#4363 ⟨a, b, c | aab=1, cccc=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ c⁷bc = c and c ⋅ 1 = c, however c⁷bc ≠ 1
Not right cancellative, because right multiplication by c⁷b is not injective:
- c⁷bc ⋅ c⁷b = c⁷b and 1 ⋅ c⁷b = c⁷b, however c⁷bc ≠ 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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	c⁸b ⇒ 1	[3]
2.	a ⇒ c⁴	[2]

# abc:aab=1,cccc=a bc/a - -
ccccccccb=1
a=cccc

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

1 total

Σ	#	Presentation	Mapping
8	4734	⟨a, b, c \| aa=b, bbbbc=1⟩	φ(a) = c, φ(b) = cc, φ(c) = b