f(f(

f(f(

g(c(

g(d(

g(c(h(0))) -> g(d(1))

g(c(1)) -> g(d(h(0)))

g(h(

R

↳Dependency Pair Analysis

F(f(x)) -> F(c(f(x)))

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

G(c(h(0))) -> G(d(1))

G(c(1)) -> G(d(h(0)))

G(h(x)) -> G(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**G(h( x)) -> G(x)**

f(f(x)) -> f(c(f(x)))

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

g(c(x)) ->x

g(d(x)) ->x

g(c(h(0))) -> g(d(1))

g(c(1)) -> g(d(h(0)))

g(h(x)) -> g(x)

The following dependency pair can be strictly oriented:

G(h(x)) -> G(x)

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:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

f(f(x)) -> f(c(f(x)))

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

g(c(x)) ->x

g(d(x)) ->x

g(c(h(0))) -> g(d(1))

g(c(1)) -> g(d(h(0)))

g(h(x)) -> g(x)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes