* 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''(foldB(triple(s(a),0(),c),b)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) fold(t,x,0()) -> t fold(t,x,s(n)) -> f(fold(t,x,n),x) foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) 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,fold/3,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3} - Obligation: innermost runtime complexity wrt. defined symbols {f,f',f'',fold,foldB,foldC,g} and constructors {0,A,B,C,s ,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''(foldB(triple(s(a),0(),c),b)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) fold(t,x,0()) -> t fold(t,x,s(n)) -> f(fold(t,x,n),x) foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) 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,fold/3,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3} - Obligation: innermost runtime complexity wrt. defined symbols {f,f',f'',fold,foldB,foldC,g} and constructors {0,A,B,C,s ,triple} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: fold(x,y,z){z -> s(z)} = fold(x,y,s(z)) ->^+ f(fold(x,y,z),y) = C[fold(x,y,z) = fold(x,y,z){}] WORST_CASE(Omega(n^1),?)