#1803 ⟨a, b | abab=1, aaabb=1⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (ba)² = a and a ⋅ 1 = a, however (ba)² ≠ 1
Not right cancellative, because right multiplication by bab is not injective:
- (ba)² ⋅ bab = bab and 1 ⋅ bab = bab, however (ba)² ≠ 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.	(ab)² ⇒ 1	[1]
2.	a³b² ⇒ 1	[2]

# ab:abab=1,aaabb=1 ab - -
abab=1
aaabb=1

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

2 total

Σ	#	Presentation	Mapping
11	11512	⟨a, b \| ababa=a, bbbaa=1⟩	φ(a) = b, φ(b) = a
11	17492	⟨a, b \| abab=1, aaabba=a⟩	φ(a) = a, φ(b) = b