#2994 ⟨a, b, c | aab=c, cab=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by b is not injective:
- a²ba ⋅ b = b and 1 ⋅ b = b, however a²ba ≠ 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.

#	Rule	Proof
1.	a(ab)² ⇒ b	[2]
2.	c ⇒ a²b	[1]

# abc:aab=c,cab=b ab/c - -
aabab=b
c=aab

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

5 total

Σ	#	Presentation	Mapping
8	2997	⟨a, b, c \| aab=c, cac=b⟩	φ(a) = a, φ(b) = bab, φ(c) = b
8	3049	⟨a, b, c \| aba=c, acb=b⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5246	⟨a, b, c \| aa=b, bcac=c⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5538	⟨a, b, c \| ab=c, acac=b⟩	φ(a) = a, φ(b) = abab, φ(c) = b
8	5579	⟨a, b, c \| ab=c, bbca=a⟩	φ(a) = b, φ(b) = a, φ(c) = ba