Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex25_Luc06_GM)
The rewrite relation of the following TRS is considered.
a__f(f(X)) |
→ |
a__c(f(g(f(X)))) |
(1) |
a__c(X) |
→ |
d(X) |
(2) |
a__h(X) |
→ |
a__c(d(X)) |
(3) |
mark(f(X)) |
→ |
a__f(mark(X)) |
(4) |
mark(c(X)) |
→ |
a__c(X) |
(5) |
mark(h(X)) |
→ |
a__h(mark(X)) |
(6) |
mark(g(X)) |
→ |
g(X) |
(7) |
mark(d(X)) |
→ |
d(X) |
(8) |
a__f(X) |
→ |
f(X) |
(9) |
a__c(X) |
→ |
c(X) |
(10) |
a__h(X) |
→ |
h(X) |
(11) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by NaTT @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
mark#(h(X)) |
→ |
mark#(X) |
(12) |
mark#(f(X)) |
→ |
a__f#(mark(X)) |
(13) |
mark#(f(X)) |
→ |
mark#(X) |
(14) |
a__f#(f(X)) |
→ |
a__c#(f(g(f(X)))) |
(15) |
mark#(c(X)) |
→ |
a__c#(X) |
(16) |
mark#(h(X)) |
→ |
a__h#(mark(X)) |
(17) |
a__h#(X) |
→ |
a__c#(d(X)) |
(18) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.