g(c(

f(c(s(

f(f(

f(

R

↳Dependency Pair Analysis

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

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

F(f(x)) -> F(d(f(x)))

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

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

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

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

f(f(x)) -> f(d(f(x)))

f(x) ->x

The following dependency pair can be strictly oriented:

G(c(x, s(y))) -> G(c(s(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) -> G(_{1}x)_{1}

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

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

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

f(f(x)) -> f(d(f(x)))

f(x) ->x

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

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

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

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

f(f(x)) -> f(d(f(x)))

f(x) ->x

The following dependency pair can be strictly oriented:

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

c > s

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

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

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

f(f(x)) -> f(d(f(x)))

f(x) ->x

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes