#8808 ⟨a, b | ab=a, bbaaaa=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, however b² ≠ 1

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

# ab:ab=a,bbaaaa=a ab - -
ab=a
bba=a
aaaa=a

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

9 total

Σ	#	Presentation	Mapping
11	15720	⟨a, b \| aab=ba, babbb=b⟩	φ(a) = b, φ(b) = a
11	15728	⟨a, b \| aab=ba, bbabb=b⟩	φ(a) = b, φ(b) = a
11	15732	⟨a, b \| aab=ba, bbbab=b⟩	φ(a) = b, φ(b) = a
11	15734	⟨a, b \| aab=ba, bbbba=b⟩	φ(a) = b, φ(b) = a
11	24526	⟨a, b \| ab=a, bbaaaab=a⟩	φ(a) = a, φ(b) = b
11	24528	⟨a, b \| ab=a, bbaaaba=a⟩	φ(a) = a, φ(b) = b
11	24532	⟨a, b \| ab=a, bbaabaa=a⟩	φ(a) = a, φ(b) = b
11	24540	⟨a, b \| ab=a, bbabaaa=a⟩	φ(a) = a, φ(b) = b
11	25053	⟨a, b \| ab=a, bbaaaa=ab⟩	φ(a) = a, φ(b) = b