g(f(

R

↳Dependency Pair Analysis

G(f(x,y)) -> G(g(x))

G(f(x,y)) -> G(x)

G(f(x,y)) -> G(g(y))

G(f(x,y)) -> G(y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**G(f( x, y)) -> G(y)**

g(f(x,y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

G(f(x,y)) -> G(g(x))

G(f(f(x'',y''),y)) -> G(f(f(g(g(x'')), g(g(y''))), f(g(g(x'')), g(g(y'')))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Narrowing Transformation

**G(f(f( x'', y''), y)) -> G(f(f(g(g(x'')), g(g(y''))), f(g(g(x'')), g(g(y'')))))**

g(f(x,y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

G(f(x,y)) -> G(g(y))

G(f(x, f(x'',y''))) -> G(f(f(g(g(x'')), g(g(y''))), f(g(g(x'')), g(g(y'')))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

**G(f( x, f(x'', y''))) -> G(f(f(g(g(x'')), g(g(y''))), f(g(g(x'')), g(g(y'')))))**

g(f(x,y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))

Duration:

0:00 minutes