```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
U11(mark(X1),X2) -> mark(U11(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
and(mark(X1),X2) -> mark(and(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
proper(0()) -> ok(0())
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/2,U21/3,and/2,isNat/1,plus/2,proper/1,s/1,top/1} / {0/0,active/1,mark/1,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U11,U21,and,isNat,plus,proper,s,top} and constructors {0
,active,mark,ok,tt}
+ 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
U11_0(2,2) -> 1
U11_1(2,2) -> 3
U21_0(2,2,2) -> 1
U21_1(2,2,2) -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
and_0(2,2) -> 1
and_1(2,2) -> 3
isNat_0(2) -> 1
isNat_1(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
plus_0(2,2) -> 1
plus_1(2,2) -> 3
proper_0(2) -> 1
proper_1(2) -> 4
s_0(2) -> 1
s_1(2) -> 3
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
tt_0() -> 2
tt_1() -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
U11(mark(X1),X2) -> mark(U11(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
and(mark(X1),X2) -> mark(and(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
proper(0()) -> ok(0())
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/2,U21/3,and/2,isNat/1,plus/2,proper/1,s/1,top/1} / {0/0,active/1,mark/1,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U11,U21,and,isNat,plus,proper,s,top} and constructors {0
,active,mark,ok,tt}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))
```