* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
active(c()) -> mark(a())
active(c()) -> mark(b())
active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
active(f(X1,X2,X3)) -> f(active(X1),X2,X3)
active(f(a(),b(),X)) -> mark(f(X,X,X))
f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
f(mark(X1),X2,X3) -> mark(f(X1,X2,X3))
f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
proper(c()) -> ok(c())
proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/3,proper/1,top/1} / {a/0,b/0,c/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {a,b,c,mark,ok}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
active(c()) -> mark(a())
active(c()) -> mark(b())
active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
active(f(X1,X2,X3)) -> f(active(X1),X2,X3)
active(f(a(),b(),X)) -> mark(f(X,X,X))
f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
f(mark(X1),X2,X3) -> mark(f(X1,X2,X3))
f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
proper(c()) -> ok(c())
proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/3,proper/1,top/1} / {a/0,b/0,c/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {a,b,c,mark,ok}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
f(x,y,z){z -> mark(z)} =
f(x,y,mark(z)) ->^+ mark(f(x,y,z))
= C[f(x,y,z) = f(x,y,z){}]
WORST_CASE(Omega(n^1),?)