:(:(

:(+(

:(

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

↳Polynomial 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))

innermost

The following dependency pairs can be strictly oriented:

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

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

There are no usable rules for innermost 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 _{2}_{ }^{ }_{ }^{ }POL(:'(x)_{1}, x_{2})= x _{1}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial 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))

innermost

The following dependency pair can be strictly oriented:

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes