#21084 ⟨a, b | bb=aa, aaaa=aaa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a³ and a ⋅ a² = a³, however a³ ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a³ and a² ⋅ a = a³, however a³ ≠ 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:bb=aa,aaaa=aaa ab - -
bb=aa
baa=aab
aaaa=aaa
aaba=aaab

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

4 total

Σ	#	Presentation	Mapping
11	21087	⟨a, b \| bb=aa, aaaa=abb⟩	φ(a) = a, φ(b) = b
11	21106	⟨a, b \| bb=aa, aabb=aaa⟩	φ(a) = a, φ(b) = b
11	21114	⟨a, b \| bb=aa, abba=aaa⟩	φ(a) = a, φ(b) = b
11	21117	⟨a, b \| bb=aa, abba=abb⟩	φ(a) = a, φ(b) = b