from(

from(

after(0,

after(s(

activate(n

activate(

R

↳Dependency Pair Analysis

AFTER(s(N), cons(X,XS)) -> AFTER(N, activate(XS))

AFTER(s(N), cons(X,XS)) -> ACTIVATE(XS)

ACTIVATE(n_{from}(X)) -> FROM(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**AFTER(s( N), cons(X, XS)) -> AFTER(N, activate(XS))**

from(X) -> cons(X, n_{from}(s(X)))

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

after(0,XS) ->XS

after(s(N), cons(X,XS)) -> after(N, activate(XS))

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

activate(X) ->X

The following dependency pair can be strictly oriented:

AFTER(s(N), cons(X,XS)) -> AFTER(N, activate(XS))

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

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

AFTER(x,_{1}x) ->_{2}x_{1}

s(x) -> s(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

from(X) -> cons(X, n_{from}(s(X)))

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

after(0,XS) ->XS

after(s(N), cons(X,XS)) -> after(N, activate(XS))

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

activate(X) ->X

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes