```* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w)))
h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w))))))
h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))
t(x) -> x
t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
t(t(x)) -> t(c(t(x),x))
- Signature:
{h/3,t/1} / {0/0,c/2,s/1}
- Obligation:
runtime complexity wrt. defined symbols {h,t} and constructors {0,c,s}
+ Applied Processor:
DependencyPairs {dpKind_ = WIDP}
+ Details:
We add the following weak dependency pairs:

Strict DPs
h#(x,c(y,z),t(w)) -> c_1(h#(c(s(y),x),z,t(c(t(w),w))))
h#(c(x,y),c(s(z),z),t(w)) -> c_2(h#(z,c(y,x),t(t(c(x,c(y,t(w)))))))
h#(c(s(x),c(s(0()),y)),z,t(x)) -> c_3(h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))))
t#(x) -> c_4(x)
t#(x) -> c_5(x)
t#(t(x)) -> c_6(t#(c(t(x),x)))
Weak DPs

and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
h#(x,c(y,z),t(w)) -> c_1(h#(c(s(y),x),z,t(c(t(w),w))))
h#(c(x,y),c(s(z),z),t(w)) -> c_2(h#(z,c(y,x),t(t(c(x,c(y,t(w)))))))
h#(c(s(x),c(s(0()),y)),z,t(x)) -> c_3(h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))))
t#(x) -> c_4(x)
t#(x) -> c_5(x)
t#(t(x)) -> c_6(t#(c(t(x),x)))
- Strict TRS:
h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w)))
h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w))))))
h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))
t(x) -> x
t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
t(t(x)) -> t(c(t(x),x))
- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
t#(x) -> c_4(x)
t#(x) -> c_5(x)
* Step 3: PredecessorEstimationCP WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
t#(x) -> c_4(x)
t#(x) -> c_5(x)
- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
+ Details:
We first use the processor NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
1: t#(x) -> c_4(x)
2: t#(x) -> c_5(x)

The strictly oriented rules are moved into the weak component.
** Step 3.a:1: NaturalMI WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
t#(x) -> c_4(x)
t#(x) -> c_5(x)
- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
+ Details:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
The following argument positions are considered usable:
none

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(0) = 
p(c) = 
p(h) = 
p(s) = 
p(t) = 
p(h#) = 
p(t#) = 
p(c_1) = 
p(c_2) = 
p(c_3) = 
p(c_4) = 
p(c_5) = 
p(c_6) = 

Following rules are strictly oriented:
t#(x) = 
> 
= c_4(x)

t#(x) = 
> 
= c_5(x)

Following rules are (at-least) weakly oriented:

** Step 3.a:2: Assumption WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
t#(x) -> c_4(x)
t#(x) -> c_5(x)
- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
+ Details:
()

** Step 3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
t#(x) -> c_4(x)
t#(x) -> c_5(x)
- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
RemoveWeakSuffixes
+ Details:
Consider the dependency graph
1:W:t#(x) -> c_4(x)
-->_1 t#(x) -> c_5(x):2
-->_1 t#(x) -> c_4(x):1

2:W:t#(x) -> c_5(x)
-->_1 t#(x) -> c_5(x):2
-->_1 t#(x) -> c_4(x):1

The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
1: t#(x) -> c_4(x)
2: t#(x) -> c_5(x)
** Step 3.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:

- Signature:
{h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1}
- Obligation:
runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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