f(

f(c(

f(d(

R

↳Dependency Pair Analysis

F(x, a(b(y))) -> F(c(d(x)),y)

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

F(d(x),y) -> F(x, b(y))

Furthermore,

R

↳DPs

→DP Problem 1

↳Instantiation Transformation

**F(d( x), y) -> F(x, b(y))**

f(x, a(b(y))) -> f(c(d(x)),y)

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

f(d(x),y) -> f(x, b(y))

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

As a result of transforming the rule

three new Dependency Pairs are created:

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

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

F(c(d(x'')),y'') -> F(d(x''), a(y''))

F(c(x''), b(y'')) -> F(x'', a(b(y'')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Instantiation Transformation

**F(c( x''), b(y'')) -> F(x'', a(b(y'')))**

f(x, a(b(y))) -> f(c(d(x)),y)

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

f(d(x),y) -> f(x, b(y))

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

As a result of transforming the rule

four new Dependency Pairs are created:

F(d(x),y) -> F(x, b(y))

F(d(x''), b(y'')) -> F(x'', b(b(y'')))

F(d(x'), a(a(y''''))) -> F(x', b(a(a(y''''))))

F(d(x'), a(y'''')) -> F(x', b(a(y'''')))

F(d(x'), a(b(y''''))) -> F(x', b(a(b(y''''))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Inst

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

**F(d( x'), a(b(y''''))) -> F(x', b(a(b(y''''))))**

f(x, a(b(y))) -> f(c(d(x)),y)

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

f(d(x),y) -> f(x, b(y))

Duration:

0:00 minutes