* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) fact(X) -> if(zero(X),s(0()),prod(X,fact(p(X)))) if(false(),X,Y) -> Y if(true(),X,Y) -> X p(s(X)) -> X prod(0(),X) -> 0() prod(s(X),Y) -> add(Y,prod(X,Y)) zero(0()) -> true() zero(s(X)) -> false() - Signature: {add/2,fact/1,if/3,p/1,prod/2,zero/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,fact,if,p,prod,zero} and constructors {0,false,s ,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) fact(X) -> if(zero(X),s(0()),prod(X,fact(p(X)))) if(false(),X,Y) -> Y if(true(),X,Y) -> X p(s(X)) -> X prod(0(),X) -> 0() prod(s(X),Y) -> add(Y,prod(X,Y)) zero(0()) -> true() zero(s(X)) -> false() - Signature: {add/2,fact/1,if/3,p/1,prod/2,zero/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,fact,if,p,prod,zero} and constructors {0,false,s ,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add(x,y){x -> s(x)} = add(s(x),y) ->^+ s(add(x,y)) = C[add(x,y) = add(x,y){}] WORST_CASE(Omega(n^1),?)