Tool CaT
stdout:
MAYBE
Problem:
minus(X,s(Y)) -> pred(minus(X,Y))
minus(X,0()) -> X
pred(s(X)) -> X
le(s(X),s(Y)) -> le(X,Y)
le(s(X),0()) -> false()
le(0(),Y) -> true()
gcd(0(),Y) -> 0()
gcd(s(X),0()) -> s(X)
gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ minus(X, s(Y)) -> pred(minus(X, Y))
, minus(X, 0()) -> X
, pred(s(X)) -> X
, le(s(X), s(Y)) -> le(X, Y)
, le(s(X), 0()) -> false()
, le(0(), Y) -> true()
, gcd(0(), Y) -> 0()
, gcd(s(X), 0()) -> s(X)
, gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y))
, if(true(), s(X), s(Y)) -> gcd(minus(X, Y), s(Y))
, if(false(), s(X), s(Y)) -> gcd(minus(Y, X), s(X))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ minus(X, s(Y)) -> pred(minus(X, Y))
, minus(X, 0()) -> X
, pred(s(X)) -> X
, le(s(X), s(Y)) -> le(X, Y)
, le(s(X), 0()) -> false()
, le(0(), Y) -> true()
, gcd(0(), Y) -> 0()
, gcd(s(X), 0()) -> s(X)
, gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y))
, if(true(), s(X), s(Y)) -> gcd(minus(X, Y), s(Y))
, if(false(), s(X), s(Y)) -> gcd(minus(Y, X), s(X))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds