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