#2984 ⟨a, b, c | aab=c, bbc=a⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = b^-1, φ(b) = a, φ(c) = ab^-1b^-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.

# abc:aab=c,bbc=a ab/c - -
bbaaa=abaab
bbaab=a
c=aab

4 unique, 9 total

Σ	#	Presentation	Properties	φ
8	2988	⟨a, b, c \| aab=c, bcb=a⟩	Can Inf	2
8	3510	⟨a, b, c \| bb=ac, aba=c⟩	Can Inf	2
8	5585	⟨a, b, c \| ab=c, bcac=a⟩	Can Inf
8	6037	⟨a, b, c \| ab=c, aca=bc⟩	Can Inf	1

5 unique, 45 total

Σ	#	Presentation	Properties	φ
8	1714	⟨a, b, c \| aab=bc, cba=1⟩	Grp Inf	38
8	3474	⟨a, b, c \| ba=ac, cbb=a⟩	Can Inf
8	3524	⟨a, b, c \| bb=ac, baa=c⟩	Can Inf	2
8	3535	⟨a, b, c \| bb=ac, bca=c⟩	Can Inf
8	5568	⟨a, b, c \| ab=c, bacc=a⟩	Can Inf

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

5 total

Σ	#	Presentation	Mapping
8	3000	⟨a, b, c \| aab=c, cba=b⟩	φ(a) = b, φ(b) = a, φ(c) = bba
8	5541	⟨a, b, c \| ab=c, acba=b⟩	φ(a) = b, φ(b) = a, φ(c) = ba
8	5547	⟨a, b, c \| ab=c, acca=b⟩	φ(a) = b, φ(b) = baab, φ(c) = a
8	5573	⟨a, b, c \| ab=c, bbac=a⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5582	⟨a, b, c \| ab=c, bbcc=a⟩	φ(a) = bbaa, φ(b) = b, φ(c) = a