#27649 ⟨a, b | aa=1, ababba=bbb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- b(ab)³ ⋅ b = ab²ab³ and (ab²)² ⋅ b = ab²ab³, however b(ab)³ ≠ (ab²)²

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,ababba=bbb reversed:a/b - -
aa=1
bbba=ababb
babba=abbb
bbababb=abababbb
babababb=abbabbb

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

2 total

Σ	#	Presentation	Mapping
11	28180	⟨a, b \| aa=1, ababb=bbba⟩	φ(a) = a, φ(b) = b
11	28206	⟨a, b \| aa=1, abbba=babb⟩	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	28196	⟨a, b \| aa=1, abbab=bbba⟩	φ(a) = a, φ(b) = b