⟨a, b | aabbaabba=ba⟩

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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 = bbbbbba
Reduction order:
- Right-to-left 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.	ca³c ⇒ a(ac)²	[74]
2.	ca⁵c ⇒ a⁴cac	[71]
3.	a⁶cac ⇒ c	[82]
4.	ca³bc ⇒ a²cabc	[75]
5.	ca⁵bc ⇒ a⁴cabc	[79]
6.	a⁶cabc ⇒ bc	[88]
7.	ca⁷bc ⇒ bc	[83]
8.	ba ⇒ a⁸bc	[44]
9.	bcac ⇒ cabc	[91]
10.	ca³b²c ⇒ a²cab²c	[93]
11.	ca⁵b²c ⇒ a⁴cab²c	[96]
12.	a⁶cab²c ⇒ b²c	[94]
13.	ca⁷b²c ⇒ b²c	[84]
14.	ca⁹b²c ⇒ a²b²c	[86]
15.	bcabc ⇒ cab²c	[97]
16.	b³c ⇒ a(ac)²	[81]
17.	bcab²c ⇒ a(ac)³	[95]

# ab:aabbaabba=ba reversed:ca/b bbbbbba=c morph:7/0 caaac=aacac caaaaac=aaaacac aaaaaacac=c caaabc=aacabc caaaaabc=aaaacabc aaaaaacabc=bc caaaaaaabc=bc ba=aaaaaaaabc bcac=cabc caaabbc=aacabbc caaaaabbc=aaaacabbc aaaaaacabbc=bbc caaaaaaabbc=bbc caaaaaaaaabbc=aabbc bcabc=cabbc bbbc=aacac bcabbc=aacacac

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#4169 ⟨a, b | aabbaabba=ba⟩

Contents

Properties

Rewriting system