#3488 ⟨a, b, c | bb=aa, aca=c⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order

Rewriting system

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. d = aba
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(d) = deg(b) = 1, d < b; deg(c) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²d ⇒ da²	[12]
2.	ba³ ⇒ ad	[10]
3.	aba ⇒ d	[3]
4.	a²b ⇒ ba²	[5]
5.	d² ⇒ a⁶	[17]
6.	dab ⇒ a⁵	[9]
7.	bda ⇒ adb	[14]
8.	bad ⇒ a⁵	[11]
9.	abd ⇒ dba	[4]
10.	b² ⇒ a²	[1]
11.	bdba² ⇒ adbab	[16]
12.	aca ⇒ c	[2]
13.	acd ⇒ cba	[7]
14.	acba² ⇒ cab	[8]
15.	bc ⇒ adca³	[19]
16.	bac ⇒ adca²	[18]
17.	ba²c ⇒ adca	[13]
18.	bdc ⇒ (ad)²ca⁴	[20]
19.	ac² ⇒ c²a	[6]

# abc:bb=aa,aca=c a/db/c aba=d morph:3/2
aad=daa
baaa=ad
aba=d
aab=baa
dd=aaaaaa
dab=aaaaa
bda=adb
bad=aaaaa
abd=dba
bb=aa
bdbaa=adbab
aca=c
acd=cba
acbaa=cab
bc=adcaaa
bac=adcaa
baac=adca
bdc=adadcaaaa
acc=cca