Certification Problem
Input (COPS 832)
The rewrite relation of the following (conditional) TRS is considered.
|
le(0,s(x)) |
→ |
true |
| |
|
le(x,0) |
→ |
false |
| |
|
le(s(x),s(y)) |
→ |
le(x,y) |
| |
|
min(cons(x,nil)) |
→ |
x |
| |
|
min(cons(x,l)) |
→ |
x |
| le(x,min(l)) ≈ true
|
|
min(cons(x,l)) |
→ |
min(l) |
| le(x,min(l)) ≈ false
|
|
min(cons(x,l)) |
→ |
min(l) |
| min(l) ≈ x
|
The question is whether the following conditions are infeasible, i.e., there is no substitution σ
such that all of the following is true:
Property / Task
Prove or disprove an infeasibility problem.Answer / Result
Yes.Proof (by nonreach @ CoCo 2023)
1 Infeasible Compound Conditions
We collect the conditions in the fresh compound-symbol
|.
1.1 Non-reachability
We show non-reachability w.r.t. the underlying TRS.
1.1.1 Non-reachability by TCAP
Non-reachability is shown by the TCAP approximation.