Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487070998
details
property
value
status
complete
benchmark
PEANO_complete_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.99302 seconds
cpu usage
4.49569
user time
4.2991
system time
0.196592
max virtual memory
1.8408912E7
max residence set size
271488.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 240 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 3 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U11(tt, V1, V2) -> U12(isNat(activate(V1)), activate(V2)) U12(tt, V2) -> U13(isNat(activate(V2))) U13(tt) -> tt U21(tt, V1) -> U22(isNat(activate(V1))) U22(tt) -> tt U31(tt, N) -> activate(N) U41(tt, M, N) -> s(plus(activate(N), activate(M))) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) plus(N, 0) -> U31(and(isNat(N), n__isNatKind(N)), N) plus(N, s(M)) -> U41(and(and(isNat(M), n__isNatKind(M)), n__and(n__isNat(N), n__isNatKind(N))), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) and(X1, X2) -> n__and(X1, X2) isNat(X) -> n__isNat(X) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(activate(X)) activate(n__and(X1, X2)) -> and(activate(X1), X2) activate(n__isNat(X)) -> isNat(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: U11/3(YES,YES,YES) tt/0) U12/2(YES,YES) isNat/1(YES) activate/1)YES( U13/1)YES( U21/2(YES,YES) U22/1(YES) U31/2(YES,YES) U41/3(YES,YES,YES) s/1(YES) plus/2(YES,YES) and/2(YES,YES) n__0/0) n__plus/2(YES,YES) isNatKind/1(YES) n__isNatKind/1(YES) n__s/1(YES) 0/0) n__and/2(YES,YES) n__isNat/1(YES) Quasi precedence: [U41_3, plus_2, n__plus_2] > U11_3 > [U12_2, isNat_1, U21_2, n__isNat_1] > tt > U22_1 [U41_3, plus_2, n__plus_2] > U31_2 [U41_3, plus_2, n__plus_2] > [s_1, and_2, isNatKind_1, n__isNatKind_1, n__s_1, n__and_2] > [U12_2, isNat_1, U21_2, n__isNat_1] > tt > U22_1 [n__0, 0] Status: U11_3: multiset status tt: multiset status U12_2: [2,1] isNat_1: [1] U21_2: [2,1] U22_1: [1] U31_2: multiset status U41_3: [3,2,1] s_1: multiset status plus_2: [1,2] and_2: multiset status
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard