#7796 ⟨a, b | aaa=1, abbab=bb⟩

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 ⋅ b⁸ = b³ and b ⋅ b² = b³, however b⁸ ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- ab²a ⋅ b = b² and b ⋅ b = b², however ab²a ≠ 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:aaa=1,abbab=bb b/a - -
bbbbbbbbb=bbb
babbbbbbbb=babb
bbbab=abbbb
aabb=bbab
ababb=babbbbbb
abbab=bb
bbabab=abb
aaa=1

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

1 total

Σ	#	Presentation	Mapping
11	23317	⟨a, b \| aaa=1, bbaa=babb⟩	φ(a) = a, φ(b) = b