#2200 ⟨a, b | ab=aa, bbaa=a⟩

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 a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a and 1 ⋅ a = a, however a³ ≠ 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:ab=aa,bbaa=a ab - -
ab=aa
bba=aaa
aaaa=a

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

10 total

Σ	#	Presentation	Mapping
9	2202	⟨a, b \| ab=aa, bbab=a⟩	φ(a) = a, φ(b) = b
10	4669	⟨a, b \| aaab=a, bbaa=a⟩	φ(a) = a, φ(b) = b
10	4717	⟨a, b \| aaba=b, aabb=b⟩	φ(a) = b, φ(b) = a
10	4724	⟨a, b \| aaba=b, baab=b⟩	φ(a) = b, φ(b) = a
10	4726	⟨a, b \| aaba=b, baba=b⟩	φ(a) = b, φ(b) = a
10	4729	⟨a, b \| aaba=b, bbaa=b⟩	φ(a) = b, φ(b) = a
11	12904	⟨a, b \| aab=aaa, bbaa=a⟩	φ(a) = a, φ(b) = b
11	13017	⟨a, b \| abb=aba, aaba=b⟩	φ(a) = b, φ(b) = a
11	13019	⟨a, b \| abb=aba, aabb=b⟩	φ(a) = b, φ(b) = a
11	13038	⟨a, b \| abb=aba, bbab=a⟩	φ(a) = a, φ(b) = b