#5685 ⟨a, b, c | aa=b, abb=cc⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a³ca has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaabb⟩
- Embedding: φ(a) = a, φ(b) = aa, φ(c) = b^-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(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aa=b,abb=cc ac/b - -
cca=acc
aaaaa=cc
b=aa

5 unique, 21 total

Σ	#	Presentation	Properties	φ
8	3749	⟨a, b, c \| aab=1, bbcac=1⟩	Grp Inf	16
8	5260	⟨a, b, c \| aa=b, cabc=b⟩	Can Inf
8	5265	⟨a, b, c \| aa=b, cbbc=a⟩	Can Inf
8	5761	⟨a, b, c \| aa=b, cac=bb⟩	Can Inf
8	5765	⟨a, b, c \| aa=b, cbc=ab⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
8	5721	⟨a, b, c \| aa=b, bab=cc⟩	φ(a) = a, φ(b) = aa, φ(c) = c