```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
chk(no(c())) -> active(c())
chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
f(mark(x)) -> mark(f(x))
f(no(x)) -> no(f(x))
mat(f(x),c()) -> no(c())
mat(f(x),f(y())) -> f(mat(x,y()))
tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
- Signature:
{chk/1,f/1,mat/2,tp/1} / {X/0,active/1,c/0,mark/1,no/1,y/0}
- Obligation:
runtime complexity wrt. defined symbols {chk,f,mat,tp} and constructors {X,active,c,mark,no,y}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
X_0() -> 2
X_1() -> 17
active_0(2) -> 2
active_1(3) -> 1
active_2(18) -> 5
c_0() -> 2
c_1() -> 3
c_2() -> 18
chk_0(2) -> 1
chk_1(6) -> 5
f_0(2) -> 1
f_1(2) -> 4
f_1(8) -> 7
f_1(9) -> 8
f_1(10) -> 9
f_1(11) -> 10
f_1(12) -> 11
f_1(13) -> 12
f_1(14) -> 13
f_1(15) -> 14
f_1(16) -> 15
f_1(17) -> 16
mark_0(2) -> 2
mark_1(4) -> 1
mark_1(4) -> 4
mat_0(2,2) -> 1
mat_1(7,2) -> 6
no_0(2) -> 2
no_1(3) -> 6
no_1(4) -> 1
no_1(4) -> 4
tp_0(2) -> 1
tp_1(5) -> 1
y_0() -> 2
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
chk(no(c())) -> active(c())
chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
f(mark(x)) -> mark(f(x))
f(no(x)) -> no(f(x))
mat(f(x),c()) -> no(c())
mat(f(x),f(y())) -> f(mat(x,y()))
tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
- Signature:
{chk/1,f/1,mat/2,tp/1} / {X/0,active/1,c/0,mark/1,no/1,y/0}
- Obligation:
runtime complexity wrt. defined symbols {chk,f,mat,tp} and constructors {X,active,c,mark,no,y}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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