f(

f(

f(

f(a(

f(b(

f(c(

R

↳Dependency Pair Analysis

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

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

The following remains to be proven:

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

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

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

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

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

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

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

Duration:

0:02 minutes