YES Termination proof of ../tpdb/TRS/CSR/ExConc_Zan97.trs
Termination of the following Term Rewriting System could be proven:

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

f(X) → g(h(f(X)))

The replacement map contains the following entries:

f: {1}
g: empty set
h: {1}


↳ CSR
  ↳ Lucas-Transformation

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

f(X) → g(h(f(X)))

The replacement map contains the following entries:

f: {1}
g: empty set
h: {1}

We applied the Lucas [26] to transform the context-sensitive TRS to an usual TRS.

↳ CSR
  ↳ Lucas-Transformation
    ↳ QTRS
      ↳ RRRPoloQTRSProof

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

f(X) → g

Q is empty.

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

f(X) → g

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

f(X) → g
Used ordering:
Polynomial interpretation [25]:

POL(f(x1)) = 2 + x1   
POL(g) = 1   




↳ CSR
  ↳ Lucas-Transformation
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RisEmptyProof

Q restricted rewrite system:
R is empty.
Q is empty.

The TRS R is empty. Hence, termination is trivially proven.