#27647 ⟨a, b | aa=1, ababba=bab⟩

Properties

Sum of relation sides is 11
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:aa=1,ababba=bab ab - -
aa=1
baba=abab
babb=bab
bbab=bab

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

3 total

Σ	#	Presentation	Mapping
11	28164	⟨a, b \| aa=1, ababa=babb⟩	φ(a) = a, φ(b) = b
11	28176	⟨a, b \| aa=1, ababb=baba⟩	φ(a) = a, φ(b) = b
11	28192	⟨a, b \| aa=1, abbab=baba⟩	φ(a) = a, φ(b) = b