#5365 ⟨a, b | aab=aa, bab=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab² = bab and b ⋅ ab = bab, however ab² ≠ ab
Not right cancellative, because right multiplication by b is not injective:
- bab ⋅ b = bab and ba ⋅ b = bab, however bab ≠ ba

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=aa,bab=aa b/a - -
babb=bab
aa=bab
baba=abab

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

1 total

Σ	#	Presentation	Mapping
11	16495	⟨a, b \| aab=aa, bab=aab⟩	φ(a) = a, φ(b) = b

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

2 total

Σ	#	Presentation	Mapping
11	16447	⟨a, b \| aba=bb, aaba=bb⟩	φ(a) = b, φ(b) = a
11	16546	⟨a, b \| aba=bb, abb=aba⟩	φ(a) = b, φ(b) = a