#10739 ⟨a, b | aaab=baa, bbbb=1⟩

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a⁶⁶ = a² and a ⋅ a = a², however a⁶⁶ ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a⁶⁶ ⋅ a = a² and a ⋅ a = a², however a⁶⁶ ≠ a

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:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a⁶⁷ ⇒ a²	[20]
2.	a²ba ⇒ a³⁶b	[22]
3.	ba² ⇒ a³b	[1]
4.	a²b²a ⇒ a⁵³b²	[21]
5.	a²b³a ⇒ a⁴⁶b³	[14]
6.	b⁴ ⇒ 1	[2]

# ab:aaab=baa,bbbb=1 reversed:a/b - -
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=aa
aaba=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab
baa=aaab
aabba=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabb
aabbba=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbb
bbbb=1

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#10739 ⟨a, b | aaab=baa, bbbb=1⟩

Contents

Properties

Rewriting system