f(nil) -> nil

f(.(nil,

f(.(.(

g(nil) -> nil

g(.(

g(.(

R

↳Dependency Pair Analysis

F(.(nil,y)) -> F(y)

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

G(.(x, nil)) -> G(x)

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

**F(.(.( x, y), z)) -> F(.(x, .(y, z)))**

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

The following dependency pair can be strictly oriented:

F(.(nil,y)) -> F(y)

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Polynomial Ordering

→DP Problem 2

↳Polo

**F(.(.( x, y), z)) -> F(.(x, .(y, z)))**

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

The following dependency pair can be strictly oriented:

F(.(.(x,y),z)) -> F(.(x, .(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 _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Polo

...

→DP Problem 4

↳Dependency Graph

→DP Problem 2

↳Polo

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**G(.( x, .(y, z))) -> G(.(.(x, y), z))**

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

The following dependency pair can be strictly oriented:

G(.(x, nil)) -> G(x)

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 5

↳Polynomial Ordering

**G(.( x, .(y, z))) -> G(.(.(x, y), z))**

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

The following dependency pair can be strictly oriented:

G(.(x, .(y,z))) -> G(.(.(x,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(G(x)_{1})= 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 5

↳Polo

...

→DP Problem 6

↳Dependency Graph

f(nil) -> nil

f(.(nil,y)) -> .(nil, f(y))

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

g(nil) -> nil

g(.(x, nil)) -> .(g(x), nil)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes