Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex4_7_77_Bor03_GM)
The rewrite relation of the following TRS is considered.
a__zeros |
→ |
cons(0,zeros) |
(1) |
a__tail(cons(X,XS)) |
→ |
mark(XS) |
(2) |
mark(zeros) |
→ |
a__zeros |
(3) |
mark(tail(X)) |
→ |
a__tail(mark(X)) |
(4) |
mark(cons(X1,X2)) |
→ |
cons(mark(X1),X2) |
(5) |
mark(0) |
→ |
0 |
(6) |
a__zeros |
→ |
zeros |
(7) |
a__tail(X) |
→ |
tail(X) |
(8) |
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#(cons(X1,X2)) |
→ |
mark#(X1) |
(9) |
mark#(tail(X)) |
→ |
mark#(X) |
(10) |
mark#(zeros) |
→ |
a__zeros# |
(11) |
a__tail#(cons(X,XS)) |
→ |
mark#(XS) |
(12) |
mark#(tail(X)) |
→ |
a__tail#(mark(X)) |
(13) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.