#1186 ⟨a, b | aa=1, abab=bb⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = ab² and ab ⋅ b = ab², however ba ≠ 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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bab ⇒ ab²	[3]

# ab:aa=1,abab=bb ab - -
aa=1
bab=abb

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

9 total

Σ	#	Presentation	Mapping
8	1251	⟨a, b \| aa=1, bab=abb⟩	φ(a) = a, φ(b) = b
10	9950	⟨a, b \| aa=1, aaabab=bb⟩	φ(a) = a, φ(b) = b
10	9989	⟨a, b \| aa=1, abaaab=bb⟩	φ(a) = a, φ(b) = b
10	10227	⟨a, b \| aa=1, aaabb=bab⟩	φ(a) = a, φ(b) = b
10	10239	⟨a, b \| aa=1, aabab=abb⟩	φ(a) = a, φ(b) = b
10	10265	⟨a, b \| aa=1, abaab=bab⟩	φ(a) = a, φ(b) = b
10	10307	⟨a, b \| aa=1, baaab=abb⟩	φ(a) = a, φ(b) = b
10	10484	⟨a, b \| aa=1, abab=aabb⟩	φ(a) = a, φ(b) = b
10	10506	⟨a, b \| aa=1, baab=abab⟩	φ(a) = a, φ(b) = b

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

6 total

Σ	#	Presentation	Mapping
10	9966	⟨a, b \| aa=1, aababa=bb⟩	φ(a) = a, φ(b) = b
10	10242	⟨a, b \| aa=1, aabab=bba⟩	φ(a) = a, φ(b) = b
10	10249	⟨a, b \| aa=1, aabba=bab⟩	φ(a) = a, φ(b) = b
10	10271	⟨a, b \| aa=1, ababa=abb⟩	φ(a) = a, φ(b) = b
10	10490	⟨a, b \| aa=1, abba=abab⟩	φ(a) = a, φ(b) = b
10	10509	⟨a, b \| aa=1, baba=aabb⟩	φ(a) = a, φ(b) = b