#5548 ⟨
a
,
b
,
c
|
ab
=
c
,
acca
=
c
⟩
Up:
Monoid enumeration
Prev:
#5546
⟨
a
,
b
,
c
|
ab
=
c
,
acca
=
a
⟩
Next:
#5549
⟨
a
,
b
,
c
|
ab
=
c
,
accb
=
a
⟩
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 recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
c
2
a
⇒
c
[2]
2.
c
3
a
⇒
a
c
3
[4]
3.
ab
⇒
c
[1]
4.
cb
⇒
a
c
3
[3]
# abc:ab=c,acca=c ac/b - - acca=c ccca=accc ab=c cb=accc