#1864 ⟨a, b, c | aba=bc, acb=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 ⋅ c²b²c = c and c ⋅ 1 = c, however c²b²c ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- c³b² ⋅ c = c and 1 ⋅ c = c, however c³b² ≠ 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(c) = deg(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aba=bc,acb=1 cb/a - -
cccbbc=c
cbbccb=ccbbcb
ab=bccb
acb=1
accbbc=a
cba=ccbbc