Problem Transformed CSR 04 Ex7 BLR02 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex7 BLR02 C

stdout:

MAYBE

Problem:
active(from(X)) -> mark(cons(X,from(s(X))))
active(head(cons(X,XS))) -> mark(X)
active(2nd(cons(X,XS))) -> mark(head(XS))
active(take(0(),XS)) -> mark(nil())
active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS)))
active(sel(0(),cons(X,XS))) -> mark(X)
active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS))
active(from(X)) -> from(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(head(X)) -> head(active(X))
active(2nd(X)) -> 2nd(active(X))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
from(mark(X)) -> mark(from(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
s(mark(X)) -> mark(s(X))
head(mark(X)) -> mark(head(X))
2nd(mark(X)) -> mark(2nd(X))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
proper(from(X)) -> from(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(head(X)) -> head(proper(X))
proper(2nd(X)) -> 2nd(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
from(ok(X)) -> ok(from(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
s(ok(X)) -> ok(s(X))
head(ok(X)) -> ok(head(X))
2nd(ok(X)) -> ok(2nd(X))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(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 Ex7 BLR02 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex7 BLR02 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(from(X)) -> mark(cons(X, from(s(X))))
     , active(head(cons(X, XS))) -> mark(X)
     , active(2nd(cons(X, XS))) -> mark(head(XS))
     , active(take(0(), XS)) -> mark(nil())
     , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(from(X)) -> from(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(head(X)) -> head(active(X))
     , active(2nd(X)) -> 2nd(active(X))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , from(mark(X)) -> mark(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , head(mark(X)) -> mark(head(X))
     , 2nd(mark(X)) -> mark(2nd(X))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(head(X)) -> head(proper(X))
     , proper(2nd(X)) -> 2nd(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , from(ok(X)) -> ok(from(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , head(ok(X)) -> ok(head(X))
     , 2nd(ok(X)) -> ok(2nd(X))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(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 Ex7 BLR02 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex7 BLR02 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(from(X)) -> mark(cons(X, from(s(X))))
     , active(head(cons(X, XS))) -> mark(X)
     , active(2nd(cons(X, XS))) -> mark(head(XS))
     , active(take(0(), XS)) -> mark(nil())
     , active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
     , active(sel(0(), cons(X, XS))) -> mark(X)
     , active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
     , active(from(X)) -> from(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(head(X)) -> head(active(X))
     , active(2nd(X)) -> 2nd(active(X))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , from(mark(X)) -> mark(from(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , head(mark(X)) -> mark(head(X))
     , 2nd(mark(X)) -> mark(2nd(X))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , proper(from(X)) -> from(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(head(X)) -> head(proper(X))
     , proper(2nd(X)) -> 2nd(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , from(ok(X)) -> ok(from(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , head(ok(X)) -> ok(head(X))
     , 2nd(ok(X)) -> ok(2nd(X))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(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