#14502 ⟨a, b | aaab=b, abbba=b⟩

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b²⁴ = b and b ⋅ 1 = b, however b²⁴ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b²⁴ ⋅ b = b and 1 ⋅ b = b, however b²⁴ ≠ 1

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(b) = 0; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b²⁵ ⇒ b	[12]
2.	bab²⁴ ⇒ ba	[13]
3.	b⁴a ⇒ ab⁴	[4]
4.	a²b ⇒ b³a	[3]
5.	ab²a ⇒ bab²¹	[9]
6.	ab³a ⇒ b	[2]
7.	ba² ⇒ ab³	[14]
8.	(ba)² ⇒ abab⁷	[8]

# ab:aaab=b,abbba=b b/a - -
bbbbbbbbbbbbbbbbbbbbbbbbb=b
babbbbbbbbbbbbbbbbbbbbbbbb=ba
bbbba=abbbb
aab=bbba
abba=babbbbbbbbbbbbbbbbbbbbb
abbba=b
baa=abbb
baba=ababbbbbbb

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#14502 ⟨a, b | aaab=b, abbba=b⟩

Contents

Properties

Rewriting system