#7131 ⟨a, b, c | aa=1, aabb=cb⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not right cancellative, because right multiplication by b is not injective:
- c ⋅ b = b² and b ⋅ b = b², however c ≠ 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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	cb ⇒ b²	[2]

# abc:aa=1,aabb=cb abc - -
aa=1
cb=bb

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

2 total

Σ	#	Presentation	Mapping
8	7141	⟨a, b, c \| aa=1, aabc=cc⟩	φ(a) = a, φ(b) = c, φ(c) = b
8	7630	⟨a, b, c \| aa=1, acb=abb⟩	φ(a) = a, φ(b) = b, φ(c) = c