#13004 ⟨a, b | abb=aab, abaa=b⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b and b ⋅ 1 = b, however b³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b² and b ⋅ b = b², however a ≠ b

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:abb=aab,abaa=b ba - -
ab=bb
baa=bbb
bbbb=b

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

11 total

Σ	#	Presentation	Mapping
11	13028	⟨a, b \| abb=aba, baaa=a⟩	φ(a) = b, φ(b) = a
11	13032	⟨a, b \| abb=aba, baba=a⟩	φ(a) = b, φ(b) = a
11	13034	⟨a, b \| abb=aba, babb=a⟩	φ(a) = b, φ(b) = a
11	13068	⟨a, b \| baa=abb, aaba=a⟩	φ(a) = b, φ(b) = a
11	13070	⟨a, b \| baa=abb, aabb=a⟩	φ(a) = b, φ(b) = a
11	13071	⟨a, b \| baa=abb, aabb=b⟩	φ(a) = a, φ(b) = b
11	13072	⟨a, b \| baa=abb, abaa=a⟩	φ(a) = b, φ(b) = a
11	13073	⟨a, b \| baa=abb, abaa=b⟩	φ(a) = a, φ(b) = b
11	13075	⟨a, b \| baa=abb, abab=b⟩	φ(a) = a, φ(b) = b
11	13076	⟨a, b \| baa=abb, abba=a⟩	φ(a) = b, φ(b) = a
11	13079	⟨a, b \| baa=abb, abbb=b⟩	φ(a) = a, φ(b) = b