#3485 ⟨
a
,
b
,
c
|
bb
=
aa
,
abc
=
c
⟩
Up:
Monoid enumeration
Prev:
#3484
⟨
a
,
b
,
c
|
bb
=
aa
,
abc
=
b
⟩
Next:
#3486
⟨
a
,
b
,
c
|
bb
=
aa
,
aca
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
ab
⋅
c
=
c
and 1 ⋅
c
=
c
, however
ab
≠ 1
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:
Right-to-left shortlex with
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒
b
2
[1]
2.
b
2
a
⇒
a
b
2
[3]
3.
abc
⇒
c
[2]
4.
b
3
c
⇒
ac
[4]
# abc:bb=aa,abc=c reversed:bac - - aa=bb bba=abb abc=c bbbc=ac