#8074 ⟨a, b | aaa=1, abbb=bba⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b²⁰ = b² and b ⋅ b = b², however b²⁰ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b²⁰ ⋅ b = b² and b ⋅ b = b², however b²⁰ ≠ 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,abbb=bba b/a - -
bbbbbbbbbbbbbbbbbbbbb=bb
babb=abbbbbbbbbbbbb
bba=abbb
baabb=aabbbbbbbbb
aaa=1

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

1 total

Σ	#	Presentation	Mapping
11	22771	⟨a, b \| aaa=1, aabba=bbb⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	22245	⟨a, b \| aaa=1, aabbba=bb⟩	φ(a) = a, φ(b) = b