#4174 ⟨a, b | baa=aab, bba=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, 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

#	Rule	Proof
1.	b²a ⇒ a	[2]
2.	a²b ⇒ ba²	[1]

# ab:baa=aab,bba=a ba - -
bba=a
aab=baa

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

1 total

Σ	#	Presentation	Mapping
10	6689	⟨a, b \| aab=b, abba=bb⟩	φ(a) = b, φ(b) = a