#19494 ⟨a, b | aab=a, bbbab=ba⟩

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 ⋅ a³ = a and a ⋅ 1 = a, however a³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a and 1 ⋅ a = a, however a³ ≠ 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,bbbab=ba a/b - -
aaaa=a
ab=aaa
bbba=baa

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

1 total

Σ	#	Presentation	Mapping
11	20036	⟨a, b \| aab=a, bbba=baa⟩	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	19695	⟨a, b \| aba=a, babbb=ab⟩	φ(a) = a, φ(b) = b