#3519 ⟨a, b | aa=1, abbba=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b⁶ = b² and b ⋅ b = b², however b⁶ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b⁶ ⋅ b = b² and b ⋅ b = b², however b⁶ ≠ 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:aa=1,abbba=bb b/a - -
bbbbbbb=bb
babb=abbbbbb
bba=abbb
aa=1

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

17 total

Σ	#	Presentation	Mapping
9	3651	⟨a, b \| aa=1, abba=bbb⟩	φ(a) = a, φ(b) = b
9	3658	⟨a, b \| aa=1, abbb=bba⟩	φ(a) = a, φ(b) = b
11	27025	⟨a, b \| aa=1, aaabbba=bb⟩	φ(a) = a, φ(b) = b
11	27102	⟨a, b \| aa=1, abaabba=bb⟩	φ(a) = a, φ(b) = b
11	27549	⟨a, b \| aa=1, aaabba=bbb⟩	φ(a) = a, φ(b) = b
11	27556	⟨a, b \| aa=1, aaabbb=bba⟩	φ(a) = a, φ(b) = b
11	27599	⟨a, b \| aa=1, aabbba=abb⟩	φ(a) = a, φ(b) = b
11	27625	⟨a, b \| aa=1, abaaba=bbb⟩	φ(a) = a, φ(b) = b
11	27632	⟨a, b \| aa=1, abaabb=bba⟩	φ(a) = a, φ(b) = b
11	27664	⟨a, b \| aa=1, abbaab=bba⟩	φ(a) = a, φ(b) = b
11	28080	⟨a, b \| aa=1, aaabb=bbba⟩	φ(a) = a, φ(b) = b
11	28115	⟨a, b \| aa=1, aabba=abbb⟩	φ(a) = a, φ(b) = b
11	28130	⟨a, b \| aa=1, aabbb=abba⟩	φ(a) = a, φ(b) = b
11	28154	⟨a, b \| aa=1, abaab=bbba⟩	φ(a) = a, φ(b) = b
11	28201	⟨a, b \| aa=1, abbba=aabb⟩	φ(a) = a, φ(b) = b
11	28205	⟨a, b \| aa=1, abbba=baab⟩	φ(a) = a, φ(b) = b
11	28240	⟨a, b \| aa=1, baabb=abba⟩	φ(a) = a, φ(b) = b