#5681 ⟨a, b, c | aa=b, abb=ac⟩

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 ⋅ c = a⁵ and a ⋅ a⁴ = a⁵, however c ≠ a⁴

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) = 0; deg(b) = deg(c) = 1, b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b ⇒ a²	[1]
2.	ac ⇒ a⁵	[2]

# abc:aa=b,abb=ac a/bc - -
b=aa
ac=aaaaa

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

1 total

Σ	#	Presentation	Mapping
8	5719	⟨a, b, c \| aa=b, bab=ac⟩	φ(a) = a, φ(b) = aa, φ(c) = c

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

1 total

Σ	#	Presentation	Mapping
8	5683	⟨a, b, c \| aa=b, abb=ca⟩	φ(a) = a, φ(b) = aa, φ(c) = c