#3196 ⟨
a
,
b
,
c
|
ba
=
ab
,
cacc
=1⟩
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Monoid enumeration
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#3193
⟨
a
,
b
,
c
|
ba
=
ab
,
accc
=1⟩
Next:
#3197
⟨
a
,
b
,
c
|
ba
=
ab
,
cccc
=1⟩
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
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
ac
[7]
2.
ba
⇒
ab
[1]
3.
a
c
3
⇒ 1
[4]
4.
b
c
3
⇒
c
3
b
[10]
# abc:ba=ab,cacc=1 acb - - ca=ac ba=ab accc=1 bccc=cccb