#4739 ⟨a, b | aabb=a, bbaa=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ac = a and a ⋅ 1 = a, however ac ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a²b ⋅ a = aba² and aba ⋅ a = aba², however a²b ≠ aba

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:aabb=a,bbaa=a bac bb=c morph:2/0
bb=c
cb=bc
ca=ac
aac=a
aaba=abaa
aabc=ab

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

2 total

Σ	#	Presentation	Mapping
11	13051	⟨a, b \| baa=aab, aabb=b⟩	φ(a) = b, φ(b) = a
11	13059	⟨a, b \| baa=aab, baab=b⟩	φ(a) = b, φ(b) = a