#27079 ⟨a, b | aa=1, aabbbba=bb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b²a and b ⋅ ba = b²a, however b³ ≠ ba

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:aa=1,aabbbba=bb ba - -
aa=1
bbbb=bba
bbab=bbba

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

5 total

Σ	#	Presentation	Mapping
11	27610	⟨a, b \| aa=1, aabbbb=bba⟩	φ(a) = a, φ(b) = b
11	27685	⟨a, b \| aa=1, abbbba=abb⟩	φ(a) = a, φ(b) = b
11	27724	⟨a, b \| aa=1, baabbb=bba⟩	φ(a) = a, φ(b) = b
11	28123	⟨a, b \| aa=1, aabba=bbbb⟩	φ(a) = a, φ(b) = b
11	28214	⟨a, b \| aa=1, abbbb=abba⟩	φ(a) = a, φ(b) = b