#2970 ⟨a, b, c | aab=c, aca=b⟩

Properties

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

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

# abc:aab=c,aca=b ba/c - -
aaabb=baaba
aaaba=b
c=aab

2 unique, 10 total

Σ	#	Presentation	Properties	φ
8	1585	⟨a, b, c \| aaa=bc, acb=1⟩	Grp Inf	7
8	2830	⟨a, b, c \| aaa=b, acb=c⟩	Can Inf	1

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

3 total

Σ	#	Presentation	Mapping
8	5189	⟨a, b, c \| aa=b, abca=c⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5503	⟨a, b, c \| ab=c, aaca=b⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5576	⟨a, b, c \| ab=c, bbbc=a⟩	φ(a) = b, φ(b) = a, φ(c) = ba