#4378 ⟨
a
,
b
,
c
|
aba
=1,
aaca
=
c
⟩
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Monoid enumeration
Prev:
#4375
⟨
a
,
b
,
c
|
aba
=1,
aabc
=
c
⟩
Next:
#4384
⟨
a
,
b
,
c
|
aba
=1,
aacc
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite 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
Reduction order:
Left-to-right shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
bc
⇒
ca
[5]
2.
ba
⇒
ab
[3]
3.
a
2
c
⇒
cab
[4]
4.
a
2
b
⇒ 1
[6]
# abc:aba=1,aaca=c cab - - bc=ca ba=ab aac=cab aab=1