/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(X1,X2) -> U105(X1,X2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(X) -> U106(X) a__U106(tt()) -> tt() a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(X1,X2) -> U114(X1,X2) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(X1,X2) -> U121(X1,X2) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(X) -> U122(X) a__U122(tt()) -> nil() a__U13(X) -> U13(X) a__U13(tt()) -> tt() a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(X1,X2) -> U21(X1,X2) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(X1,X2) -> U22(X1,X2) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(X) -> U23(X) a__U23(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(X1,X2) -> U32(X1,X2) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(X) -> U33(X) a__U33(tt()) -> tt() a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(X1,X2) -> U45(X1,X2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(X) -> U46(X) a__U46(tt()) -> tt() a__U51(X1,X2) -> U51(X1,X2) a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(X) -> U52(X) a__U52(tt()) -> tt() a__U61(X1,X2) -> U61(X1,X2) a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(X) -> U62(X) a__U62(tt()) -> tt() a__U71(X) -> U71(X) a__U71(tt()) -> tt() a__U81(X) -> U81(X) a__U81(tt()) -> tt() a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(X1,X2) -> U95(X1,X2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(X) -> U96(X) a__U96(tt()) -> tt() a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(X) -> isNatIList(X) a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIList(zeros()) -> tt() a__isNatIListKind(X) -> isNatIListKind(X) a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatIListKind(zeros()) -> tt() a__isNatKind(X) -> isNatKind(X) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(X) -> isNatList(X) a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(nil()) -> tt() a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(U106(X)) -> a__U106(mark(X)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(isNatList(X)) -> a__isNatList(X) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U101/3,a__U102/3,a__U103/3,a__U104/3,a__U105/2,a__U106/1,a__U11/2,a__U111/3,a__U112/3,a__U113/3 ,a__U114/2,a__U12/2,a__U121/2,a__U122/1,a__U13/1,a__U131/4,a__U132/4,a__U133/4,a__U134/4,a__U135/4,a__U136/4 ,a__U21/2,a__U22/2,a__U23/1,a__U31/2,a__U32/2,a__U33/1,a__U41/3,a__U42/3,a__U43/3,a__U44/3,a__U45/2,a__U46/1 ,a__U51/2,a__U52/1,a__U61/2,a__U62/1,a__U71/1,a__U81/1,a__U91/3,a__U92/3,a__U93/3,a__U94/3,a__U95/2,a__U96/1 ,a__isNat/1,a__isNatIList/1,a__isNatIListKind/1,a__isNatKind/1,a__isNatList/1,a__length/1,a__take/2 ,a__zeros/0,mark/1} / {0/0,U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/2,U111/3,U112/3,U113/3,U114/2,U12/2 ,U121/2,U122/1,U13/1,U131/4,U132/4,U133/4,U134/4,U135/4,U136/4,U21/2,U22/2,U23/1,U31/2,U32/2,U33/1,U41/3 ,U42/3,U43/3,U44/3,U45/2,U46/1,U51/2,U52/1,U61/2,U62/1,U71/1,U81/1,U91/3,U92/3,U93/3,U94/3,U95/2,U96/1 ,cons/2,isNat/1,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,tt/0 ,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U101,a__U102,a__U103,a__U104,a__U105,a__U106,a__U11,a__U111 ,a__U112,a__U113,a__U114,a__U12,a__U121,a__U122,a__U13,a__U131,a__U132,a__U133,a__U134,a__U135,a__U136 ,a__U21,a__U22,a__U23,a__U31,a__U32,a__U33,a__U41,a__U42,a__U43,a__U44,a__U45,a__U46,a__U51,a__U52,a__U61 ,a__U62,a__U71,a__U81,a__U91,a__U92,a__U93,a__U94,a__U95,a__U96,a__isNat,a__isNatIList,a__isNatIListKind ,a__isNatKind,a__isNatList,a__length,a__take,a__zeros,mark} and constructors {0,U101,U102,U103,U104,U105 ,U106,U11,U111,U112,U113,U114,U12,U121,U122,U13,U131,U132,U133,U134,U135,U136,U21,U22,U23,U31,U32,U33,U41 ,U42,U43,U44,U45,U46,U51,U52,U61,U62,U71,U81,U91,U92,U93,U94,U95,U96,cons,isNat,isNatIList,isNatIListKind ,isNatKind,isNatList,length,nil,s,take,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(X1,X2) -> U105(X1,X2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(X) -> U106(X) a__U106(tt()) -> tt() a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(X1,X2) -> U114(X1,X2) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(X1,X2) -> U121(X1,X2) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(X) -> U122(X) a__U122(tt()) -> nil() a__U13(X) -> U13(X) a__U13(tt()) -> tt() a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(X1,X2) -> U21(X1,X2) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(X1,X2) -> U22(X1,X2) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(X) -> U23(X) a__U23(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(X1,X2) -> U32(X1,X2) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(X) -> U33(X) a__U33(tt()) -> tt() a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(X1,X2) -> U45(X1,X2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(X) -> U46(X) a__U46(tt()) -> tt() a__U51(X1,X2) -> U51(X1,X2) a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(X) -> U52(X) a__U52(tt()) -> tt() a__U61(X1,X2) -> U61(X1,X2) a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(X) -> U62(X) a__U62(tt()) -> tt() a__U71(X) -> U71(X) a__U71(tt()) -> tt() a__U81(X) -> U81(X) a__U81(tt()) -> tt() a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(X1,X2) -> U95(X1,X2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(X) -> U96(X) a__U96(tt()) -> tt() a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(X) -> isNatIList(X) a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIList(zeros()) -> tt() a__isNatIListKind(X) -> isNatIListKind(X) a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatIListKind(zeros()) -> tt() a__isNatKind(X) -> isNatKind(X) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(X) -> isNatList(X) a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(nil()) -> tt() a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(U106(X)) -> a__U106(mark(X)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(isNatList(X)) -> a__isNatList(X) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U101/3,a__U102/3,a__U103/3,a__U104/3,a__U105/2,a__U106/1,a__U11/2,a__U111/3,a__U112/3,a__U113/3 ,a__U114/2,a__U12/2,a__U121/2,a__U122/1,a__U13/1,a__U131/4,a__U132/4,a__U133/4,a__U134/4,a__U135/4,a__U136/4 ,a__U21/2,a__U22/2,a__U23/1,a__U31/2,a__U32/2,a__U33/1,a__U41/3,a__U42/3,a__U43/3,a__U44/3,a__U45/2,a__U46/1 ,a__U51/2,a__U52/1,a__U61/2,a__U62/1,a__U71/1,a__U81/1,a__U91/3,a__U92/3,a__U93/3,a__U94/3,a__U95/2,a__U96/1 ,a__isNat/1,a__isNatIList/1,a__isNatIListKind/1,a__isNatKind/1,a__isNatList/1,a__length/1,a__take/2 ,a__zeros/0,mark/1} / {0/0,U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/2,U111/3,U112/3,U113/3,U114/2,U12/2 ,U121/2,U122/1,U13/1,U131/4,U132/4,U133/4,U134/4,U135/4,U136/4,U21/2,U22/2,U23/1,U31/2,U32/2,U33/1,U41/3 ,U42/3,U43/3,U44/3,U45/2,U46/1,U51/2,U52/1,U61/2,U62/1,U71/1,U81/1,U91/3,U92/3,U93/3,U94/3,U95/2,U96/1 ,cons/2,isNat/1,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,tt/0 ,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U101,a__U102,a__U103,a__U104,a__U105,a__U106,a__U11,a__U111 ,a__U112,a__U113,a__U114,a__U12,a__U121,a__U122,a__U13,a__U131,a__U132,a__U133,a__U134,a__U135,a__U136 ,a__U21,a__U22,a__U23,a__U31,a__U32,a__U33,a__U41,a__U42,a__U43,a__U44,a__U45,a__U46,a__U51,a__U52,a__U61 ,a__U62,a__U71,a__U81,a__U91,a__U92,a__U93,a__U94,a__U95,a__U96,a__isNat,a__isNatIList,a__isNatIListKind ,a__isNatKind,a__isNatList,a__length,a__take,a__zeros,mark} and constructors {0,U101,U102,U103,U104,U105 ,U106,U11,U111,U112,U113,U114,U12,U121,U122,U13,U131,U132,U133,U134,U135,U136,U21,U22,U23,U31,U32,U33,U41 ,U42,U43,U44,U45,U46,U51,U52,U61,U62,U71,U81,U91,U92,U93,U94,U95,U96,cons,isNat,isNatIList,isNatIListKind ,isNatKind,isNatList,length,nil,s,take,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(X1,X2) -> U105(X1,X2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(X) -> U106(X) a__U106(tt()) -> tt() a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(X1,X2) -> U114(X1,X2) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(X1,X2) -> U121(X1,X2) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(X) -> U122(X) a__U122(tt()) -> nil() a__U13(X) -> U13(X) a__U13(tt()) -> tt() a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(X1,X2) -> U21(X1,X2) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(X1,X2) -> U22(X1,X2) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(X) -> U23(X) a__U23(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(X1,X2) -> U32(X1,X2) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(X) -> U33(X) a__U33(tt()) -> tt() a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(X1,X2) -> U45(X1,X2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(X) -> U46(X) a__U46(tt()) -> tt() a__U51(X1,X2) -> U51(X1,X2) a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(X) -> U52(X) a__U52(tt()) -> tt() a__U61(X1,X2) -> U61(X1,X2) a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(X) -> U62(X) a__U62(tt()) -> tt() a__U71(X) -> U71(X) a__U71(tt()) -> tt() a__U81(X) -> U81(X) a__U81(tt()) -> tt() a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(X1,X2) -> U95(X1,X2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(X) -> U96(X) a__U96(tt()) -> tt() a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(X) -> isNatIList(X) a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIList(zeros()) -> tt() a__isNatIListKind(X) -> isNatIListKind(X) a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatIListKind(zeros()) -> tt() a__isNatKind(X) -> isNatKind(X) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(X) -> isNatList(X) a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(nil()) -> tt() a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(U106(X)) -> a__U106(mark(X)) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(isNatList(X)) -> a__isNatList(X) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U101/3,a__U102/3,a__U103/3,a__U104/3,a__U105/2,a__U106/1,a__U11/2,a__U111/3,a__U112/3,a__U113/3 ,a__U114/2,a__U12/2,a__U121/2,a__U122/1,a__U13/1,a__U131/4,a__U132/4,a__U133/4,a__U134/4,a__U135/4,a__U136/4 ,a__U21/2,a__U22/2,a__U23/1,a__U31/2,a__U32/2,a__U33/1,a__U41/3,a__U42/3,a__U43/3,a__U44/3,a__U45/2,a__U46/1 ,a__U51/2,a__U52/1,a__U61/2,a__U62/1,a__U71/1,a__U81/1,a__U91/3,a__U92/3,a__U93/3,a__U94/3,a__U95/2,a__U96/1 ,a__isNat/1,a__isNatIList/1,a__isNatIListKind/1,a__isNatKind/1,a__isNatList/1,a__length/1,a__take/2 ,a__zeros/0,mark/1} / {0/0,U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/2,U111/3,U112/3,U113/3,U114/2,U12/2 ,U121/2,U122/1,U13/1,U131/4,U132/4,U133/4,U134/4,U135/4,U136/4,U21/2,U22/2,U23/1,U31/2,U32/2,U33/1,U41/3 ,U42/3,U43/3,U44/3,U45/2,U46/1,U51/2,U52/1,U61/2,U62/1,U71/1,U81/1,U91/3,U92/3,U93/3,U94/3,U95/2,U96/1 ,cons/2,isNat/1,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,tt/0 ,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U101,a__U102,a__U103,a__U104,a__U105,a__U106,a__U11,a__U111 ,a__U112,a__U113,a__U114,a__U12,a__U121,a__U122,a__U13,a__U131,a__U132,a__U133,a__U134,a__U135,a__U136 ,a__U21,a__U22,a__U23,a__U31,a__U32,a__U33,a__U41,a__U42,a__U43,a__U44,a__U45,a__U46,a__U51,a__U52,a__U61 ,a__U62,a__U71,a__U81,a__U91,a__U92,a__U93,a__U94,a__U95,a__U96,a__isNat,a__isNatIList,a__isNatIListKind ,a__isNatKind,a__isNatList,a__length,a__take,a__zeros,mark} and constructors {0,U101,U102,U103,U104,U105 ,U106,U11,U111,U112,U113,U114,U12,U121,U122,U13,U131,U132,U133,U134,U135,U136,U21,U22,U23,U31,U32,U33,U41 ,U42,U43,U44,U45,U46,U51,U52,U61,U62,U71,U81,U91,U92,U93,U94,U95,U96,cons,isNat,isNatIList,isNatIListKind ,isNatKind,isNatList,length,nil,s,take,tt,zeros} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: a__isNatKind(x){x -> s(x)} = a__isNatKind(s(x)) ->^+ a__U81(a__isNatKind(x)) = C[a__isNatKind(x) = a__isNatKind(x){}] WORST_CASE(Omega(n^1),?)