Problem Transformed CSR 04 ExSec4 2 DLMMU04 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 C

stdout:

MAYBE

Problem:
active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
active(fst(pair(XS,YS))) -> mark(XS)
active(snd(pair(XS,YS))) -> mark(YS)
active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(u(splitAt(N,XS),N,X,XS))
active(u(pair(YS,ZS),N,X,XS)) -> mark(pair(cons(X,YS),ZS))
active(head(cons(N,XS))) -> mark(N)
active(tail(cons(N,XS))) -> mark(XS)
active(sel(N,XS)) -> mark(head(afterNth(N,XS)))
active(take(N,XS)) -> mark(fst(splitAt(N,XS)))
active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
active(natsFrom(X)) -> natsFrom(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(s(X)) -> s(active(X))
active(fst(X)) -> fst(active(X))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(pair(X1,X2)) -> pair(X1,active(X2))
active(snd(X)) -> snd(active(X))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(u(X1,X2,X3,X4)) -> u(active(X1),X2,X3,X4)
active(head(X)) -> head(active(X))
active(tail(X)) -> tail(active(X))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
natsFrom(mark(X)) -> mark(natsFrom(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
s(mark(X)) -> mark(s(X))
fst(mark(X)) -> mark(fst(X))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
snd(mark(X)) -> mark(snd(X))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
u(mark(X1),X2,X3,X4) -> mark(u(X1,X2,X3,X4))
head(mark(X)) -> mark(head(X))
tail(mark(X)) -> mark(tail(X))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(fst(X)) -> fst(proper(X))
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
proper(u(X1,X2,X3,X4)) -> u(proper(X1),proper(X2),proper(X3),proper(X4))
proper(head(X)) -> head(proper(X))
proper(tail(X)) -> tail(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
natsFrom(ok(X)) -> ok(natsFrom(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
s(ok(X)) -> ok(s(X))
fst(ok(X)) -> ok(fst(X))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
snd(ok(X)) -> ok(snd(X))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
u(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(u(X1,X2,X3,X4))
head(ok(X)) -> ok(head(X))
tail(ok(X)) -> ok(tail(X))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(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 ExSec4 2 DLMMU04 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExSec4 2 DLMMU04 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(fst(pair(XS, YS))) -> mark(XS)
     , active(snd(pair(XS, YS))) -> mark(YS)
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(splitAt(s(N), cons(X, XS))) ->
       mark(u(splitAt(N, XS), N, X, XS))
     , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
     , active(head(cons(N, XS))) -> mark(N)
     , active(tail(cons(N, XS))) -> mark(XS)
     , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
     , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(natsFrom(X)) -> natsFrom(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(fst(X)) -> fst(active(X))
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(snd(X)) -> snd(active(X))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
     , active(head(X)) -> head(active(X))
     , active(tail(X)) -> tail(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , fst(mark(X)) -> mark(fst(X))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , snd(mark(X)) -> mark(snd(X))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
     , head(mark(X)) -> mark(head(X))
     , tail(mark(X)) -> mark(tail(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , proper(natsFrom(X)) -> natsFrom(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(fst(X)) -> fst(proper(X))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(u(X1, X2, X3, X4)) ->
       u(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(head(X)) -> head(proper(X))
     , proper(tail(X)) -> tail(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , natsFrom(ok(X)) -> ok(natsFrom(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , fst(ok(X)) -> ok(fst(X))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
     , head(ok(X)) -> ok(head(X))
     , tail(ok(X)) -> ok(tail(X))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , take(ok(X1), ok(X2)) -> ok(take(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 ExSec4 2 DLMMU04 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExSec4 2 DLMMU04 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(fst(pair(XS, YS))) -> mark(XS)
     , active(snd(pair(XS, YS))) -> mark(YS)
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(splitAt(s(N), cons(X, XS))) ->
       mark(u(splitAt(N, XS), N, X, XS))
     , active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
     , active(head(cons(N, XS))) -> mark(N)
     , active(tail(cons(N, XS))) -> mark(XS)
     , active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
     , active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(natsFrom(X)) -> natsFrom(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(fst(X)) -> fst(active(X))
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(snd(X)) -> snd(active(X))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
     , active(head(X)) -> head(active(X))
     , active(tail(X)) -> tail(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , fst(mark(X)) -> mark(fst(X))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , snd(mark(X)) -> mark(snd(X))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
     , head(mark(X)) -> mark(head(X))
     , tail(mark(X)) -> mark(tail(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , proper(natsFrom(X)) -> natsFrom(proper(X))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(fst(X)) -> fst(proper(X))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(u(X1, X2, X3, X4)) ->
       u(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(head(X)) -> head(proper(X))
     , proper(tail(X)) -> tail(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , natsFrom(ok(X)) -> ok(natsFrom(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , fst(ok(X)) -> ok(fst(X))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
     , head(ok(X)) -> ok(head(X))
     , tail(ok(X)) -> ok(tail(X))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , take(ok(X1), ok(X2)) -> ok(take(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