* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
add(0(),X) -> X
add(s(X),Y) -> s(add(X,Y))
fib(N) -> sel(N,fib1(s(0()),s(0())))
fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
sel(0(),cons(X,XS)) -> X
sel(s(N),cons(X,XS)) -> sel(N,XS)
- Signature:
{add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {add,fib,fib1,sel} and constructors {0,cons,s}
+ 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))
fib(N) -> sel(N,fib1(s(0()),s(0())))
fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
sel(0(),cons(X,XS)) -> X
sel(s(N),cons(X,XS)) -> sel(N,XS)
- Signature:
{add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {add,fib,fib1,sel} and constructors {0,cons,s}
+ 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),?)