Termination w.r.t. Q proof of /tmp/tmpn

Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(g(i(a, b, b'), c), d) → if(e, f(.(b, c), d'), f(.(b', c), d'))
f(g(h(a, b), c), d) → if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

f(g(i(a, b, b'), c), d) → if(e, f(.(b, c), d'), f(.(b', c), d'))
f(g(h(a, b), c), d) → if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F(g(i(a, b, b'), c), d) → F(.(b', c), d')
F(g(i(a, b, b'), c), d) → F(.(b, c), d')
F(g(h(a, b), c), d) → F(c, d')
F(g(h(a, b), c), d) → F(.(b, g(h(a, b), c)), d)

The TRS R consists of the following rules:

f(g(i(a, b, b'), c), d) → if(e, f(.(b, c), d'), f(.(b', c), d'))
f(g(h(a, b), c), d) → if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

F(g(i(a, b, b'), c), d) → F(.(b', c), d')
F(g(i(a, b, b'), c), d) → F(.(b, c), d')
F(g(h(a, b), c), d) → F(c, d')
F(g(h(a, b), c), d) → F(.(b, g(h(a, b), c)), d)

The TRS R consists of the following rules:

f(g(i(a, b, b'), c), d) → if(e, f(.(b, c), d'), f(.(b', c), d'))
f(g(h(a, b), c), d) → if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 4 less nodes.