#21016 ⟨a, b | ab=aa, bbaa=aaa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- b²a ⋅ a = a³ and a² ⋅ a = a³, however b²a ≠ a²

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=aa,bbaa=aaa ab - -
ab=aa
bbaa=aaa
aaaaa=aaaa

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

7 total

Σ	#	Presentation	Mapping
11	21017	⟨a, b \| ab=aa, bbaa=aab⟩	φ(a) = a, φ(b) = b
11	21018	⟨a, b \| ab=aa, bbaa=aba⟩	φ(a) = a, φ(b) = b
11	21019	⟨a, b \| ab=aa, bbaa=abb⟩	φ(a) = a, φ(b) = b
11	21024	⟨a, b \| ab=aa, bbab=aaa⟩	φ(a) = a, φ(b) = b
11	21025	⟨a, b \| ab=aa, bbab=aab⟩	φ(a) = a, φ(b) = b
11	21026	⟨a, b \| ab=aa, bbab=aba⟩	φ(a) = a, φ(b) = b
11	21027	⟨a, b \| ab=aa, bbab=abb⟩	φ(a) = a, φ(b) = b