#8061 ⟨a, b | aaa=1, abab=bbb⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ba² has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b¹⁰ = b⁵ and b ⋅ b⁴ = b⁵, however b¹⁰ ≠ b⁴
Not right cancellative, because right multiplication by b is not injective:
- aba ⋅ b = b³ and b² ⋅ b = b³, however aba ≠ b²

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:aaa=1,abab=bbb b/a - -
bbbbbbbbbbb=bbbbb
babbbbbbbbb=babbb
bbabbbbbbbb=bbabb
bbbab=abbbb
aabbb=bab
abab=bbb
abbabb=bbabbbb
babbab=abbbbbb
aaa=1

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

1 total

Σ	#	Presentation	Mapping
11	22777	⟨a, b \| aaa=1, aabbb=bab⟩	φ(a) = a, φ(b) = b