* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X) -> a__if(mark(X),c(),f(true())) a__f(X) -> f(X) a__if(X1,X2,X3) -> if(X1,X2,X3) a__if(false(),X,Y) -> mark(Y) a__if(true(),X,Y) -> mark(X) mark(c()) -> c() mark(f(X)) -> a__f(mark(X)) mark(false()) -> false() mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(true()) -> true() - Signature: {a__f/1,a__if/3,mark/1} / {c/0,f/1,false/0,if/3,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,a__if,mark} and constructors {c,f,false,if,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X) -> a__if(mark(X),c(),f(true())) a__f(X) -> f(X) a__if(X1,X2,X3) -> if(X1,X2,X3) a__if(false(),X,Y) -> mark(Y) a__if(true(),X,Y) -> mark(X) mark(c()) -> c() mark(f(X)) -> a__f(mark(X)) mark(false()) -> false() mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(true()) -> true() - Signature: {a__f/1,a__if/3,mark/1} / {c/0,f/1,false/0,if/3,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,a__if,mark} and constructors {c,f,false,if,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> f(x)} = mark(f(x)) ->^+ a__f(mark(x)) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)