/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() U11(tt()) -> tt() U21(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) 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__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatList(activate(V1))) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatIList(n__zeros()) -> tt() isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) isNatList(n__nil()) -> tt() length(X) -> n__length(X) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {0/0,U11/1,U21/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/3,U62/2,activate/1,cons/2,isNat/1,isNatIList/1 ,isNatList/1,length/1,nil/0,s/1,zeros/0} / {n__0/0,n__cons/2,n__length/1,n__nil/0,n__s/1,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,U42,U51,U52,U61,U62,activate,cons,isNat ,isNatIList,isNatList,length,nil,s,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,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() U11(tt()) -> tt() U21(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) 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__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatList(activate(V1))) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatIList(n__zeros()) -> tt() isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) isNatList(n__nil()) -> tt() length(X) -> n__length(X) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {0/0,U11/1,U21/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/3,U62/2,activate/1,cons/2,isNat/1,isNatIList/1 ,isNatList/1,length/1,nil/0,s/1,zeros/0} / {n__0/0,n__cons/2,n__length/1,n__nil/0,n__s/1,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,U42,U51,U52,U61,U62,activate,cons,isNat ,isNatIList,isNatList,length,nil,s,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,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() U11(tt()) -> tt() U21(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) 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__zeros()) -> zeros() cons(X1,X2) -> n__cons(X1,X2) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatList(activate(V1))) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatIList(n__zeros()) -> tt() isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) isNatList(n__nil()) -> tt() length(X) -> n__length(X) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) length(nil()) -> 0() nil() -> n__nil() s(X) -> n__s(X) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {0/0,U11/1,U21/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/3,U62/2,activate/1,cons/2,isNat/1,isNatIList/1 ,isNatList/1,length/1,nil/0,s/1,zeros/0} / {n__0/0,n__cons/2,n__length/1,n__nil/0,n__s/1,n__zeros/0,tt/0} - Obligation: runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,U42,U51,U52,U61,U62,activate,cons,isNat ,isNatIList,isNatList,length,nil,s,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__zeros,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: isNat(x){x -> n__s(x)} = isNat(n__s(x)) ->^+ U21(isNat(x)) = C[isNat(x) = isNat(x){}] WORST_CASE(Omega(n^1),?)