```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a__c(X) -> c(X)
a__c(X) -> d(X)
a__f(X) -> f(X)
a__f(f(X)) -> a__c(f(g(f(X))))
a__h(X) -> a__c(d(X))
a__h(X) -> h(X)
mark(c(X)) -> a__c(X)
mark(d(X)) -> d(X)
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> a__h(mark(X))
- Signature:
{a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
- Obligation:
runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,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(X) -> c(X)
a__c(X) -> d(X)
a__f(X) -> f(X)
a__f(f(X)) -> a__c(f(g(f(X))))
a__h(X) -> a__c(d(X))
a__h(X) -> h(X)
mark(c(X)) -> a__c(X)
mark(d(X)) -> d(X)
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> a__h(mark(X))
- Signature:
{a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
a__c_0(2) -> 1
a__c_1(1) -> 1
a__c_1(2) -> 1
a__c_1(2) -> 5
a__c_1(3) -> 1
a__c_2(6) -> 1
a__c_2(6) -> 5
a__f_0(2) -> 1
a__f_1(5) -> 1
a__f_1(5) -> 5
a__h_0(2) -> 1
a__h_1(5) -> 1
a__h_1(5) -> 5
c_0(2) -> 2
c_1(2) -> 1
c_2(1) -> 1
c_2(2) -> 1
c_2(2) -> 5
c_2(3) -> 1
c_3(6) -> 1
c_3(6) -> 5
d_0(2) -> 2
d_1(2) -> 1
d_1(2) -> 5
d_2(1) -> 1
d_2(2) -> 1
d_2(2) -> 5
d_2(3) -> 1
d_2(5) -> 6
d_3(6) -> 1
d_3(6) -> 5
f_0(2) -> 2
f_1(2) -> 1
f_1(4) -> 3
f_2(5) -> 1
f_2(5) -> 5
f_2(7) -> 6
g_0(2) -> 2
g_1(1) -> 4
g_1(2) -> 1
g_1(2) -> 5
g_2(5) -> 7
h_0(2) -> 2
h_1(2) -> 1
h_2(5) -> 1
h_2(5) -> 5
mark_0(2) -> 1
mark_1(2) -> 5
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a__c(X) -> c(X)
a__c(X) -> d(X)
a__f(X) -> f(X)
a__f(f(X)) -> a__c(f(g(f(X))))
a__h(X) -> a__c(d(X))
a__h(X) -> h(X)
mark(c(X)) -> a__c(X)
mark(d(X)) -> d(X)
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> a__h(mark(X))
- Signature:
{a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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