```* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
- Signature:
{and/3} / {band/2,not/1}
- Obligation:
runtime complexity wrt. defined symbols {and} and constructors {band,not}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following weak dependency pairs:

Strict DPs
and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
Weak DPs

and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
- Strict TRS:
and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
- Signature:
{and/3,and#/3} / {band/2,not/1,c_1/1}
- Obligation:
runtime complexity wrt. defined symbols {and#} and constructors {band,not}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
* Step 3: WeightGap WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
- Signature:
{and/3,and#/3} / {band/2,not/1,c_1/1}
- Obligation:
runtime complexity wrt. defined symbols {and#} and constructors {band,not}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following constant growth matrix-interpretation:
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:
uargs(c_1) = {1}

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(and) = [4] x1 + [2] x2 + [1] x3 + [4]
p(band) = [0]
p(not) = [1]
p(and#) = [1] x1 + [2] x2 + [0]
p(c_1) = [1] x1 + [0]

Following rules are strictly oriented:
and#(not(not(x)),y,not(z)) = [2] y + [1]
> [1] y + [0]
= c_1(and#(y,band(x,z),x))

Following rules are (at-least) weakly oriented:

Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
- Signature:
{and/3,and#/3} / {band/2,not/1,c_1/1}
- Obligation:
runtime complexity wrt. defined symbols {and#} and constructors {band,not}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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