#18954 ⟨a, b | aab=a, bbbbab=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a⁵ = a and a ⋅ 1 = a, however a⁵ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁵ ⋅ a = a and 1 ⋅ a = a, however a⁵ ≠ 1

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:aab=a,bbbbab=a a/b - -
aaaaaa=a
ab=aaaaa
bbbba=aa

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

1 total

Σ	#	Presentation	Mapping
11	19496	⟨a, b \| aab=a, bbbba=aa⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	19152	⟨a, b \| aba=a, babbbb=a⟩	φ(a) = a, φ(b) = b