Problem Transformed CSR 04 Ex26 Luc03b GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex26 Luc03b GM

stdout:

MAYBE

Problem:
a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
a__sqr(0()) -> 0()
a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
a__dbl(0()) -> 0()
a__dbl(s(X)) -> s(s(dbl(X)))
a__add(0(),X) -> mark(X)
a__add(s(X),Y) -> s(add(X,Y))
a__first(0(),X) -> nil()
a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
mark(terms(X)) -> a__terms(mark(X))
mark(sqr(X)) -> a__sqr(mark(X))
mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
mark(dbl(X)) -> a__dbl(mark(X))
mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(recip(X)) -> recip(mark(X))
mark(s(X)) -> s(X)
mark(0()) -> 0()
mark(nil()) -> nil()
a__terms(X) -> terms(X)
a__sqr(X) -> sqr(X)
a__add(X1,X2) -> add(X1,X2)
a__dbl(X) -> dbl(X)
a__first(X1,X2) -> first(X1,X2)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex26 Luc03b GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex26 Luc03b GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(dbl(X)))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(add(X, Y))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(X)
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex26 Luc03b GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex26 Luc03b GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(dbl(X)))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(add(X, Y))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(X)
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds