Tool CaT
stdout:
MAYBE
Problem:
sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
sum(cons(0(),x),y) -> sum(x,y)
sum(nil(),y) -> y
empty(nil()) -> true()
empty(cons(n,x)) -> false()
tail(nil()) -> nil()
tail(cons(n,x)) -> x
head(cons(n,x)) -> n
weight(x) -> if(empty(x),empty(tail(x)),x)
if(true(),b,x) -> weight_undefined_error()
if(false(),b,x) -> if2(b,x)
if2(true(),x) -> head(x)
if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(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:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(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:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds