Problem Transformed CSR 04 ExSec11 1 Luc02a FR

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a FR

stdout:

MAYBE

Problem:
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
sqr(0()) -> 0()
sqr(s(X)) -> s(add(sqr(X),dbl(X)))
dbl(0()) -> 0()
dbl(s(X)) -> s(s(dbl(X)))
add(0(),X) -> X
add(s(X),Y) -> s(add(X,Y))
first(0(),X) -> nil()
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(X))) -> s(half(X))
half(dbl(X)) -> X
terms(X) -> n__terms(X)
s(X) -> n__s(X)
first(X1,X2) -> n__first(X1,X2)
activate(n__terms(X)) -> terms(activate(X))
activate(n__s(X)) -> s(activate(X))
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a FR

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExSec11 1 Luc02a FR

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(X))) -> s(half(X))
     , half(dbl(X)) -> X
     , terms(X) -> n__terms(X)
     , s(X) -> n__s(X)
     , first(X1, X2) -> n__first(X1, X2)
     , activate(n__terms(X)) -> terms(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a FR

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExSec11 1 Luc02a FR

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(X))) -> s(half(X))
     , half(dbl(X)) -> X
     , terms(X) -> n__terms(X)
     , s(X) -> n__s(X)
     , first(X1, X2) -> n__first(X1, X2)
     , activate(n__terms(X)) -> terms(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds