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