YES
Termination proof of ../tpdb/TRS/CSR/Ex6_GM04.trs
Termination of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
c → f(g(c))
f(g(X)) → g(X)
The replacement map contains the following entries:c: empty set
f: empty set
g: empty set
↳ CSR
↳ Lucas-Transformation
Q restricted rewrite system:
The TRS R consists of the following rules:
c → f(g(c))
f(g(X)) → g(X)
The replacement map contains the following entries:c: empty set
f: empty set
g: empty set
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:
c → f
f → g
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
c → f
f → 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 → g
Used ordering:
Polynomial interpretation [25]:
POL(c) = 2
POL(f) = 2
POL(g) = 1
↳ CSR
↳ Lucas-Transformation
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
c → f
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
c → f
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
c → f
Used ordering:
Polynomial interpretation [25]:
POL(c) = 2
POL(f) = 1
↳ CSR
↳ Lucas-Transformation
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RisEmptyProof
Q restricted rewrite system:
R is empty.
Q is empty.
The TRS R is empty. Hence, termination is trivially proven.