Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/PEANO_complete-noand_L)
The rewrite relation of the following TRS is considered.
U52(tt) |
→ |
N |
(1) |
U64(tt) |
→ |
s(plus(N,M)) |
(2) |
U11(tt) |
→ |
U12(isNatKind) |
(3) |
U12(tt) |
→ |
U13(isNatKind) |
(4) |
U13(tt) |
→ |
U14(isNatKind) |
(5) |
U14(tt) |
→ |
U15(isNat) |
(6) |
U15(tt) |
→ |
U16(isNat) |
(7) |
U16(tt) |
→ |
tt |
(8) |
U21(tt) |
→ |
U22(isNatKind) |
(9) |
U22(tt) |
→ |
U23(isNat) |
(10) |
U23(tt) |
→ |
tt |
(11) |
U31(tt) |
→ |
U32(isNatKind) |
(12) |
U32(tt) |
→ |
tt |
(13) |
U41(tt) |
→ |
tt |
(14) |
U51(tt) |
→ |
U52(isNatKind) |
(15) |
U61(tt) |
→ |
U62(isNatKind) |
(16) |
U62(tt) |
→ |
U63(isNat) |
(17) |
U63(tt) |
→ |
U64(isNatKind) |
(18) |
isNat |
→ |
tt |
(19) |
isNat |
→ |
U11(isNatKind) |
(20) |
isNat |
→ |
U21(isNatKind) |
(21) |
isNatKind |
→ |
tt |
(22) |
isNatKind |
→ |
U31(isNatKind) |
(23) |
isNatKind |
→ |
U41(isNatKind) |
(24) |
plus(N,0) |
→ |
U51(isNat) |
(25) |
plus(N,s(M)) |
→ |
U61(isNat) |
(26) |
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
|
= |
U52(tt) |
|
→
|
U52(tt) |
|
= |
t1
|
where t1 =
t0