* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c)) f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c) foldf(x,cons(y,z)) -> f(foldf(x,z),y) foldf(x,nil()) -> x g(A()) -> A() g(B()) -> A() g(B()) -> B() g(C()) -> A() g(C()) -> B() g(C()) -> C() - Signature: {f/2,f'/2,f''/1,foldf/2,g/1} / {A/0,B/0,C/0,cons/2,nil/0,triple/3} - Obligation: innermost runtime complexity wrt. defined symbols {f,f',f'',foldf,g} and constructors {A,B,C,cons,nil ,triple} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c)) f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c) foldf(x,cons(y,z)) -> f(foldf(x,z),y) foldf(x,nil()) -> x g(A()) -> A() g(B()) -> A() g(B()) -> B() g(C()) -> A() g(C()) -> B() g(C()) -> C() - Signature: {f/2,f'/2,f''/1,foldf/2,g/1} / {A/0,B/0,C/0,cons/2,nil/0,triple/3} - Obligation: innermost runtime complexity wrt. defined symbols {f,f',f'',foldf,g} and constructors {A,B,C,cons,nil ,triple} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: foldf(x,z){z -> cons(y,z)} = foldf(x,cons(y,z)) ->^+ f(foldf(x,z),y) = C[foldf(x,z) = foldf(x,z){}] WORST_CASE(Omega(n^1),?)