```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
diff(X1,mark(X2)) -> mark(diff(X1,X2))
diff(mark(X1),X2) -> mark(diff(X1,X2))
diff(ok(X1),ok(X2)) -> ok(diff(X1,X2))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
leq(X1,mark(X2)) -> mark(leq(X1,X2))
leq(mark(X1),X2) -> mark(leq(X1,X2))
leq(ok(X1),ok(X2)) -> ok(leq(X1,X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
proper(0()) -> ok(0())
proper(false()) -> ok(false())
proper(true()) -> ok(true())
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:
{diff/2,if/3,leq/2,p/1,proper/1,s/1,top/1} / {0/0,active/1,false/0,mark/1,ok/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {diff,if,leq,p,proper,s,top} and constructors {0,active
,false,mark,ok,true}
+ 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
diff_0(2,2) -> 1
diff_1(2,2) -> 3
false_0() -> 2
false_1() -> 3
if_0(2,2,2) -> 1
if_1(2,2,2) -> 3
leq_0(2,2) -> 1
leq_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
p_0(2) -> 1
p_1(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
true_0() -> 2
true_1() -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
diff(X1,mark(X2)) -> mark(diff(X1,X2))
diff(mark(X1),X2) -> mark(diff(X1,X2))
diff(ok(X1),ok(X2)) -> ok(diff(X1,X2))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
leq(X1,mark(X2)) -> mark(leq(X1,X2))
leq(mark(X1),X2) -> mark(leq(X1,X2))
leq(ok(X1),ok(X2)) -> ok(leq(X1,X2))
p(mark(X)) -> mark(p(X))
p(ok(X)) -> ok(p(X))
proper(0()) -> ok(0())
proper(false()) -> ok(false())
proper(true()) -> ok(true())
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:
{diff/2,if/3,leq/2,p/1,proper/1,s/1,top/1} / {0/0,active/1,false/0,mark/1,ok/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {diff,if,leq,p,proper,s,top} and constructors {0,active
,false,mark,ok,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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