merge(

merge(nil,

merge(++(

merge(++(

R

↳Dependency Pair Analysis

MERGE(++(x,y), ++(u, v)) -> MERGE(y, ++(u, v))

MERGE(++(x,y), ++(u, v)) -> MERGE(++(x,y), v)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**MERGE(++( x, y), ++(u, v)) -> MERGE(y, ++(u, v))**

merge(x, nil) ->x

merge(nil,y) ->y

merge(++(x,y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))

merge(++(x,y), ++(u, v)) -> ++(u, merge(++(x,y), v))

The following dependency pair can be strictly oriented:

MERGE(++(x,y), ++(u, v)) -> MERGE(y, ++(u, v))

There are no usable rules using the Ce-refinement that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(v)= 0 _{ }^{ }_{ }^{ }POL(++(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(MERGE(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(u)= 0 _{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

MERGE(x,_{1}x) -> MERGE(_{2}x,_{1}x)_{2}

++(x,_{1}x) -> ++(_{2}x,_{1}x)_{2}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

merge(x, nil) ->x

merge(nil,y) ->y

merge(++(x,y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))

merge(++(x,y), ++(u, v)) -> ++(u, merge(++(x,y), v))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes