#2077 ⟨a, b | aab=b, bbaa=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b = b and b ⋅ 1 = b, however b ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b ⋅ b = b and 1 ⋅ b = b, however b ≠ 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,bbaa=b ab - -
bb=b
aab=b
baa=b

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

5 total

Σ	#	Presentation	Mapping
11	12397	⟨a, b \| aaba=ba, bbaa=b⟩	φ(a) = a, φ(b) = b
11	18985	⟨a, b \| aab=b, aabbaa=b⟩	φ(a) = a, φ(b) = b
11	19033	⟨a, b \| aab=b, baabaa=b⟩	φ(a) = a, φ(b) = b
11	19553	⟨a, b \| aab=b, abbaa=ab⟩	φ(a) = a, φ(b) = b
11	20145	⟨a, b \| aab=b, bbaa=aab⟩	φ(a) = a, φ(b) = b

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

2 total

Σ	#	Presentation	Mapping
11	12446	⟨a, b \| aabb=aa, bbaa=a⟩	φ(a) = b, φ(b) = a
11	14713	⟨a, b \| aabb=a, bbaaa=a⟩	φ(a) = b, φ(b) = a