#2551 ⟨a, b, c | aab=c, ccab=1⟩

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 ⋅ (aba)²ba = a and a ⋅ 1 = a, however (aba)²ba ≠ 1
Not right cancellative, because right multiplication by (aba)²b is not injective:
- (aba)²ba ⋅ (aba)²b = (aba)²b and 1 ⋅ (aba)²b = (aba)²b, however (aba)²ba ≠ 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.	(a²b)²ab ⇒ 1	[2]
2.	c ⇒ a²b	[1]

# abc:aab=c,ccab=1 ab/c - -
aabaabab=1
c=aab

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

2 total

Σ	#	Presentation	Mapping
8	2651	⟨a, b, c \| aba=c, accb=1⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5038	⟨a, b, c \| ab=c, acacc=1⟩	φ(a) = a, φ(b) = b, φ(c) = ab