f(

f(

h(

activate(n

activate(n

activate(

R

↳Dependency Pair Analysis

ACTIVATE(n_{h}(X)) -> H(activate(X))

ACTIVATE(n_{h}(X)) -> ACTIVATE(X)

ACTIVATE(n_{f}(X)) -> F(activate(X))

ACTIVATE(n_{f}(X)) -> ACTIVATE(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**ACTIVATE(n _{f}(X)) -> ACTIVATE(X)**

f(X) -> g(n_{h}(n_{f}(X)))

f(X) -> n_{f}(X)

h(X) -> n_{h}(X)

activate(n_{h}(X)) -> h(activate(X))

activate(n_{f}(X)) -> f(activate(X))

activate(X) ->X

innermost

The following dependency pair can be strictly oriented:

ACTIVATE(n_{f}(X)) -> ACTIVATE(X)

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(n__h(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(n__f(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(ACTIVATE(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**ACTIVATE(n _{h}(X)) -> ACTIVATE(X)**

f(X) -> g(n_{h}(n_{f}(X)))

f(X) -> n_{f}(X)

h(X) -> n_{h}(X)

activate(n_{h}(X)) -> h(activate(X))

activate(n_{f}(X)) -> f(activate(X))

activate(X) ->X

innermost

The following dependency pair can be strictly oriented:

ACTIVATE(n_{h}(X)) -> ACTIVATE(X)

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(n__h(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(ACTIVATE(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

f(X) -> g(n_{h}(n_{f}(X)))

f(X) -> n_{f}(X)

h(X) -> n_{h}(X)

activate(n_{h}(X)) -> h(activate(X))

activate(n_{f}(X)) -> f(activate(X))

activate(X) ->X

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes