:(:(

:(+(

:(

R

↳Dependency Pair Analysis

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

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

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

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

:'(z, +(x, f(y))) -> :'(g(z,y), +(x, a))

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

:(z, +(x, f(y))) -> :(g(z,y), +(x, a))

The following dependency pairs can be strictly oriented:

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

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

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

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

The following usable rules w.r.t. to the AFS can be oriented:

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

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

:(z, +(x, f(y))) -> :(g(z,y), +(x, a))

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

{:, :'} > +

f > a

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

:(z, +(x, f(y))) -> :(g(z,y), +(x, a))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes