Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

Q is empty.


↳ QTRS
  ↳ Non-Overlap Check

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

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

Q is empty.

The TRS is non-overlapping. Hence, we can switch to innermost.

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof

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

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

The set Q consists of the following terms:

g1(x0)
c
h1(d)


Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

G1(X) -> H1(X)
H1(d) -> G1(c)
H1(d) -> C

The TRS R consists of the following rules:

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

The set Q consists of the following terms:

g1(x0)
c
h1(d)

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

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ DependencyGraphProof

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

G1(X) -> H1(X)
H1(d) -> G1(c)
H1(d) -> C

The TRS R consists of the following rules:

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

The set Q consists of the following terms:

g1(x0)
c
h1(d)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [13,14,18] contains 1 SCC with 1 less node.

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ DependencyGraphProof
            ↳ QDP

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

G1(X) -> H1(X)
H1(d) -> G1(c)

The TRS R consists of the following rules:

g1(X) -> h1(X)
c -> d
h1(d) -> g1(c)

The set Q consists of the following terms:

g1(x0)
c
h1(d)

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