Problem Transformed CSR 04 LISTUTILITIES nosorts noand C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts noand C

stdout:

MAYBE

Problem:
active(U11(tt(),N,XS)) -> mark(U12(tt(),N,XS))
active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
active(U21(tt(),X)) -> mark(U22(tt(),X))
active(U22(tt(),X)) -> mark(X)
active(U31(tt(),N)) -> mark(U32(tt(),N))
active(U32(tt(),N)) -> mark(N)
active(U41(tt(),N,XS)) -> mark(U42(tt(),N,XS))
active(U42(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
active(U51(tt(),Y)) -> mark(U52(tt(),Y))
active(U52(tt(),Y)) -> mark(Y)
active(U61(tt(),N,X,XS)) -> mark(U62(tt(),N,X,XS))
active(U62(tt(),N,X,XS)) -> mark(U63(tt(),N,X,XS))
active(U63(tt(),N,X,XS)) -> mark(U64(splitAt(N,XS),X))
active(U64(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(U71(tt(),XS)) -> mark(U72(tt(),XS))
active(U72(tt(),XS)) -> mark(XS)
active(U81(tt(),N,XS)) -> mark(U82(tt(),N,XS))
active(U82(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
active(afterNth(N,XS)) -> mark(U11(tt(),N,XS))
active(fst(pair(X,Y))) -> mark(U21(tt(),X))
active(head(cons(N,XS))) -> mark(U31(tt(),N))
active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
active(sel(N,XS)) -> mark(U41(tt(),N,XS))
active(snd(pair(X,Y))) -> mark(U51(tt(),Y))
active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U61(tt(),N,X,XS))
active(tail(cons(N,XS))) -> mark(U71(tt(),XS))
active(take(N,XS)) -> mark(U81(tt(),N,XS))
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
active(snd(X)) -> snd(active(X))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U22(X1,X2)) -> U22(active(X1),X2)
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(head(X)) -> head(active(X))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(U51(X1,X2)) -> U51(active(X1),X2)
active(U52(X1,X2)) -> U52(active(X1),X2)
active(U61(X1,X2,X3,X4)) -> U61(active(X1),X2,X3,X4)
active(U62(X1,X2,X3,X4)) -> U62(active(X1),X2,X3,X4)
active(U63(X1,X2,X3,X4)) -> U63(active(X1),X2,X3,X4)
active(U64(X1,X2)) -> U64(active(X1),X2)
active(pair(X1,X2)) -> pair(active(X1),X2)
active(pair(X1,X2)) -> pair(X1,active(X2))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U71(X1,X2)) -> U71(active(X1),X2)
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
active(fst(X)) -> fst(active(X))
active(natsFrom(X)) -> natsFrom(active(X))
active(s(X)) -> s(active(X))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(tail(X)) -> tail(active(X))
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
snd(mark(X)) -> mark(snd(X))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U22(mark(X1),X2) -> mark(U22(X1,X2))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
head(mark(X)) -> mark(head(X))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
U51(mark(X1),X2) -> mark(U51(X1,X2))
U52(mark(X1),X2) -> mark(U52(X1,X2))
U61(mark(X1),X2,X3,X4) -> mark(U61(X1,X2,X3,X4))
U62(mark(X1),X2,X3,X4) -> mark(U62(X1,X2,X3,X4))
U63(mark(X1),X2,X3,X4) -> mark(U63(X1,X2,X3,X4))
U64(mark(X1),X2) -> mark(U64(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U71(mark(X1),X2) -> mark(U71(X1,X2))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
fst(mark(X)) -> mark(fst(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
s(mark(X)) -> mark(s(X))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
tail(mark(X)) -> mark(tail(X))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(tt()) -> ok(tt())
proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(head(X)) -> head(proper(X))
proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
proper(U61(X1,X2,X3,X4)) -> U61(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U62(X1,X2,X3,X4)) -> U62(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U63(X1,X2,X3,X4)) -> U63(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U64(X1,X2)) -> U64(proper(X1),proper(X2))
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
proper(fst(X)) -> fst(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
snd(ok(X)) -> ok(snd(X))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
head(ok(X)) -> ok(head(X))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
U61(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U61(X1,X2,X3,X4))
U62(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U62(X1,X2,X3,X4))
U63(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U63(X1,X2,X3,X4))
U64(ok(X1),ok(X2)) -> ok(U64(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
fst(ok(X)) -> ok(fst(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
s(ok(X)) -> ok(s(X))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
tail(ok(X)) -> ok(tail(X))
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 LISTUTILITIES nosorts noand C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nosorts noand C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(U11(tt(), N, XS)) -> mark(U12(tt(), N, XS))
     , active(U12(tt(), N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(U21(tt(), X)) -> mark(U22(tt(), X))
     , active(U22(tt(), X)) -> mark(X)
     , active(U31(tt(), N)) -> mark(U32(tt(), N))
     , active(U32(tt(), N)) -> mark(N)
     , active(U41(tt(), N, XS)) -> mark(U42(tt(), N, XS))
     , active(U42(tt(), N, XS)) -> mark(head(afterNth(N, XS)))
     , active(U51(tt(), Y)) -> mark(U52(tt(), Y))
     , active(U52(tt(), Y)) -> mark(Y)
     , active(U61(tt(), N, X, XS)) -> mark(U62(tt(), N, X, XS))
     , active(U62(tt(), N, X, XS)) -> mark(U63(tt(), N, X, XS))
     , active(U63(tt(), N, X, XS)) -> mark(U64(splitAt(N, XS), X))
     , active(U64(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS))
     , active(U71(tt(), XS)) -> mark(U72(tt(), XS))
     , active(U72(tt(), XS)) -> mark(XS)
     , active(U81(tt(), N, XS)) -> mark(U82(tt(), N, XS))
     , active(U82(tt(), N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(afterNth(N, XS)) -> mark(U11(tt(), N, XS))
     , active(fst(pair(X, Y))) -> mark(U21(tt(), X))
     , active(head(cons(N, XS))) -> mark(U31(tt(), N))
     , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(sel(N, XS)) -> mark(U41(tt(), N, XS))
     , active(snd(pair(X, Y))) -> mark(U51(tt(), Y))
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(splitAt(s(N), cons(X, XS))) -> mark(U61(tt(), N, X, XS))
     , active(tail(cons(N, XS))) -> mark(U71(tt(), XS))
     , active(take(N, XS)) -> mark(U81(tt(), N, XS))
     , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
     , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
     , active(snd(X)) -> snd(active(X))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(U21(X1, X2)) -> U21(active(X1), X2)
     , active(U22(X1, X2)) -> U22(active(X1), X2)
     , active(U31(X1, X2)) -> U31(active(X1), X2)
     , active(U32(X1, X2)) -> U32(active(X1), X2)
     , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
     , active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
     , active(head(X)) -> head(active(X))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(U51(X1, X2)) -> U51(active(X1), X2)
     , active(U52(X1, X2)) -> U52(active(X1), X2)
     , active(U61(X1, X2, X3, X4)) -> U61(active(X1), X2, X3, X4)
     , active(U62(X1, X2, X3, X4)) -> U62(active(X1), X2, X3, X4)
     , active(U63(X1, X2, X3, X4)) -> U63(active(X1), X2, X3, X4)
     , active(U64(X1, X2)) -> U64(active(X1), X2)
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U71(X1, X2)) -> U71(active(X1), X2)
     , active(U72(X1, X2)) -> U72(active(X1), X2)
     , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3)
     , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3)
     , active(fst(X)) -> fst(active(X))
     , active(natsFrom(X)) -> natsFrom(active(X))
     , active(s(X)) -> s(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(tail(X)) -> tail(active(X))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
     , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3))
     , snd(mark(X)) -> mark(snd(X))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , U21(mark(X1), X2) -> mark(U21(X1, X2))
     , U22(mark(X1), X2) -> mark(U22(X1, X2))
     , U31(mark(X1), X2) -> mark(U31(X1, X2))
     , U32(mark(X1), X2) -> mark(U32(X1, X2))
     , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
     , U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3))
     , head(mark(X)) -> mark(head(X))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , U51(mark(X1), X2) -> mark(U51(X1, X2))
     , U52(mark(X1), X2) -> mark(U52(X1, X2))
     , U61(mark(X1), X2, X3, X4) -> mark(U61(X1, X2, X3, X4))
     , U62(mark(X1), X2, X3, X4) -> mark(U62(X1, X2, X3, X4))
     , U63(mark(X1), X2, X3, X4) -> mark(U63(X1, X2, X3, X4))
     , U64(mark(X1), X2) -> mark(U64(X1, X2))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U71(mark(X1), X2) -> mark(U71(X1, X2))
     , U72(mark(X1), X2) -> mark(U72(X1, X2))
     , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3))
     , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3))
     , fst(mark(X)) -> mark(fst(X))
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , s(mark(X)) -> mark(s(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , tail(mark(X)) -> mark(tail(X))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , proper(U11(X1, X2, X3)) ->
       U11(proper(X1), proper(X2), proper(X3))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2, X3)) ->
       U12(proper(X1), proper(X2), proper(X3))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
     , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2))
     , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
     , proper(U32(X1, X2)) -> U32(proper(X1), proper(X2))
     , proper(U41(X1, X2, X3)) ->
       U41(proper(X1), proper(X2), proper(X3))
     , proper(U42(X1, X2, X3)) ->
       U42(proper(X1), proper(X2), proper(X3))
     , proper(head(X)) -> head(proper(X))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
     , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2))
     , proper(U61(X1, X2, X3, X4)) ->
       U61(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U62(X1, X2, X3, X4)) ->
       U62(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U63(X1, X2, X3, X4)) ->
       U63(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U64(X1, X2)) -> U64(proper(X1), proper(X2))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2))
     , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2))
     , proper(U81(X1, X2, X3)) ->
       U81(proper(X1), proper(X2), proper(X3))
     , proper(U82(X1, X2, X3)) ->
       U82(proper(X1), proper(X2), proper(X3))
     , proper(fst(X)) -> fst(proper(X))
     , proper(natsFrom(X)) -> natsFrom(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(tail(X)) -> tail(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
     , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
     , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
     , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
     , U32(ok(X1), ok(X2)) -> ok(U32(X1, X2))
     , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
     , U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
     , head(ok(X)) -> ok(head(X))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
     , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
     , U61(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U61(X1, X2, X3, X4))
     , U62(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U62(X1, X2, X3, X4))
     , U63(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U63(X1, X2, X3, X4))
     , U64(ok(X1), ok(X2)) -> ok(U64(X1, X2))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2))
     , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2))
     , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3))
     , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3))
     , fst(ok(X)) -> ok(fst(X))
     , natsFrom(ok(X)) -> ok(natsFrom(X))
     , s(ok(X)) -> ok(s(X))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , tail(ok(X)) -> ok(tail(X))
     , 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 LISTUTILITIES nosorts noand C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nosorts noand C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(U11(tt(), N, XS)) -> mark(U12(tt(), N, XS))
     , active(U12(tt(), N, XS)) -> mark(snd(splitAt(N, XS)))
     , active(U21(tt(), X)) -> mark(U22(tt(), X))
     , active(U22(tt(), X)) -> mark(X)
     , active(U31(tt(), N)) -> mark(U32(tt(), N))
     , active(U32(tt(), N)) -> mark(N)
     , active(U41(tt(), N, XS)) -> mark(U42(tt(), N, XS))
     , active(U42(tt(), N, XS)) -> mark(head(afterNth(N, XS)))
     , active(U51(tt(), Y)) -> mark(U52(tt(), Y))
     , active(U52(tt(), Y)) -> mark(Y)
     , active(U61(tt(), N, X, XS)) -> mark(U62(tt(), N, X, XS))
     , active(U62(tt(), N, X, XS)) -> mark(U63(tt(), N, X, XS))
     , active(U63(tt(), N, X, XS)) -> mark(U64(splitAt(N, XS), X))
     , active(U64(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS))
     , active(U71(tt(), XS)) -> mark(U72(tt(), XS))
     , active(U72(tt(), XS)) -> mark(XS)
     , active(U81(tt(), N, XS)) -> mark(U82(tt(), N, XS))
     , active(U82(tt(), N, XS)) -> mark(fst(splitAt(N, XS)))
     , active(afterNth(N, XS)) -> mark(U11(tt(), N, XS))
     , active(fst(pair(X, Y))) -> mark(U21(tt(), X))
     , active(head(cons(N, XS))) -> mark(U31(tt(), N))
     , active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
     , active(sel(N, XS)) -> mark(U41(tt(), N, XS))
     , active(snd(pair(X, Y))) -> mark(U51(tt(), Y))
     , active(splitAt(0(), XS)) -> mark(pair(nil(), XS))
     , active(splitAt(s(N), cons(X, XS))) -> mark(U61(tt(), N, X, XS))
     , active(tail(cons(N, XS))) -> mark(U71(tt(), XS))
     , active(take(N, XS)) -> mark(U81(tt(), N, XS))
     , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
     , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
     , active(snd(X)) -> snd(active(X))
     , active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
     , active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
     , active(U21(X1, X2)) -> U21(active(X1), X2)
     , active(U22(X1, X2)) -> U22(active(X1), X2)
     , active(U31(X1, X2)) -> U31(active(X1), X2)
     , active(U32(X1, X2)) -> U32(active(X1), X2)
     , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
     , active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
     , active(head(X)) -> head(active(X))
     , active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
     , active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
     , active(U51(X1, X2)) -> U51(active(X1), X2)
     , active(U52(X1, X2)) -> U52(active(X1), X2)
     , active(U61(X1, X2, X3, X4)) -> U61(active(X1), X2, X3, X4)
     , active(U62(X1, X2, X3, X4)) -> U62(active(X1), X2, X3, X4)
     , active(U63(X1, X2, X3, X4)) -> U63(active(X1), X2, X3, X4)
     , active(U64(X1, X2)) -> U64(active(X1), X2)
     , active(pair(X1, X2)) -> pair(active(X1), X2)
     , active(pair(X1, X2)) -> pair(X1, active(X2))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U71(X1, X2)) -> U71(active(X1), X2)
     , active(U72(X1, X2)) -> U72(active(X1), X2)
     , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3)
     , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3)
     , active(fst(X)) -> fst(active(X))
     , active(natsFrom(X)) -> natsFrom(active(X))
     , active(s(X)) -> s(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(tail(X)) -> tail(active(X))
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
     , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3))
     , snd(mark(X)) -> mark(snd(X))
     , splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
     , splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
     , U21(mark(X1), X2) -> mark(U21(X1, X2))
     , U22(mark(X1), X2) -> mark(U22(X1, X2))
     , U31(mark(X1), X2) -> mark(U31(X1, X2))
     , U32(mark(X1), X2) -> mark(U32(X1, X2))
     , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
     , U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3))
     , head(mark(X)) -> mark(head(X))
     , afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
     , afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
     , U51(mark(X1), X2) -> mark(U51(X1, X2))
     , U52(mark(X1), X2) -> mark(U52(X1, X2))
     , U61(mark(X1), X2, X3, X4) -> mark(U61(X1, X2, X3, X4))
     , U62(mark(X1), X2, X3, X4) -> mark(U62(X1, X2, X3, X4))
     , U63(mark(X1), X2, X3, X4) -> mark(U63(X1, X2, X3, X4))
     , U64(mark(X1), X2) -> mark(U64(X1, X2))
     , pair(mark(X1), X2) -> mark(pair(X1, X2))
     , pair(X1, mark(X2)) -> mark(pair(X1, X2))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U71(mark(X1), X2) -> mark(U71(X1, X2))
     , U72(mark(X1), X2) -> mark(U72(X1, X2))
     , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3))
     , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3))
     , fst(mark(X)) -> mark(fst(X))
     , natsFrom(mark(X)) -> mark(natsFrom(X))
     , s(mark(X)) -> mark(s(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , tail(mark(X)) -> mark(tail(X))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , proper(U11(X1, X2, X3)) ->
       U11(proper(X1), proper(X2), proper(X3))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2, X3)) ->
       U12(proper(X1), proper(X2), proper(X3))
     , proper(snd(X)) -> snd(proper(X))
     , proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
     , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
     , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2))
     , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
     , proper(U32(X1, X2)) -> U32(proper(X1), proper(X2))
     , proper(U41(X1, X2, X3)) ->
       U41(proper(X1), proper(X2), proper(X3))
     , proper(U42(X1, X2, X3)) ->
       U42(proper(X1), proper(X2), proper(X3))
     , proper(head(X)) -> head(proper(X))
     , proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
     , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
     , proper(U52(X1, X2)) -> U52(proper(X1), proper(X2))
     , proper(U61(X1, X2, X3, X4)) ->
       U61(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U62(X1, X2, X3, X4)) ->
       U62(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U63(X1, X2, X3, X4)) ->
       U63(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U64(X1, X2)) -> U64(proper(X1), proper(X2))
     , proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2))
     , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2))
     , proper(U81(X1, X2, X3)) ->
       U81(proper(X1), proper(X2), proper(X3))
     , proper(U82(X1, X2, X3)) ->
       U82(proper(X1), proper(X2), proper(X3))
     , proper(fst(X)) -> fst(proper(X))
     , proper(natsFrom(X)) -> natsFrom(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(nil()) -> ok(nil())
     , proper(tail(X)) -> tail(proper(X))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
     , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3))
     , snd(ok(X)) -> ok(snd(X))
     , splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
     , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
     , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
     , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
     , U32(ok(X1), ok(X2)) -> ok(U32(X1, X2))
     , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
     , U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
     , head(ok(X)) -> ok(head(X))
     , afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
     , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
     , U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
     , U61(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U61(X1, X2, X3, X4))
     , U62(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U62(X1, X2, X3, X4))
     , U63(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U63(X1, X2, X3, X4))
     , U64(ok(X1), ok(X2)) -> ok(U64(X1, X2))
     , pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2))
     , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2))
     , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3))
     , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3))
     , fst(ok(X)) -> ok(fst(X))
     , natsFrom(ok(X)) -> ok(natsFrom(X))
     , s(ok(X)) -> ok(s(X))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , tail(ok(X)) -> ok(tail(X))
     , 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