#3002 ⟨a, b, c | aab=c, cbc=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ bc(cb)² = c and c ⋅ 1 = c, however bc(cb)² ≠ 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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=c,cbc=a bc/a - -
cccbcb=cbccbc
cbccbcb=c
a=cbc

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

1 total

Σ	#	Presentation	Mapping
8	5601	⟨a, b, c \| ab=c, cacc=a⟩	φ(a) = c, φ(b) = b, φ(c) = cb