#2578 ⟨a, b | aaa=1, abab=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = a²b² and a²b ⋅ b = a²b², however ba ≠ a²b

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:aaa=1,abab=bb reversed:a/b - -
aaa=1
bab=aabb
baabb=abbb

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

2 total

Σ	#	Presentation	Mapping
10	8051	⟨a, b \| aaa=1, aabb=bab⟩	φ(a) = a, φ(b) = b
11	22759	⟨a, b \| aaa=1, aabab=abb⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	22791	⟨a, b \| aaa=1, ababa=abb⟩	φ(a) = a, φ(b) = b