```* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
gcd(x,0()) -> x
gcd(0(),y) -> y
gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
- Signature:
{gcd/2} / {-/2,0/0, c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
Weak DPs

and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
gcd#(x,0()) -> c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
- Strict TRS:
gcd(x,0()) -> x
gcd(0(),y) -> y
gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
- Signature:
{gcd/2,gcd#/2} / {-/2,0/0, c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
* Step 3: SimplifyRHS WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
gcd#(x,0()) -> c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
- Signature:
{gcd/2,gcd#/2} / {-/2,0/0, c_1(x)
-->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
-->_1 gcd#(0(),y) -> c_2(y):2
-->_1 gcd#(x,0()) -> c_1(x):1

2:S:gcd#(0(),y) -> c_2(y)
-->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
-->_1 gcd#(0(),y) -> c_2(y):2
-->_1 gcd#(x,0()) -> c_1(x):1

3:S:gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
-->_2 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
-->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
-->_2 gcd#(0(),y) -> c_2(y):2
-->_1 gcd#(0(),y) -> c_2(y):2
-->_2 gcd#(x,0()) -> c_1(x):1
-->_1 gcd#(x,0()) -> c_1(x):1

Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
gcd#(s(x),s(y)) -> c_3(x,y)
* Step 4: MI WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
gcd#(x,0()) -> c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y)
- Signature:
{gcd/2,gcd#/2} / {-/2,0/0,  x + 
= c_1(x)

gcd#(0(),y) = 
> 
= c_2(y)

gcd#(s(x),s(y)) = 
> 
= c_3(x,y)

Following rules are (at-least) weakly oriented:

* Step 5: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak DPs:
gcd#(x,0()) -> c_1(x)
gcd#(0(),y) -> c_2(y)
gcd#(s(x),s(y)) -> c_3(x,y)
- Signature:
{gcd/2,gcd#/2} / {-/2,0/0,
```