#1119 ⟨a, b | aa=1, abbab=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b and 1 ⋅ b = b, however b² ≠ 1

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,abbab=b ab - -
aa=1
bbb=b
bbab=ab

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

7 total

Σ	#	Presentation	Mapping
10	9683	⟨a, b \| aa=1, aaabbab=b⟩	φ(a) = a, φ(b) = b
10	9723	⟨a, b \| aa=1, abaabab=b⟩	φ(a) = a, φ(b) = b
10	9741	⟨a, b \| aa=1, abbaaab=b⟩	φ(a) = a, φ(b) = b
10	9975	⟨a, b \| aa=1, aabbab=ab⟩	φ(a) = a, φ(b) = b
10	10036	⟨a, b \| aa=1, baabab=ab⟩	φ(a) = a, φ(b) = b
10	10283	⟨a, b \| aa=1, abbab=aab⟩	φ(a) = a, φ(b) = b
10	10286	⟨a, b \| aa=1, abbab=baa⟩	φ(a) = a, φ(b) = b

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

8 total

Σ	#	Presentation	Mapping
8	1199	⟨a, b \| aa=1, babb=ba⟩	φ(a) = a, φ(b) = b
10	9699	⟨a, b \| aa=1, aababba=b⟩	φ(a) = a, φ(b) = b
10	9969	⟨a, b \| aa=1, aababb=ba⟩	φ(a) = a, φ(b) = b
10	10002	⟨a, b \| aa=1, ababba=ab⟩	φ(a) = a, φ(b) = b
10	10033	⟨a, b \| aa=1, baaabb=ba⟩	φ(a) = a, φ(b) = b
10	10276	⟨a, b \| aa=1, ababb=aba⟩	φ(a) = a, φ(b) = b
10	10514	⟨a, b \| aa=1, babb=aaba⟩	φ(a) = a, φ(b) = b
10	10520	⟨a, b \| aa=1, babb=baaa⟩	φ(a) = a, φ(b) = b