#7206 ⟨
a
,
b
|
bb
=
aa
,
bab
=
aba
⟩
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Monoid enumeration
Prev:
#7200
⟨
a
,
b
|
bb
=
aa
,
abb
=
aaa
⟩
Next:
#7249
⟨
a
,
b
|
aaa
=1,
ababbbb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
⇒
a
2
[1]
2.
b
a
2
⇒
a
2
b
[3]
3.
bab
⇒
aba
[2]
# ab:bb=aa,bab=aba ab - - bb=aa baa=aab bab=aba