h(

f(

g(0,

g(

R

↳Dependency Pair Analysis

H(X,Z) -> F(X, s(X),Z)

F(X,Y, g(X,Y)) -> H(0, g(X,Y))

G(X, s(Y)) -> G(X,Y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳Remaining

**G( X, s(Y)) -> G(X, Y)**

h(X,Z) -> f(X, s(X),Z)

f(X,Y, g(X,Y)) -> h(0, g(X,Y))

g(0,Y) -> 0

g(X, s(Y)) -> g(X,Y)

The following dependency pair can be strictly oriented:

G(X, s(Y)) -> G(X,Y)

There are no usable rules using the Ce-refinement 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:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

h(X,Z) -> f(X, s(X),Z)

f(X,Y, g(X,Y)) -> h(0, g(X,Y))

g(0,Y) -> 0

g(X, s(Y)) -> g(X,Y)

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:

**F( X, Y, g(X, Y)) -> H(0, g(X, Y))**

h(X,Z) -> f(X, s(X),Z)

f(X,Y, g(X,Y)) -> h(0, g(X,Y))

g(0,Y) -> 0

g(X, s(Y)) -> g(X,Y)

Duration:

0:00 minutes