#14493 ⟨a, b | aaab=b, ababa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba² 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:aaab=b,ababa=a ab - -
aaaa=a
aaab=b
baba=aaa
babb=aab

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

1 total

Σ	#	Presentation	Mapping
11	14513	⟨a, b \| aaab=b, babaa=a⟩	φ(a) = a, φ(b) = b