#596 ⟨a, b | aab=b, bab=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 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=b,bab=a ab - -
aaa=a
aab=b
baa=b
bab=a

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

2 total

Σ	#	Presentation	Mapping
10	6392	⟨a, b \| aab=b, aabab=a⟩	φ(a) = a, φ(b) = b
10	6416	⟨a, b \| aab=b, baaab=a⟩	φ(a) = a, φ(b) = b