#20884 ⟨a, b | bb=aa, aaaaa=aa⟩

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 ⋅ a⁴ = a² and a ⋅ a = a², however a⁴ ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a⁴ ⋅ a = a² and a ⋅ a = a², however a⁴ ≠ 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,aaaaa=aa ab - -
bb=aa
baa=aab
aaba=aaab
aaaaa=aa

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

17 total

Σ	#	Presentation	Mapping
11	20886	⟨a, b \| bb=aa, aaaaa=bb⟩	φ(a) = a, φ(b) = b
11	20887	⟨a, b \| bb=aa, aaaab=aa⟩	φ(a) = b, φ(b) = a
11	20890	⟨a, b \| bb=aa, aaaab=bb⟩	φ(a) = b, φ(b) = a
11	20891	⟨a, b \| bb=aa, aaaba=aa⟩	φ(a) = b, φ(b) = a
11	20894	⟨a, b \| bb=aa, aaaba=bb⟩	φ(a) = b, φ(b) = a
11	20895	⟨a, b \| bb=aa, aaabb=aa⟩	φ(a) = a, φ(b) = b
11	20898	⟨a, b \| bb=aa, aaabb=bb⟩	φ(a) = a, φ(b) = b
11	20899	⟨a, b \| bb=aa, aabaa=aa⟩	φ(a) = b, φ(b) = a
11	20901	⟨a, b \| bb=aa, aabaa=bb⟩	φ(a) = b, φ(b) = a
11	20902	⟨a, b \| bb=aa, aabab=aa⟩	φ(a) = a, φ(b) = b
11	20905	⟨a, b \| bb=aa, aabab=bb⟩	φ(a) = a, φ(b) = b
11	20906	⟨a, b \| bb=aa, aabba=aa⟩	φ(a) = a, φ(b) = b
11	20909	⟨a, b \| bb=aa, aabba=bb⟩	φ(a) = a, φ(b) = b
11	20910	⟨a, b \| bb=aa, abaab=aa⟩	φ(a) = a, φ(b) = b
11	20913	⟨a, b \| bb=aa, abaab=bb⟩	φ(a) = a, φ(b) = b
11	20917	⟨a, b \| bb=aa, abbba=aa⟩	φ(a) = b, φ(b) = a
11	20919	⟨a, b \| bb=aa, abbba=bb⟩	φ(a) = b, φ(b) = a