#2081 ⟨a, b | aab=b, bbba=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 ⋅ b⁴ = b and b ⋅ 1 = b, however b⁴ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = b and 1 ⋅ b = b, 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,bbba=b b/a - -
bbbbb=b
ba=bbb
aab=b

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

7 total

Σ	#	Presentation	Mapping
11	12401	⟨a, b \| aaba=ba, bbba=b⟩	φ(a) = a, φ(b) = b
11	18989	⟨a, b \| aab=b, aabbba=b⟩	φ(a) = a, φ(b) = b
11	19037	⟨a, b \| aab=b, baabba=b⟩	φ(a) = a, φ(b) = b
11	19045	⟨a, b \| aab=b, bababa=b⟩	φ(a) = a, φ(b) = b
11	19061	⟨a, b \| aab=b, bbaaba=b⟩	φ(a) = a, φ(b) = b
11	19561	⟨a, b \| aab=b, abbba=ab⟩	φ(a) = a, φ(b) = b
11	20161	⟨a, b \| aab=b, bbba=aab⟩	φ(a) = a, φ(b) = b

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

3 total

Σ	#	Presentation	Mapping
11	12438	⟨a, b \| aabb=aa, baaa=a⟩	φ(a) = b, φ(b) = a
11	19017	⟨a, b \| aab=b, abbbaa=b⟩	φ(a) = a, φ(b) = b
11	19617	⟨a, b \| aab=b, bbbaa=ab⟩	φ(a) = a, φ(b) = b