f(c(s(

g(c(

R

↳Dependency Pair Analysis

F(c(s(x),y)) -> F(c(x, s(y)))

G(c(x, s(y))) -> G(c(s(x),y))

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

**F(c(s( x), y)) -> F(c(x, s(y)))**

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

The following dependency pair can be strictly oriented:

F(c(s(x),y)) -> F(c(x, s(y)))

The following rules can be oriented:

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

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

g(x) -> g_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

**G(c( x, s(y))) -> G(c(s(x), y))**

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

The following dependency pair can be strictly oriented:

G(c(x, s(y))) -> G(c(s(x),y))

The following rules can be oriented:

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f)= 0 _{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

f(x) -> f_{1}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

f(c(s(x),y)) -> f(c(x, s(y)))

g(c(x, s(y))) -> g(c(s(x),y))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes