f(

f(s(

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

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

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

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

The following dependency pair can be strictly oriented:

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

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

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

F > c

F > s

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

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

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

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

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

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

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

The following dependency pair can be strictly oriented:

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

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

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

c > F

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes