/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: 0() -> n__0() U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2)) U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2)) U105(tt(),V2) -> U106(isNatIList(activate(V2))) U106(tt()) -> tt() U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1)) U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N)) U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N)) U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L)) U114(tt(),L) -> s(length(activate(L))) U12(tt(),V1) -> U13(isNatList(activate(V1))) U121(tt(),IL) -> U122(isNatIListKind(activate(IL))) U122(tt()) -> nil() U13(tt()) -> tt() U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N)) U132(tt(),IL,M,N) -> U133(isNat(activate(M)),activate(IL),activate(M),activate(N)) U133(tt(),IL,M,N) -> U134(isNatKind(activate(M)),activate(IL),activate(M),activate(N)) U134(tt(),IL,M,N) -> U135(isNat(activate(N)),activate(IL),activate(M),activate(N)) U135(tt(),IL,M,N) -> U136(isNatKind(activate(N)),activate(IL),activate(M),activate(N)) U136(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt(),V1) -> U23(isNat(activate(V1))) U23(tt()) -> tt() U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isNatList(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isNat(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNatIList(activate(V2))) U46(tt()) -> tt() U51(tt(),V2) -> U52(isNatIListKind(activate(V2))) U52(tt()) -> tt() U61(tt(),V2) -> U62(isNatIListKind(activate(V2))) U62(tt()) -> tt() U71(tt()) -> tt() U81(tt()) -> tt() U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2)) U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U93(tt(),V1,V2) -> U94(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U94(tt(),V1,V2) -> U95(isNat(activate(V1)),activate(V2)) U95(tt(),V2) -> U96(isNatList(activate(V2))) U96(tt()) -> tt() activate(X) -> X activate(n__0()) -> 0() activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__length(X)) -> length(X) activate(n__nil()) -> nil() activate(n__s(X)) -> s(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__cons(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatIList(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__zeros()) -> tt() isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatList(n__nil()) -> tt() isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2)) length(X) -> n__length(X) length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> U121(isNatIList(IL),IL) take(s(M),cons(N,IL)) -> U131(isNatIList(activate(IL)),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {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,activate/1,cons/2,isNat/1 ,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,zeros/0} / {n__0/0 ,n__cons/2,n__length/1,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {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,activate,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList,length,nil,s ,take,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 0() -> n__0() U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2)) U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2)) U105(tt(),V2) -> U106(isNatIList(activate(V2))) U106(tt()) -> tt() U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1)) U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N)) U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N)) U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L)) U114(tt(),L) -> s(length(activate(L))) U12(tt(),V1) -> U13(isNatList(activate(V1))) U121(tt(),IL) -> U122(isNatIListKind(activate(IL))) U122(tt()) -> nil() U13(tt()) -> tt() U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N)) U132(tt(),IL,M,N) -> U133(isNat(activate(M)),activate(IL),activate(M),activate(N)) U133(tt(),IL,M,N) -> U134(isNatKind(activate(M)),activate(IL),activate(M),activate(N)) U134(tt(),IL,M,N) -> U135(isNat(activate(N)),activate(IL),activate(M),activate(N)) U135(tt(),IL,M,N) -> U136(isNatKind(activate(N)),activate(IL),activate(M),activate(N)) U136(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt(),V1) -> U23(isNat(activate(V1))) U23(tt()) -> tt() U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isNatList(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isNat(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNatIList(activate(V2))) U46(tt()) -> tt() U51(tt(),V2) -> U52(isNatIListKind(activate(V2))) U52(tt()) -> tt() U61(tt(),V2) -> U62(isNatIListKind(activate(V2))) U62(tt()) -> tt() U71(tt()) -> tt() U81(tt()) -> tt() U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2)) U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U93(tt(),V1,V2) -> U94(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U94(tt(),V1,V2) -> U95(isNat(activate(V1)),activate(V2)) U95(tt(),V2) -> U96(isNatList(activate(V2))) U96(tt()) -> tt() activate(X) -> X activate(n__0()) -> 0() activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__length(X)) -> length(X) activate(n__nil()) -> nil() activate(n__s(X)) -> s(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__cons(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatIList(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__zeros()) -> tt() isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatList(n__nil()) -> tt() isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2)) length(X) -> n__length(X) length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> U121(isNatIList(IL),IL) take(s(M),cons(N,IL)) -> U131(isNatIList(activate(IL)),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {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,activate/1,cons/2,isNat/1 ,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,zeros/0} / {n__0/0 ,n__cons/2,n__length/1,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {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,activate,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList,length,nil,s ,take,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 0() -> n__0() U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2)) U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2)) U105(tt(),V2) -> U106(isNatIList(activate(V2))) U106(tt()) -> tt() U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1)) U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N)) U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N)) U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L)) U114(tt(),L) -> s(length(activate(L))) U12(tt(),V1) -> U13(isNatList(activate(V1))) U121(tt(),IL) -> U122(isNatIListKind(activate(IL))) U122(tt()) -> nil() U13(tt()) -> tt() U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N)) U132(tt(),IL,M,N) -> U133(isNat(activate(M)),activate(IL),activate(M),activate(N)) U133(tt(),IL,M,N) -> U134(isNatKind(activate(M)),activate(IL),activate(M),activate(N)) U134(tt(),IL,M,N) -> U135(isNat(activate(N)),activate(IL),activate(M),activate(N)) U135(tt(),IL,M,N) -> U136(isNatKind(activate(N)),activate(IL),activate(M),activate(N)) U136(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt(),V1) -> U23(isNat(activate(V1))) U23(tt()) -> tt() U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V)) U32(tt(),V) -> U33(isNatList(activate(V))) U33(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2)) U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U43(tt(),V1,V2) -> U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U44(tt(),V1,V2) -> U45(isNat(activate(V1)),activate(V2)) U45(tt(),V2) -> U46(isNatIList(activate(V2))) U46(tt()) -> tt() U51(tt(),V2) -> U52(isNatIListKind(activate(V2))) U52(tt()) -> tt() U61(tt(),V2) -> U62(isNatIListKind(activate(V2))) U62(tt()) -> tt() U71(tt()) -> tt() U81(tt()) -> tt() U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2)) U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U93(tt(),V1,V2) -> U94(isNatIListKind(activate(V2)),activate(V1),activate(V2)) U94(tt(),V1,V2) -> U95(isNat(activate(V1)),activate(V2)) U95(tt(),V2) -> U96(isNatList(activate(V2))) U96(tt()) -> tt() activate(X) -> X activate(n__0()) -> 0() activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__length(X)) -> length(X) activate(n__nil()) -> nil() activate(n__s(X)) -> s(X) activate(n__take(X1,X2)) -> take(X1,X2) activate(n__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__cons(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatIList(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) isNatIListKind(n__zeros()) -> tt() isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))) isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))) isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatList(n__nil()) -> tt() isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2)) length(X) -> n__length(X) length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> U121(isNatIList(IL),IL) take(s(M),cons(N,IL)) -> U131(isNatIList(activate(IL)),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {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,activate/1,cons/2,isNat/1 ,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0,s/1,take/2,zeros/0} / {n__0/0 ,n__cons/2,n__length/1,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {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,activate,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList,length,nil,s ,take,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: isNatKind(x){x -> n__s(x)} = isNatKind(n__s(x)) ->^+ U81(isNatKind(x)) = C[isNatKind(x) = isNatKind(x){}] WORST_CASE(Omega(n^1),?)