```* 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))
dbl(mark(X)) -> mark(dbl(X))
dbl(ok(X)) -> ok(dbl(X))
first(X1,mark(X2)) -> mark(first(X1,X2))
first(mark(X1),X2) -> mark(first(X1,X2))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
half(mark(X)) -> mark(half(X))
half(ok(X)) -> ok(half(X))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
recip(mark(X)) -> mark(recip(X))
recip(ok(X)) -> ok(recip(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sqr(mark(X)) -> mark(sqr(X))
sqr(ok(X)) -> ok(sqr(X))
terms(mark(X)) -> mark(terms(X))
terms(ok(X)) -> ok(terms(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {add,cons,dbl,first,half,proper,recip,s,sqr,terms
,top} and constructors {0,active,mark,nil,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
dbl_0(2) -> 1
dbl_1(2) -> 3
first_0(2,2) -> 1
first_1(2,2) -> 3
half_0(2) -> 1
half_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
nil_0() -> 2
nil_1() -> 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
recip_0(2) -> 1
recip_1(2) -> 3
s_0(2) -> 1
s_1(2) -> 3
sqr_0(2) -> 1
sqr_1(2) -> 3
terms_0(2) -> 1
terms_1(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))
dbl(mark(X)) -> mark(dbl(X))
dbl(ok(X)) -> ok(dbl(X))
first(X1,mark(X2)) -> mark(first(X1,X2))
first(mark(X1),X2) -> mark(first(X1,X2))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
half(mark(X)) -> mark(half(X))
half(ok(X)) -> ok(half(X))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
recip(mark(X)) -> mark(recip(X))
recip(ok(X)) -> ok(recip(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sqr(mark(X)) -> mark(sqr(X))
sqr(ok(X)) -> ok(sqr(X))
terms(mark(X)) -> mark(terms(X))
terms(ok(X)) -> ok(terms(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature: