* 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),?)