* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(cons(h,t),x) -> cons(h,app(t,x)) app(nil(),x) -> x empty(cons(h,t)) -> false() empty(nil()) -> true() fstsplit(0(),x) -> nil() fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t)) fstsplit(s(n),nil()) -> nil() if1(store,m,false()) -> if3(store,m,empty(fstsplit(m,app(map_f(self(),nil()),store)))) if1(store,m,true()) -> if2(store,m,empty(fstsplit(m,store))) if2(store,m,false()) -> process(app(map_f(self(),nil()),sndsplit(m,store)),m) if3(store,m,false()) -> process(sndsplit(m,app(map_f(self(),nil()),store)),m) length(cons(h,t)) -> s(length(t)) length(nil()) -> 0() leq(0(),m) -> true() leq(s(n),0()) -> false() leq(s(n),s(m)) -> leq(n,m) map_f(pid,cons(h,t)) -> app(f(pid,h),map_f(pid,t)) map_f(pid,nil()) -> nil() process(store,m) -> if1(store,m,leq(m,length(store))) sndsplit(0(),x) -> x sndsplit(s(n),cons(h,t)) -> sndsplit(n,t) sndsplit(s(n),nil()) -> nil() - Signature: {app/2,empty/1,fstsplit/2,if1/3,if2/3,if3/3,length/1,leq/2,map_f/2,process/2,sndsplit/2} / {0/0,cons/2,f/2 ,false/0,nil/0,s/1,self/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,empty,fstsplit,if1,if2,if3,length,leq,map_f,process ,sndsplit} and constructors {0,cons,f,false,nil,s,self,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(cons(h,t),x) -> cons(h,app(t,x)) app(nil(),x) -> x empty(cons(h,t)) -> false() empty(nil()) -> true() fstsplit(0(),x) -> nil() fstsplit(s(n),cons(h,t)) -> cons(h,fstsplit(n,t)) fstsplit(s(n),nil()) -> nil() if1(store,m,false()) -> if3(store,m,empty(fstsplit(m,app(map_f(self(),nil()),store)))) if1(store,m,true()) -> if2(store,m,empty(fstsplit(m,store))) if2(store,m,false()) -> process(app(map_f(self(),nil()),sndsplit(m,store)),m) if3(store,m,false()) -> process(sndsplit(m,app(map_f(self(),nil()),store)),m) length(cons(h,t)) -> s(length(t)) length(nil()) -> 0() leq(0(),m) -> true() leq(s(n),0()) -> false() leq(s(n),s(m)) -> leq(n,m) map_f(pid,cons(h,t)) -> app(f(pid,h),map_f(pid,t)) map_f(pid,nil()) -> nil() process(store,m) -> if1(store,m,leq(m,length(store))) sndsplit(0(),x) -> x sndsplit(s(n),cons(h,t)) -> sndsplit(n,t) sndsplit(s(n),nil()) -> nil() - Signature: {app/2,empty/1,fstsplit/2,if1/3,if2/3,if3/3,length/1,leq/2,map_f/2,process/2,sndsplit/2} / {0/0,cons/2,f/2 ,false/0,nil/0,s/1,self/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,empty,fstsplit,if1,if2,if3,length,leq,map_f,process ,sndsplit} and constructors {0,cons,f,false,nil,s,self,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: app(y,z){y -> cons(x,y)} = app(cons(x,y),z) ->^+ cons(x,app(y,z)) = C[app(y,z) = app(y,z){}] WORST_CASE(Omega(n^1),?)