#1257 ⟨a, b | aa=1, bbb=bab⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab = b³ and b ⋅ b² = b³, however ab ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = b³ and b² ⋅ b = b³, however ba ≠ 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.	bab ⇒ b³	[2]

# ab:aa=1,bbb=bab ba - -
aa=1
bab=bbb

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

5 total

Σ	#	Presentation	Mapping
10	10243	⟨a, b \| aa=1, aabab=bbb⟩	φ(a) = a, φ(b) = b
10	10257	⟨a, b \| aa=1, aabbb=bab⟩	φ(a) = a, φ(b) = b
10	10309	⟨a, b \| aa=1, baaab=bbb⟩	φ(a) = a, φ(b) = b
10	10315	⟨a, b \| aa=1, baabb=bab⟩	φ(a) = a, φ(b) = b
10	10496	⟨a, b \| aa=1, abbb=abab⟩	φ(a) = a, φ(b) = b