* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(mark(X1),X2) -> mark(U22(X1,X2))
U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U51(mark(X1),X2) -> mark(U51(X1,X2))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(mark(X1),X2) -> mark(U52(X1,X2))
U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
U61(mark(X1),X2,X3,X4) -> mark(U61(X1,X2,X3,X4))
U61(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U61(X1,X2,X3,X4))
U62(mark(X1),X2,X3,X4) -> mark(U62(X1,X2,X3,X4))
U62(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U62(X1,X2,X3,X4))
U63(mark(X1),X2,X3,X4) -> mark(U63(X1,X2,X3,X4))
U63(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U63(X1,X2,X3,X4))
U64(mark(X1),X2) -> mark(U64(X1,X2))
U64(ok(X1),ok(X2)) -> ok(U64(X1,X2))
U71(mark(X1),X2) -> mark(U71(X1,X2))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U11(tt(),N,XS)) -> mark(U12(tt(),N,XS))
active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U21(tt(),X)) -> mark(U22(tt(),X))
active(U22(X1,X2)) -> U22(active(X1),X2)
active(U22(tt(),X)) -> mark(X)
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U31(tt(),N)) -> mark(U32(tt(),N))
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U32(tt(),N)) -> mark(N)
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),N,XS)) -> mark(U42(tt(),N,XS))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
active(U51(X1,X2)) -> U51(active(X1),X2)
active(U51(tt(),Y)) -> mark(U52(tt(),Y))
active(U52(X1,X2)) -> U52(active(X1),X2)
active(U52(tt(),Y)) -> mark(Y)
active(U61(X1,X2,X3,X4)) -> U61(active(X1),X2,X3,X4)
active(U61(tt(),N,X,XS)) -> mark(U62(tt(),N,X,XS))
active(U62(X1,X2,X3,X4)) -> U62(active(X1),X2,X3,X4)
active(U62(tt(),N,X,XS)) -> mark(U63(tt(),N,X,XS))
active(U63(X1,X2,X3,X4)) -> U63(active(X1),X2,X3,X4)
active(U63(tt(),N,X,XS)) -> mark(U64(splitAt(N,XS),X))
active(U64(X1,X2)) -> U64(active(X1),X2)
active(U64(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(U71(X1,X2)) -> U71(active(X1),X2)
active(U71(tt(),XS)) -> mark(U72(tt(),XS))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),XS)) -> mark(XS)
active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
active(U81(tt(),N,XS)) -> mark(U82(tt(),N,XS))
active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
active(U82(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
active(afterNth(N,XS)) -> mark(U11(tt(),N,XS))
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(cons(X1,X2)) -> cons(active(X1),X2)
active(fst(X)) -> fst(active(X))
active(fst(pair(X,Y))) -> mark(U21(tt(),X))
active(head(X)) -> head(active(X))
active(head(cons(N,XS))) -> mark(U31(tt(),N))
active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
active(natsFrom(X)) -> natsFrom(active(X))
active(pair(X1,X2)) -> pair(X1,active(X2))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(s(X)) -> s(active(X))
active(sel(N,XS)) -> mark(U41(tt(),N,XS))
active(sel(X1,X2)) -> sel(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(snd(X)) -> snd(active(X))
active(snd(pair(X,Y))) -> mark(U51(tt(),Y))
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U61(tt(),N,X,XS))
active(tail(X)) -> tail(active(X))
active(tail(cons(N,XS))) -> mark(U71(tt(),XS))
active(take(N,XS)) -> mark(U81(tt(),N,XS))
active(take(X1,X2)) -> take(X1,active(X2))
active(take(X1,X2)) -> take(active(X1),X2)
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fst(mark(X)) -> mark(fst(X))
fst(ok(X)) -> ok(fst(X))
head(mark(X)) -> mark(head(X))
head(ok(X)) -> ok(head(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
proper(0()) -> ok(0())
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
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(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(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(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(fst(X)) -> fst(proper(X))
proper(head(X)) -> head(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(nil()) -> ok(nil())
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
snd(mark(X)) -> mark(snd(X))
snd(ok(X)) -> ok(snd(X))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/3,U12/3,U21/2,U22/2,U31/2,U32/2,U41/3,U42/3,U51/2,U52/2,U61/4,U62/4,U63/4,U64/2,U71/2,U72/2,U81/3,U82/3
,active/1,afterNth/2,cons/2,fst/1,head/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2
,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U31,U32,U41,U42,U51,U52,U61,U62,U63,U64
,U71,U72,U81,U82,active,afterNth,cons,fst,head,natsFrom,pair,proper,s,sel,snd,splitAt,tail,take
,top} and constructors {0,mark,nil,ok,tt}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(mark(X1),X2) -> mark(U22(X1,X2))
U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U51(mark(X1),X2) -> mark(U51(X1,X2))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(mark(X1),X2) -> mark(U52(X1,X2))
U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
U61(mark(X1),X2,X3,X4) -> mark(U61(X1,X2,X3,X4))
U61(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U61(X1,X2,X3,X4))
U62(mark(X1),X2,X3,X4) -> mark(U62(X1,X2,X3,X4))
U62(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U62(X1,X2,X3,X4))
U63(mark(X1),X2,X3,X4) -> mark(U63(X1,X2,X3,X4))
U63(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U63(X1,X2,X3,X4))
U64(mark(X1),X2) -> mark(U64(X1,X2))
U64(ok(X1),ok(X2)) -> ok(U64(X1,X2))
U71(mark(X1),X2) -> mark(U71(X1,X2))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U11(tt(),N,XS)) -> mark(U12(tt(),N,XS))
active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U21(tt(),X)) -> mark(U22(tt(),X))
active(U22(X1,X2)) -> U22(active(X1),X2)
active(U22(tt(),X)) -> mark(X)
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U31(tt(),N)) -> mark(U32(tt(),N))
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U32(tt(),N)) -> mark(N)
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),N,XS)) -> mark(U42(tt(),N,XS))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
active(U51(X1,X2)) -> U51(active(X1),X2)
active(U51(tt(),Y)) -> mark(U52(tt(),Y))
active(U52(X1,X2)) -> U52(active(X1),X2)
active(U52(tt(),Y)) -> mark(Y)
active(U61(X1,X2,X3,X4)) -> U61(active(X1),X2,X3,X4)
active(U61(tt(),N,X,XS)) -> mark(U62(tt(),N,X,XS))
active(U62(X1,X2,X3,X4)) -> U62(active(X1),X2,X3,X4)
active(U62(tt(),N,X,XS)) -> mark(U63(tt(),N,X,XS))
active(U63(X1,X2,X3,X4)) -> U63(active(X1),X2,X3,X4)
active(U63(tt(),N,X,XS)) -> mark(U64(splitAt(N,XS),X))
active(U64(X1,X2)) -> U64(active(X1),X2)
active(U64(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(U71(X1,X2)) -> U71(active(X1),X2)
active(U71(tt(),XS)) -> mark(U72(tt(),XS))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),XS)) -> mark(XS)
active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
active(U81(tt(),N,XS)) -> mark(U82(tt(),N,XS))
active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
active(U82(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
active(afterNth(N,XS)) -> mark(U11(tt(),N,XS))
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(cons(X1,X2)) -> cons(active(X1),X2)
active(fst(X)) -> fst(active(X))
active(fst(pair(X,Y))) -> mark(U21(tt(),X))
active(head(X)) -> head(active(X))
active(head(cons(N,XS))) -> mark(U31(tt(),N))
active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
active(natsFrom(X)) -> natsFrom(active(X))
active(pair(X1,X2)) -> pair(X1,active(X2))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(s(X)) -> s(active(X))
active(sel(N,XS)) -> mark(U41(tt(),N,XS))
active(sel(X1,X2)) -> sel(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(snd(X)) -> snd(active(X))
active(snd(pair(X,Y))) -> mark(U51(tt(),Y))
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U61(tt(),N,X,XS))
active(tail(X)) -> tail(active(X))
active(tail(cons(N,XS))) -> mark(U71(tt(),XS))
active(take(N,XS)) -> mark(U81(tt(),N,XS))
active(take(X1,X2)) -> take(X1,active(X2))
active(take(X1,X2)) -> take(active(X1),X2)
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fst(mark(X)) -> mark(fst(X))
fst(ok(X)) -> ok(fst(X))
head(mark(X)) -> mark(head(X))
head(ok(X)) -> ok(head(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
proper(0()) -> ok(0())
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
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(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(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(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(fst(X)) -> fst(proper(X))
proper(head(X)) -> head(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(nil()) -> ok(nil())
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
snd(mark(X)) -> mark(snd(X))
snd(ok(X)) -> ok(snd(X))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/3,U12/3,U21/2,U22/2,U31/2,U32/2,U41/3,U42/3,U51/2,U52/2,U61/4,U62/4,U63/4,U64/2,U71/2,U72/2,U81/3,U82/3
,active/1,afterNth/2,cons/2,fst/1,head/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2
,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U31,U32,U41,U42,U51,U52,U61,U62,U63,U64
,U71,U72,U81,U82,active,afterNth,cons,fst,head,natsFrom,pair,proper,s,sel,snd,splitAt,tail,take
,top} and constructors {0,mark,nil,ok,tt}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
U11(x,y,z){x -> mark(x)} =
U11(mark(x),y,z) ->^+ mark(U11(x,y,z))
= C[U11(x,y,z) = U11(x,y,z){}]
WORST_CASE(Omega(n^1),?)