```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a__c() -> c()
a__c() -> d()
a__g(X) -> a__h(X)
a__g(X) -> g(X)
a__h(X) -> h(X)
a__h(d()) -> a__g(c())
mark(c()) -> a__c()
mark(d()) -> d()
mark(g(X)) -> a__g(X)
mark(h(X)) -> a__h(X)
- Signature:
{a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
- Obligation:
runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
+ Applied Processor:
ToInnermost
+ Details:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a__c() -> c()
a__c() -> d()
a__g(X) -> a__h(X)
a__g(X) -> g(X)
a__h(X) -> h(X)
a__h(d()) -> a__g(c())
mark(c()) -> a__c()
mark(d()) -> d()
mark(g(X)) -> a__g(X)
mark(h(X)) -> a__h(X)
- Signature:
{a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 5.
The enriched problem is compatible with follwoing automaton.
a__c_0() -> 1
a__c_1() -> 1
a__g_0(2) -> 1
a__g_1(1) -> 1
a__g_1(2) -> 1
a__g_2(1) -> 1
a__g_3(3) -> 1
a__h_0(2) -> 1
a__h_1(2) -> 1
a__h_2(1) -> 1
a__h_2(2) -> 1
a__h_3(1) -> 1
a__h_4(3) -> 1
c_0() -> 2
c_1() -> 1
c_2() -> 1
c_3() -> 3
d_0() -> 2
d_1() -> 1
d_2() -> 1
g_0(2) -> 2
g_1(2) -> 1
g_2(1) -> 1
g_2(2) -> 1
g_3(1) -> 1
g_4(3) -> 1
h_0(2) -> 2
h_1(2) -> 1
h_2(2) -> 1
h_3(1) -> 1
h_3(2) -> 1
h_4(1) -> 1
h_5(3) -> 1
mark_0(2) -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a__c() -> c()
a__c() -> d()
a__g(X) -> a__h(X)
a__g(X) -> g(X)
a__h(X) -> h(X)
a__h(d()) -> a__g(c())
mark(c()) -> a__c()
mark(d()) -> d()
mark(g(X)) -> a__g(X)
mark(h(X)) -> a__h(X)
- Signature:
{a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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