#7138 ⟨a, b | bb=aa, aaaa=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a² and a ⋅ a = a², however a³ ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a² and a ⋅ a = a², however a³ ≠ a

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=aa ab - -
bb=aa
baa=aab
aaaa=aa

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

4 total

Σ	#	Presentation	Mapping
10	7140	⟨a, b \| bb=aa, aaaa=bb⟩	φ(a) = a, φ(b) = b
10	7149	⟨a, b \| bb=aa, aabb=aa⟩	φ(a) = a, φ(b) = b
10	7155	⟨a, b \| bb=aa, abba=aa⟩	φ(a) = a, φ(b) = b
10	7157	⟨a, b \| bb=aa, abba=bb⟩	φ(a) = a, φ(b) = b