#5388 ⟨a, b | aab=ab, bba=ab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ba² = b²a and b ⋅ ba = b²a, however ba² ≠ ba
Not right cancellative, because right multiplication by a is not injective:
- b²a ⋅ a = b²a and b² ⋅ a = b²a, however b²a ≠ b²

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=ab,bba=ab reversed:b/a - -
bbbba=bba
ab=bba
bbaa=bba

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

5 total

Σ	#	Presentation	Mapping
11	16247	⟨a, b \| aab=ba, baab=ba⟩	φ(a) = b, φ(b) = a
11	16251	⟨a, b \| aab=ba, baba=ba⟩	φ(a) = b, φ(b) = a
11	16259	⟨a, b \| aab=ba, bbaa=ba⟩	φ(a) = b, φ(b) = a
11	16505	⟨a, b \| aab=ab, bba=aab⟩	φ(a) = a, φ(b) = b
11	16514	⟨a, b \| aab=ba, bba=aab⟩	φ(a) = b, φ(b) = a