#3523 ⟨a, b | aa=1, abbbb=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = ab² and ab ⋅ b = ab², however b³ ≠ ab

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,abbbb=bb ab - -
aa=1
babb=abbb
bbbb=abb

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

15 total

Σ	#	Presentation	Mapping
9	3677	⟨a, b \| aa=1, bbbb=abb⟩	φ(a) = a, φ(b) = b
11	27029	⟨a, b \| aa=1, aaabbbb=bb⟩	φ(a) = a, φ(b) = b
11	27106	⟨a, b \| aa=1, abaabbb=bb⟩	φ(a) = a, φ(b) = b
11	27117	⟨a, b \| aa=1, abababb=bb⟩	φ(a) = a, φ(b) = b
11	27137	⟨a, b \| aa=1, abbaabb=bb⟩	φ(a) = a, φ(b) = b
11	27152	⟨a, b \| aa=1, abbbaab=bb⟩	φ(a) = a, φ(b) = b
11	27607	⟨a, b \| aa=1, aabbbb=abb⟩	φ(a) = a, φ(b) = b
11	27721	⟨a, b \| aa=1, baabbb=abb⟩	φ(a) = a, φ(b) = b
11	27729	⟨a, b \| aa=1, bababb=abb⟩	φ(a) = a, φ(b) = b
11	27751	⟨a, b \| aa=1, bbaabb=abb⟩	φ(a) = a, φ(b) = b
11	28081	⟨a, b \| aa=1, aaabb=bbbb⟩	φ(a) = a, φ(b) = b
11	28155	⟨a, b \| aa=1, abaab=bbbb⟩	φ(a) = a, φ(b) = b
11	28211	⟨a, b \| aa=1, abbbb=aabb⟩	φ(a) = a, φ(b) = b
11	28217	⟨a, b \| aa=1, abbbb=baab⟩	φ(a) = a, φ(b) = b
11	28220	⟨a, b \| aa=1, abbbb=bbaa⟩	φ(a) = a, φ(b) = b