒ bab²	[1]
5.	bab²a²c ⇒ cb(a³b)²	[12]
6.	b²ab² ⇒ c	[2]
7.	bab²a²bac ⇒ cba³bab²	[13]
8.	ab²a⁴b²a²c ⇒ bacb(a³b)²	[14]
9.	bab³a³c ⇒ ab²a²baca³b	[8]
10.	bab³a³b ⇒ ab²a²bab²	[4]
11.	ab²a⁴b²a²bac ⇒ bacba³bab²	[15]
12.	bab²a²bab² ⇒ cba³b	[10]
13.	bab³a⁴b²a²c ⇒ ab²a²bacb(a³b)²	[16]
14.	ab²a⁴b²a²bab² ⇒ bacba³b	[9]
15.	bab³a⁴b²a²bac ⇒ ab²a²bacba³bab²	[17]
16.	bab³a⁴b²a²bab² ⇒ ab²a²bacba³b	[11]

# ab:abbaaab=babb reversed:ac/b bbabb=c morph:5/1 bc=caaab bbac=cabb abbaaac=bacaaab abbaaab=babb babbaac=cbaaabaaab bbabb=c babbaabac=cbaaababb abbaaaabbaac=bacbaaabaaab babbbaaac=abbaabacaaab babbbaaab=abbaababb abbaaaabbaabac=bacbaaababb babbaababb=cbaaab babbbaaaabbaac=abbaabacbaaabaaab abbaaaabbaababb=bacbaaab babbbaaaabbaabac=abbaabacbaaababb babbbaaaabbaababb=abbaabacbaaab

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#5392 ⟨a, b | abbaaab=babb⟩

Contents

Properties

Rewriting system