#5219 ⟨a, b | aab=bb, bbba=b⟩

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 b is not injective:
- b ⋅ b⁵ = b and b ⋅ 1 = b, however b⁵ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = b² and b ⋅ b = b², however a² ≠ 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:aab=bb,bbba=b b/a - -
bbbbbb=b
ba=bbbb
aab=bb

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

5 total

Σ	#	Presentation	Mapping
11	14459	⟨a, b \| aaab=a, bbaab=a⟩	φ(a) = b, φ(b) = a
11	14461	⟨a, b \| aaab=a, bbaba=a⟩	φ(a) = b, φ(b) = a
11	14587	⟨a, b \| aaba=a, bbaab=a⟩	φ(a) = b, φ(b) = a
11	15750	⟨a, b \| aab=bb, aabba=b⟩	φ(a) = a, φ(b) = b
11	15774	⟨a, b \| aab=bb, baaba=b⟩	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	14575	⟨a, b \| aaba=a, baabb=a⟩	φ(a) = b, φ(b) = a
11	15762	⟨a, b \| aab=bb, abbaa=b⟩	φ(a) = a, φ(b) = b