#5106 ⟨a, b | aab=aa, abba=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b²a = a and a ⋅ 1 = a, however b²a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ab² ⋅ a = a and 1 ⋅ a = a, however ab² ≠ 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:aab=aa,abba=a ab - -
aaa=aa
aab=aa
abba=a

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

1 total

Σ	#	Presentation	Mapping
11	12222	⟨a, b \| aaab=aa, abba=a⟩	φ(a) = a, φ(b) = b