#2985 ⟨a, b, c | aab=c, bca=a⟩

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 a is not injective:
- ba²b ⋅ a = a and 1 ⋅ a = a, however ba²b ≠ 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,bca=a ab/c - -
baaa=aaba
baaba=a
c=aab

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

3 total

Σ	#	Presentation	Mapping
8	3052	⟨a, b, c \| aba=c, bac=a⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5523	⟨a, b, c \| ab=c, abbc=b⟩	φ(a) = b, φ(b) = a, φ(c) = ba
8	5565	⟨a, b, c \| ab=c, baca=a⟩	φ(a) = a, φ(b) = b, φ(c) = ab