#3399 ⟨a, b | aa=1, babbab=b⟩

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 b is not injective:
- b ⋅ abab² = b and b ⋅ 1 = b, however abab² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b(ab)² ⋅ b = b and 1 ⋅ b = b, however b(ab)² ≠ 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:aa=1,babbab=b ab - -
aa=1
bbab=babb
bababb=b

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

5 total

Σ	#	Presentation	Mapping
11	26525	⟨a, b \| aa=1, aababbab=b⟩	φ(a) = a, φ(b) = b
11	26653	⟨a, b \| aa=1, baaabbab=b⟩	φ(a) = a, φ(b) = b
11	26673	⟨a, b \| aa=1, babaabab=b⟩	φ(a) = a, φ(b) = b
11	27119	⟨a, b \| aa=1, ababbab=ab⟩	φ(a) = a, φ(b) = b
11	27735	⟨a, b \| aa=1, babbab=aab⟩	φ(a) = a, φ(b) = b