#2979 ⟨a, b, c | aab=c, bab=c⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = bab and ba ⋅ b = bab, however a² ≠ ba

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

Reduction order:
- Left-to-right recursive path with deg(b) = deg(a) = 0, b < a; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a²b ⇒ bab	[2]
2.	c ⇒ bab	[3]

# abc:aab=c,bab=c ba/c - -
aab=bab
c=bab

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

2 total

Σ	#	Presentation	Mapping
8	5762	⟨a, b, c \| aa=b, cac=bc⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	6001	⟨a, b, c \| ab=c, aab=bc⟩	φ(a) = a, φ(b) = b, φ(c) = ab