average(s(

average(

average(0, 0) -> 0

average(0, s(0)) -> 0

average(0, s(s(0))) -> s(0)

R

↳Dependency Pair Analysis

AVERAGE(s(x),y) -> AVERAGE(x, s(y))

AVERAGE(x, s(s(s(y)))) -> AVERAGE(s(x),y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**AVERAGE( x, s(s(s(y)))) -> AVERAGE(s(x), y)**

average(s(x),y) -> average(x, s(y))

average(x, s(s(s(y)))) -> s(average(s(x),y))

average(0, 0) -> 0

average(0, s(0)) -> 0

average(0, s(s(0))) -> s(0)

The following dependency pair can be strictly oriented:

AVERAGE(x, s(s(s(y)))) -> AVERAGE(s(x),y)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(AVERAGE(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

**AVERAGE(s( x), y) -> AVERAGE(x, s(y))**

average(s(x),y) -> average(x, s(y))

average(x, s(s(s(y)))) -> s(average(s(x),y))

average(0, 0) -> 0

average(0, s(0)) -> 0

average(0, s(s(0))) -> s(0)

The following dependency pair can be strictly oriented:

AVERAGE(s(x),y) -> AVERAGE(x, s(y))

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

...

→DP Problem 3

↳Dependency Graph

average(s(x),y) -> average(x, s(y))

average(x, s(s(s(y)))) -> s(average(s(x),y))

average(0, 0) -> 0

average(0, s(0)) -> 0

average(0, s(s(0))) -> s(0)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes