#21085 ⟨a, b | bb=aa, aaaa=aab⟩

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 = a²b and a ⋅ ab = a²b, however a³ ≠ ab

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

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

5 total

Σ	#	Presentation	Mapping
11	21089	⟨a, b \| bb=aa, aaaa=bbb⟩	φ(a) = a, φ(b) = b
11	21107	⟨a, b \| bb=aa, aabb=aab⟩	φ(a) = a, φ(b) = b
11	21109	⟨a, b \| bb=aa, aabb=baa⟩	φ(a) = a, φ(b) = b
11	21115	⟨a, b \| bb=aa, abba=aab⟩	φ(a) = a, φ(b) = b
11	21119	⟨a, b \| bb=aa, abba=bbb⟩	φ(a) = a, φ(b) = b