f(a) -> g(h(a))

h(g(

k(

k(f(

R

↳Dependency Pair Analysis

F(a) -> H(a)

H(g(x)) -> H(f(x))

H(g(x)) -> F(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

**H(g( x)) -> H(f(x))**

f(a) -> g(h(a))

h(g(x)) -> g(h(f(x)))

k(x, h(x), a) -> h(x)

k(f(x),y,x) -> f(x)

innermost

As we are in the innermost case, we can delete all 3 non-usable-rules.

R

↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 2

↳Narrowing Transformation

**H(g( x)) -> H(f(x))**

f(a) -> g(h(a))

innermost

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

H(g(x)) -> H(f(x))

H(g(a)) -> H(g(h(a)))

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes