purge(nil) -> nil

purge(.(

remove(

remove(

R

↳Dependency Pair Analysis

PURGE(.(x,y)) -> PURGE(remove(x,y))

PURGE(.(x,y)) -> REMOVE(x,y)

REMOVE(x, .(y,z)) -> REMOVE(x,z)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

**REMOVE( x, .(y, z)) -> REMOVE(x, z)**

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

The following dependency pair can be strictly oriented:

REMOVE(x, .(y,z)) -> REMOVE(x,z)

The following rules can be oriented:

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

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

purge > . > {=, remove}

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

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

if(x,_{1}x,_{2}x) ->_{3}x_{1}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

**PURGE(.( x, y)) -> PURGE(remove(x, y))**

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

The following dependency pair can be strictly oriented:

PURGE(.(x,y)) -> PURGE(remove(x,y))

The following rules can be oriented:

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

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

purge > . > remove > =

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

if(x,_{1}x,_{2}x) ->_{3}x_{1}

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

purge(nil) -> nil

purge(.(x,y)) -> .(x, purge(remove(x,y)))

remove(x, nil) -> nil

remove(x, .(y,z)) -> if(=(x,y), remove(x,z), .(y, remove(x,z)))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes