D(t) -> 1

D(constant) -> 0

D(+(

D(*(

D(-(

R

↳Dependency Pair Analysis

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

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

D'(*(x,y)) -> D'(x)

D'(*(x,y)) -> D'(y)

D'(-(x,y)) -> D'(x)

D'(-(x,y)) -> D'(y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**D'(-( x, y)) -> D'(y)**

D(t) -> 1

D(constant) -> 0

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

D(*(x,y)) -> +(*(y, D(x)), *(x, D(y)))

D(-(x,y)) -> -(D(x), D(y))

The following dependency pairs can be strictly oriented:

D'(-(x,y)) -> D'(y)

D'(-(x,y)) -> D'(x)

D'(*(x,y)) -> D'(y)

D'(*(x,y)) -> D'(x)

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

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

The following rules can be oriented:

D(t) -> 1

D(constant) -> 0

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

D(*(x,y)) -> +(*(y, D(x)), *(x, D(y)))

D(-(x,y)) -> -(D(x), D(y))

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

D > -

D > +

D > 0

D > *

D > 1

resulting in one new DP problem.

Used Argument Filtering System:

D'(x) -> D'(_{1}x)_{1}

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

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

D(t) -> 1

D(constant) -> 0

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

D(*(x,y)) -> +(*(y, D(x)), *(x, D(y)))

D(-(x,y)) -> -(D(x), D(y))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes