Certification Problem
Input (TPDB TRS_Standard/SK90/2.40)
The rewrite relation of the following TRS is considered.
|
or(true,y) |
→ |
true |
(1) |
|
or(x,true) |
→ |
true |
(2) |
|
or(false,false) |
→ |
false |
(3) |
|
mem(x,nil) |
→ |
false |
(4) |
|
mem(x,set(y)) |
→ |
=(x,y) |
(5) |
|
mem(x,union(y,z)) |
→ |
or(mem(x,y),mem(x,z)) |
(6) |
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.
|
mem#(x,union(y,z)) |
→ |
mem#(x,y) |
(7) |
|
mem#(x,union(y,z)) |
→ |
mem#(x,z) |
(8) |
|
mem#(x,union(y,z)) |
→ |
or#(mem(x,y),mem(x,z)) |
(9) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.