#5201 ⟨a, b | aab=bb, abab=b⟩

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 ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b and 1 ⋅ b = b, however b² ≠ 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=bb,abab=b ab - -
aab=bb
bab=abb
bbb=b

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

4 total

Σ	#	Presentation	Mapping
11	12258	⟨a, b \| aaab=ab, baba=a⟩	φ(a) = b, φ(b) = a
11	12384	⟨a, b \| aaba=ba, abba=a⟩	φ(a) = b, φ(b) = a
11	12392	⟨a, b \| aaba=ba, baba=a⟩	φ(a) = b, φ(b) = a
11	12396	⟨a, b \| aaba=ba, bbaa=a⟩	φ(a) = b, φ(b) = a