Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/MYNAT_complete_L)
The rewrite relation of the following TRS is considered.
|
U41(tt) |
→ |
N |
(1) |
|
U51(tt) |
→ |
s(plus(N,M)) |
(2) |
|
U71(tt) |
→ |
plus(x(N,M),N) |
(3) |
|
and(tt) |
→ |
X |
(4) |
|
U11(tt) |
→ |
U12(isNat) |
(5) |
|
U12(tt) |
→ |
U13(isNat) |
(6) |
|
U13(tt) |
→ |
tt |
(7) |
|
U21(tt) |
→ |
U22(isNat) |
(8) |
|
U22(tt) |
→ |
tt |
(9) |
|
U31(tt) |
→ |
U32(isNat) |
(10) |
|
U32(tt) |
→ |
U33(isNat) |
(11) |
|
U33(tt) |
→ |
tt |
(12) |
|
U61(tt) |
→ |
0 |
(13) |
| isNat |
→ |
tt |
(14) |
| isNat |
→ |
U11(and(isNatKind)) |
(15) |
| isNat |
→ |
U21(isNatKind) |
(16) |
| isNat |
→ |
U31(and(isNatKind)) |
(17) |
| isNatKind |
→ |
tt |
(18) |
| isNatKind |
→ |
and(isNatKind) |
(19) |
| isNatKind |
→ |
isNatKind |
(20) |
|
plus(N,0) |
→ |
U41(and(isNat)) |
(21) |
|
plus(N,s(M)) |
→ |
U51(and(and(isNat))) |
(22) |
|
x(N,0) |
→ |
U61(and(isNat)) |
(23) |
|
x(N,s(M)) |
→ |
U71(and(and(isNat))) |
(24) |
The evaluation strategy is outermostProperty / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
U41(tt) |
|
→
|
U41(tt) |
|
= |
t1
|
where t1 =
t0