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