#862 ⟨a, b, c | ab=c, accb=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ abab²a = a and a ⋅ 1 = a, however abab²a ≠ 1
Not right cancellative, because right multiplication by abab² is not injective:
- abab²a ⋅ abab² = abab² and 1 ⋅ abab² = abab², however abab²a ≠ 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

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

#	Rule	Proof
1.	a²bab² ⇒ 1	[2]
2.	c ⇒ ab	[1]

# abc:ab=c,accb=1 ab/c - -
aababb=1
c=ab

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

8 total

Σ	#	Presentation	Mapping
8	2536	⟨a, b, c \| aab=c, cabb=1⟩	φ(a) = a, φ(b) = b, φ(c) = aab
8	2648	⟨a, b, c \| aba=c, acbb=1⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	4310	⟨a, b, c \| aab=1, cacc=b⟩	φ(a) = a, φ(b) = babb, φ(c) = b
8	4537	⟨a, b, c \| abc=1, acac=b⟩	φ(a) = a, φ(b) = abab, φ(c) = b
8	4745	⟨a, b, c \| aa=b, bcacc=1⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	4998	⟨a, b, c \| ab=c, aabcb=1⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5078	⟨a, b, c \| ab=c, bbcaa=1⟩	φ(a) = b, φ(b) = a, φ(c) = ba
8	6920	⟨a, b, c \| ab=1, acacc=b⟩	φ(a) = a, φ(b) = ababb, φ(c) = b