Certification Problem
Input (TPDB TRS_Standard/AProVE_04/LPAR_intlist)
The rewrite relation of the following TRS is considered.
intlist(nil) |
→ |
nil |
(1) |
int(s(x),0) |
→ |
nil |
(2) |
int(x,x) |
→ |
cons(x,nil) |
(3) |
intlist(cons(x,y)) |
→ |
cons(s(x),intlist(y)) |
(4) |
int(s(x),s(y)) |
→ |
intlist(int(x,y)) |
(5) |
int(0,s(y)) |
→ |
cons(0,int(s(0),s(y))) |
(6) |
intlist(cons(x,nil)) |
→ |
cons(s(x),nil) |
(7) |
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.
int#(s(x),s(y)) |
→ |
intlist#(int(x,y)) |
(8) |
int#(s(x),s(y)) |
→ |
int#(x,y) |
(9) |
int#(0,s(y)) |
→ |
int#(s(0),s(y)) |
(10) |
intlist#(cons(x,y)) |
→ |
intlist#(y) |
(11) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.