Problem Transformed CSR 04 Ex2 Luc02a C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a C

stdout:

MAYBE

Problem:
active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N))))
active(sqr(0())) -> mark(0())
active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X))))
active(dbl(0())) -> mark(0())
active(dbl(s(X))) -> mark(s(s(dbl(X))))
active(add(0(),X)) -> mark(X)
active(add(s(X),Y)) -> mark(s(add(X,Y)))
active(first(0(),X)) -> mark(nil())
active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
active(terms(X)) -> terms(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(recip(X)) -> recip(active(X))
active(sqr(X)) -> sqr(active(X))
active(s(X)) -> s(active(X))
active(add(X1,X2)) -> add(active(X1),X2)
active(add(X1,X2)) -> add(X1,active(X2))
active(dbl(X)) -> dbl(active(X))
active(first(X1,X2)) -> first(active(X1),X2)
active(first(X1,X2)) -> first(X1,active(X2))
terms(mark(X)) -> mark(terms(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
recip(mark(X)) -> mark(recip(X))
sqr(mark(X)) -> mark(sqr(X))
s(mark(X)) -> mark(s(X))
add(mark(X1),X2) -> mark(add(X1,X2))
add(X1,mark(X2)) -> mark(add(X1,X2))
dbl(mark(X)) -> mark(dbl(X))
first(mark(X1),X2) -> mark(first(X1,X2))
first(X1,mark(X2)) -> mark(first(X1,X2))
proper(terms(X)) -> terms(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(recip(X)) -> recip(proper(X))
proper(sqr(X)) -> sqr(proper(X))
proper(s(X)) -> s(proper(X))
proper(0()) -> ok(0())
proper(add(X1,X2)) -> add(proper(X1),proper(X2))
proper(dbl(X)) -> dbl(proper(X))
proper(first(X1,X2)) -> first(proper(X1),proper(X2))
proper(nil()) -> ok(nil())
terms(ok(X)) -> ok(terms(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
recip(ok(X)) -> ok(recip(X))
sqr(ok(X)) -> ok(sqr(X))
s(ok(X)) -> ok(s(X))
add(ok(X1),ok(X2)) -> ok(add(X1,X2))
dbl(ok(X)) -> ok(dbl(X))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex2 Luc02a C

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex2 Luc02a C

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds