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

↳Argument Filtering and Ordering

→DP Problem 2

↳Remaining

**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 pairs can be strictly oriented:

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

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

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

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

trivial

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

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

↳AFS

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**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

Duration:

0:00 minutes