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

↳Instantiation Transformation

**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)))

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Instantiation Transformation

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

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

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

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 3

↳Polynomial Ordering

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(c(x)_{1}, x_{2})= x _{2}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 4

↳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