* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
active(a()) -> mark(b())
active(f(X,X)) -> mark(h(a()))
active(f(X1,X2)) -> f(active(X1),X2)
active(g(X1,X2)) -> g(active(X1),X2)
active(g(a(),X)) -> mark(f(b(),X))
active(h(X)) -> h(active(X))
active(h(X)) -> mark(g(X,X))
f(mark(X1),X2) -> mark(f(X1,X2))
f(ok(X1),ok(X2)) -> ok(f(X1,X2))
g(mark(X1),X2) -> mark(g(X1,X2))
g(ok(X1),ok(X2)) -> ok(g(X1,X2))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
proper(f(X1,X2)) -> f(proper(X1),proper(X2))
proper(g(X1,X2)) -> g(proper(X1),proper(X2))
proper(h(X)) -> h(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
active(a()) -> mark(b())
active(f(X,X)) -> mark(h(a()))
active(f(X1,X2)) -> f(active(X1),X2)
active(g(X1,X2)) -> g(active(X1),X2)
active(g(a(),X)) -> mark(f(b(),X))
active(h(X)) -> h(active(X))
active(h(X)) -> mark(g(X,X))
f(mark(X1),X2) -> mark(f(X1,X2))
f(ok(X1),ok(X2)) -> ok(f(X1,X2))
g(mark(X1),X2) -> mark(g(X1,X2))
g(ok(X1),ok(X2)) -> ok(g(X1,X2))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
proper(f(X1,X2)) -> f(proper(X1),proper(X2))
proper(g(X1,X2)) -> g(proper(X1),proper(X2))
proper(h(X)) -> h(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
f(x,y){x -> mark(x)} =
f(mark(x),y) ->^+ mark(f(x,y))
= C[f(x,y) = f(x,y){}]
WORST_CASE(Omega(n^1),?)