++(nil,

++(

++(.(

++(++(

R

↳Dependency Pair Analysis

++'(.(x,y),z) -> ++'(y,z)

++'(++(x,y),z) -> ++'(x, ++(y,z))

++'(++(x,y),z) -> ++'(y,z)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**++'(++( x, y), z) -> ++'(y, z)**

++(nil,y) ->y

++(x, nil) ->x

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

++(++(x,y),z) -> ++(x, ++(y,z))

The following dependency pairs can be strictly oriented:

++'(++(x,y),z) -> ++'(y,z)

++'(++(x,y),z) -> ++'(x, ++(y,z))

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(++'(x)_{1}, x_{2})= x _{1}_{ }^{ }_{ }^{ }POL(++(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(nil)= 0 _{ }^{ }_{ }^{ }POL(.(x)_{1}, x_{2})= x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**++'(.( x, y), z) -> ++'(y, z)**

++(nil,y) ->y

++(x, nil) ->x

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

++(++(x,y),z) -> ++(x, ++(y,z))

The following dependency pair can be strictly oriented:

++'(.(x,y),z) -> ++'(y,z)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(++'(x)_{1}, x_{2})= x _{1}_{ }^{ }_{ }^{ }POL(.(x)_{1}, x_{2})= 1 + x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

++(nil,y) ->y

++(x, nil) ->x

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

++(++(x,y),z) -> ++(x, ++(y,z))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes