```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fib(mark(X)) -> mark(fib(X))
fib(ok(X)) -> ok(fib(X))
fib1(X1,mark(X2)) -> mark(fib1(X1,X2))
fib1(mark(X1),X2) -> mark(fib1(X1,X2))
fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2))
proper(0()) -> ok(0())
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:
- Obligation:
innermost runtime complexity wrt. defined symbols {add,cons,fib,fib1,proper,s,sel,top} and constructors {0
,active,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
0_1() -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
cons_0(2,2) -> 1
cons_1(2,2) -> 3
fib_0(2) -> 1
fib_1(2) -> 3
fib1_0(2,2) -> 1
fib1_1(2,2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
proper_0(2) -> 1
proper_1(2) -> 4
s_0(2) -> 1
s_1(2) -> 3
sel_0(2,2) -> 1
sel_1(2,2) -> 3
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fib(mark(X)) -> mark(fib(X))
fib(ok(X)) -> ok(fib(X))
fib1(X1,mark(X2)) -> mark(fib1(X1,X2))
fib1(mark(X1),X2) -> mark(fib1(X1,X2))
fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2))
proper(0()) -> ok(0())
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: