#1063 ⟨
a
,
b
,
c
|
ab
=
c
,
bc
=
ab
⟩
Up:
Monoid enumeration
Prev:
#1062
⟨
a
,
b
,
c
|
ab
=
c
,
bb
=
ab
⟩
Next:
#1072
⟨
a
,
b
,
c
|
aa
=1,
ababc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
b
⋅
c
=
c
and 1 ⋅
c
=
c
, however
b
≠ 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:
Left-to-right shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
c
2
[3]
2.
ab
⇒
c
[1]
3.
bc
⇒
c
[2]
# abc:ab=c,bc=ab cab - - ac=cc ab=c bc=c