#1882 ⟨a, b, c | aba=bc, ccb=1⟩

Properties

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

# abc:aba=bc,ccb=1 reversed:cb/a - -
ccb=1
abb=bcbacb
acbc=a
aba=bc