* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a(x,s(y),h()) -> a(x,y,s(h()))
a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
a(h(),h(),x) -> s(x)
a(s(x),h(),z) -> a(x,z,z)
app(l,nil()) -> l
app(cons(x,l),k) -> cons(x,app(l,k))
app(nil(),k) -> k
sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
sum(cons(x,nil())) -> cons(x,nil())
- Signature:
{a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a(x,s(y),h()) -> a(x,y,s(h()))
a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
a(h(),h(),x) -> s(x)
a(s(x),h(),z) -> a(x,z,z)
app(l,nil()) -> l
app(cons(x,l),k) -> cons(x,app(l,k))
app(nil(),k) -> k
sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
sum(cons(x,nil())) -> cons(x,nil())
- Signature:
{a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
a(x,s(y),z){z -> s(z)} =
a(x,s(y),s(z)) ->^+ a(x,y,a(x,s(y),z))
= C[a(x,s(y),z) = a(x,s(y),z){}]
WORST_CASE(Omega(n^1),?)