#4447 ⟨
a
,
b
,
c
|
aba
=1,
bbcb
=
c
⟩
Up:
Monoid enumeration
Prev:
#4444
⟨
a
,
b
,
c
|
aba
=1,
bbbc
=
c
⟩
Next:
#4450
⟨
a
,
b
,
c
|
aba
=1,
bbcc
=
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 recursive path with deg(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[3]
2.
a
2
b
⇒ 1
[6]
3.
a
2
c
⇒
bcb
[8]
4.
b
2
c
⇒
c
a
2
[5]
# abc:aba=1,bbcb=c ab/c - - ba=ab aab=1 aac=bcb bbc=caa