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