Tool CaT
stdout:
MAYBE
Problem:
active(eq(0(),0())) -> mark(true())
active(eq(s(X),s(Y))) -> mark(eq(X,Y))
active(eq(X,Y)) -> mark(false())
active(inf(X)) -> mark(cons(X,inf(s(X))))
active(take(0(),X)) -> mark(nil())
active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L)))
active(length(nil())) -> mark(0())
active(length(cons(X,L))) -> mark(s(length(L)))
active(inf(X)) -> inf(active(X))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(length(X)) -> length(active(X))
inf(mark(X)) -> mark(inf(X))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
length(mark(X)) -> mark(length(X))
proper(eq(X1,X2)) -> eq(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(true()) -> ok(true())
proper(s(X)) -> s(proper(X))
proper(false()) -> ok(false())
proper(inf(X)) -> inf(proper(X))
proper(cons(any(X1),X2)) -> cons(any(any(proper(X1))),any(proper(X2)))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(nil()) -> ok(nil())
proper(length(X)) -> length(proper(X))
eq(ok(X1),ok(X2)) -> ok(eq(X1,X2))
s(ok(X)) -> ok(s(X))
inf(ok(X)) -> ok(inf(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
length(ok(X)) -> ok(length(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
any(X) -> s(X)
any(proper(X)) -> any(any(any(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:
{ active(eq(0(), 0())) -> mark(true())
, active(eq(s(X), s(Y))) -> mark(eq(X, Y))
, active(eq(X, Y)) -> mark(false())
, active(inf(X)) -> mark(cons(X, inf(s(X))))
, active(take(0(), X)) -> mark(nil())
, active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
, active(length(nil())) -> mark(0())
, active(length(cons(X, L))) -> mark(s(length(L)))
, active(inf(X)) -> inf(active(X))
, active(take(X1, X2)) -> take(active(X1), X2)
, active(take(X1, X2)) -> take(X1, active(X2))
, active(length(X)) -> length(active(X))
, inf(mark(X)) -> mark(inf(X))
, take(mark(X1), X2) -> mark(take(X1, X2))
, take(X1, mark(X2)) -> mark(take(X1, X2))
, length(mark(X)) -> mark(length(X))
, proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
, proper(0()) -> ok(0())
, proper(true()) -> ok(true())
, proper(s(X)) -> s(proper(X))
, proper(false()) -> ok(false())
, proper(inf(X)) -> inf(proper(X))
, proper(cons(any(X1), X2)) ->
cons(any(any(proper(X1))), any(proper(X2)))
, proper(take(X1, X2)) -> take(proper(X1), proper(X2))
, proper(nil()) -> ok(nil())
, proper(length(X)) -> length(proper(X))
, eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
, s(ok(X)) -> ok(s(X))
, inf(ok(X)) -> ok(inf(X))
, cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
, take(ok(X1), ok(X2)) -> ok(take(X1, X2))
, length(ok(X)) -> ok(length(X))
, top(mark(X)) -> top(proper(X))
, top(ok(X)) -> top(active(X))
, any(X) -> s(X)
, any(proper(X)) -> any(any(any(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:
{ active(eq(0(), 0())) -> mark(true())
, active(eq(s(X), s(Y))) -> mark(eq(X, Y))
, active(eq(X, Y)) -> mark(false())
, active(inf(X)) -> mark(cons(X, inf(s(X))))
, active(take(0(), X)) -> mark(nil())
, active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
, active(length(nil())) -> mark(0())
, active(length(cons(X, L))) -> mark(s(length(L)))
, active(inf(X)) -> inf(active(X))
, active(take(X1, X2)) -> take(active(X1), X2)
, active(take(X1, X2)) -> take(X1, active(X2))
, active(length(X)) -> length(active(X))
, inf(mark(X)) -> mark(inf(X))
, take(mark(X1), X2) -> mark(take(X1, X2))
, take(X1, mark(X2)) -> mark(take(X1, X2))
, length(mark(X)) -> mark(length(X))
, proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
, proper(0()) -> ok(0())
, proper(true()) -> ok(true())
, proper(s(X)) -> s(proper(X))
, proper(false()) -> ok(false())
, proper(inf(X)) -> inf(proper(X))
, proper(cons(any(X1), X2)) ->
cons(any(any(proper(X1))), any(proper(X2)))
, proper(take(X1, X2)) -> take(proper(X1), proper(X2))
, proper(nil()) -> ok(nil())
, proper(length(X)) -> length(proper(X))
, eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
, s(ok(X)) -> ok(s(X))
, inf(ok(X)) -> ok(inf(X))
, cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
, take(ok(X1), ok(X2)) -> ok(take(X1, X2))
, length(ok(X)) -> ok(length(X))
, top(mark(X)) -> top(proper(X))
, top(ok(X)) -> top(active(X))
, any(X) -> s(X)
, any(proper(X)) -> any(any(any(X)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds