#21090 ⟨a, b | bb=aa, aaab=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 ⋅ a²b = a³ and a ⋅ a² = a³, however a²b ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- a²b ⋅ a = a³ and a² ⋅ a = a³, however a²b ≠ 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,aaab=aaa ab - -
bb=aa
baa=aab
aaab=aaa
aaba=aaa
aaaaa=aaa

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

11 total

Σ	#	Presentation	Mapping
11	21091	⟨a, b \| bb=aa, aaab=aab⟩	φ(a) = b, φ(b) = a
11	21093	⟨a, b \| bb=aa, aaab=abb⟩	φ(a) = a, φ(b) = b
11	21094	⟨a, b \| bb=aa, aaab=baa⟩	φ(a) = b, φ(b) = a
11	21096	⟨a, b \| bb=aa, aaab=bba⟩	φ(a) = a, φ(b) = b
11	21097	⟨a, b \| bb=aa, aaab=bbb⟩	φ(a) = b, φ(b) = a
11	21098	⟨a, b \| bb=aa, aaba=aaa⟩	φ(a) = a, φ(b) = b
11	21099	⟨a, b \| bb=aa, aaba=aab⟩	φ(a) = b, φ(b) = a
11	21101	⟨a, b \| bb=aa, aaba=abb⟩	φ(a) = a, φ(b) = b
11	21102	⟨a, b \| bb=aa, aaba=baa⟩	φ(a) = b, φ(b) = a
11	21104	⟨a, b \| bb=aa, aaba=bba⟩	φ(a) = a, φ(b) = b
11	21105	⟨a, b \| bb=aa, aaba=bbb⟩	φ(a) = b, φ(b) = a