Tool CaT
stdout:
MAYBE
Problem:
empty(nil()) -> true()
empty(cons(x,y)) -> false()
tail(nil()) -> nil()
tail(cons(x,y)) -> y
head(cons(x,y)) -> x
zero(0()) -> true()
zero(s(x)) -> false()
p(0()) -> 0()
p(s(0())) -> 0()
p(s(s(x))) -> s(p(s(x)))
intlist(x) -> if_intlist(empty(x),x)
if_intlist(true(),x) -> nil()
if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
int(x,y) -> if_int(zero(x),zero(y),x,y)
if_int(true(),b,x,y) -> if1(b,x,y)
if_int(false(),b,x,y) -> if2(b,x,y)
if1(true(),x,y) -> cons(0(),nil())
if1(false(),x,y) -> cons(0(),int(s(0()),y))
if2(true(),x,y) -> nil()
if2(false(),x,y) -> intlist(int(p(x),p(y)))
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:
{ empty(nil()) -> true()
, empty(cons(x, y)) -> false()
, tail(nil()) -> nil()
, tail(cons(x, y)) -> y
, head(cons(x, y)) -> x
, zero(0()) -> true()
, zero(s(x)) -> false()
, p(0()) -> 0()
, p(s(0())) -> 0()
, p(s(s(x))) -> s(p(s(x)))
, intlist(x) -> if_intlist(empty(x), x)
, if_intlist(true(), x) -> nil()
, if_intlist(false(), x) -> cons(s(head(x)), intlist(tail(x)))
, int(x, y) -> if_int(zero(x), zero(y), x, y)
, if_int(true(), b, x, y) -> if1(b, x, y)
, if_int(false(), b, x, y) -> if2(b, x, y)
, if1(true(), x, y) -> cons(0(), nil())
, if1(false(), x, y) -> cons(0(), int(s(0()), y))
, if2(true(), x, y) -> nil()
, if2(false(), x, y) -> intlist(int(p(x), p(y)))}
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:
{ empty(nil()) -> true()
, empty(cons(x, y)) -> false()
, tail(nil()) -> nil()
, tail(cons(x, y)) -> y
, head(cons(x, y)) -> x
, zero(0()) -> true()
, zero(s(x)) -> false()
, p(0()) -> 0()
, p(s(0())) -> 0()
, p(s(s(x))) -> s(p(s(x)))
, intlist(x) -> if_intlist(empty(x), x)
, if_intlist(true(), x) -> nil()
, if_intlist(false(), x) -> cons(s(head(x)), intlist(tail(x)))
, int(x, y) -> if_int(zero(x), zero(y), x, y)
, if_int(true(), b, x, y) -> if1(b, x, y)
, if_int(false(), b, x, y) -> if2(b, x, y)
, if1(true(), x, y) -> cons(0(), nil())
, if1(false(), x, y) -> cons(0(), int(s(0()), y))
, if2(true(), x, y) -> nil()
, if2(false(), x, y) -> intlist(int(p(x), p(y)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds