#3533 ⟨a, b | aa=1, babab=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ (ab)² = b² and b ⋅ b = b², however (ab)² ≠ b
Not right cancellative, because right multiplication by b is not injective:
- (ba)² ⋅ b = b² and b ⋅ b = b², however (ba)² ≠ b

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,babab=bb ab - -
aa=1
bbab=babb
babab=bb

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

5 total

Σ	#	Presentation	Mapping
11	27048	⟨a, b \| aa=1, aababab=bb⟩	φ(a) = a, φ(b) = b
11	27178	⟨a, b \| aa=1, baaabab=bb⟩	φ(a) = a, φ(b) = b
11	27637	⟨a, b \| aa=1, ababab=abb⟩	φ(a) = a, φ(b) = b
11	28253	⟨a, b \| aa=1, babab=aabb⟩	φ(a) = a, φ(b) = b
11	28257	⟨a, b \| aa=1, babab=baab⟩	φ(a) = a, φ(b) = b