#2080 ⟨a, b | aab=b, bbba=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 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=b,bbba=a ab - -
aaa=a
aab=b
bbba=a
bbbb=b

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

5 total

Σ	#	Presentation	Mapping
11	18988	⟨a, b \| aab=b, aabbba=a⟩	φ(a) = a, φ(b) = b
11	19016	⟨a, b \| aab=b, abbbaa=a⟩	φ(a) = a, φ(b) = b
11	19036	⟨a, b \| aab=b, baabba=a⟩	φ(a) = a, φ(b) = b
11	19060	⟨a, b \| aab=b, bbaaba=a⟩	φ(a) = a, φ(b) = b
11	19072	⟨a, b \| aab=b, bbbaaa=a⟩	φ(a) = a, φ(b) = b