* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(false(),n,l) -> tail(nthtail(s(n),l)) cond(true(),n,l) -> l ge(u,0()) -> true() ge(0(),s(v)) -> false() ge(s(u),s(v)) -> ge(u,v) length(cons(x,l)) -> s(length(l)) length(nil()) -> 0() nthtail(n,l) -> cond(ge(n,length(l)),n,l) tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons ,false,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(false(),n,l) -> tail(nthtail(s(n),l)) cond(true(),n,l) -> l ge(u,0()) -> true() ge(0(),s(v)) -> false() ge(s(u),s(v)) -> ge(u,v) length(cons(x,l)) -> s(length(l)) length(nil()) -> 0() nthtail(n,l) -> cond(ge(n,length(l)),n,l) tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons ,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ge(x,y){x -> s(x),y -> s(y)} = ge(s(x),s(y)) ->^+ ge(x,y) = C[ge(x,y) = ge(x,y){}] WORST_CASE(Omega(n^1),?)