f(c(

g(c(s(

R

↳Dependency Pair Analysis

F(c(X, s(Y))) -> F(c(s(X),Y))

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**F(c( X, s(Y))) -> F(c(s(X), Y))**

f(c(X, s(Y))) -> f(c(s(X),Y))

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

The following dependency pair can be strictly oriented:

F(c(X, s(Y))) -> F(c(s(X),Y))

The following rules can be oriented:

f(c(X, s(Y))) -> f(c(s(X),Y))

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

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

g > f

g > s

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

f(c(X, s(Y))) -> f(c(s(X),Y))

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes