#3056 ⟨a, b, c | aba=c, cbc=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (ba)³ = a and a ⋅ 1 = a, however (ba)³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- (ab)³ ⋅ a = a and 1 ⋅ a = a, however (ab)³ ≠ 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.	a(ba)³ ⇒ a	[2]
2.	c ⇒ aba	[1]

# abc:aba=c,cbc=a ab/c - -
abababa=a
c=aba

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

1 total

Σ	#	Presentation	Mapping
8	5594	⟨a, b, c \| ab=c, bccc=b⟩	φ(a) = b, φ(b) = a, φ(c) = ba