#3659 ⟨a, b | aa=1, abbb=bbb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- ab² ⋅ b = b³ and b² ⋅ b = b³, however ab² ≠ b²

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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	ab³ ⇒ b³	[2]

# ab:aa=1,abbb=bbb ab - -
aa=1
abbb=bbb

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

5 total

Σ	#	Presentation	Mapping
11	27557	⟨a, b \| aa=1, aaabbb=bbb⟩	φ(a) = a, φ(b) = b
11	27633	⟨a, b \| aa=1, abaabb=bbb⟩	φ(a) = a, φ(b) = b
11	27665	⟨a, b \| aa=1, abbaab=bbb⟩	φ(a) = a, φ(b) = b
11	28131	⟨a, b \| aa=1, aabbb=abbb⟩	φ(a) = a, φ(b) = b
11	28241	⟨a, b \| aa=1, baabb=abbb⟩	φ(a) = a, φ(b) = b

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

4 total

Σ	#	Presentation	Mapping
11	27603	⟨a, b \| aa=1, aabbba=bbb⟩	φ(a) = a, φ(b) = b
11	28138	⟨a, b \| aa=1, aabbb=bbba⟩	φ(a) = a, φ(b) = b
11	28204	⟨a, b \| aa=1, abbba=abbb⟩	φ(a) = a, φ(b) = b
11	28248	⟨a, b \| aa=1, baabb=bbba⟩	φ(a) = a, φ(b) = b