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))

The following rules can be oriented:

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))

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

nil > u

MERGE > u

{++, merge} > u

v > u

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}

merge(x,_{1}x) -> merge(_{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