#48 ⟨
a
,
b
,
c
|
bb
=
aa
,
cc
=1⟩
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Monoid enumeration
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#47
⟨
a
,
b
,
c
|
bb
=
aa
,
bc
=1⟩
Next:
#49
⟨
a
,
b
,
c
|
bb
=
ac
,
bc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 6
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
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
⇒
a
2
[1]
2.
c
2
⇒ 1
[2]
3.
b
a
2
⇒
a
2
b
[3]
# abc:bb=aa,cc=1 abc - - bb=aa cc=1 baa=aab