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TRS Stand 20472 pair #381713061
details
property
value
status
complete
benchmark
MYNAT_nokinds_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.86165809631 seconds
cpu usage
4.399412349
max memory
2.73440768E8
stage attributes
key
value
output-size
22501
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QCSDP (8) QCSDPSubtermProof [EQUIVALENT, 1 ms] (9) QCSDP (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (11) TRUE (12) QCSDP (13) QCSDPSubtermProof [EQUIVALENT, 0 ms] (14) QCSDP (15) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (16) TRUE (17) QCSDP (18) QCSDPSubtermProof [EQUIVALENT, 7 ms] (19) QCSDP (20) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (21) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, V2)) -> mark(U32(isNat(V2))) active(U32(tt)) -> mark(tt) active(U41(tt, N)) -> mark(N) active(U51(tt, M, N)) -> mark(U52(isNat(N), M, N)) active(U52(tt, M, N)) -> mark(s(plus(N, M))) active(U61(tt)) -> mark(0) active(U71(tt, M, N)) -> mark(U72(isNat(N), M, N)) active(U72(tt, M, N)) -> mark(plus(x(N, M), N)) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNat(x(V1, V2))) -> mark(U31(isNat(V1), V2)) active(plus(N, 0)) -> mark(U41(isNat(N), N)) active(plus(N, s(M))) -> mark(U51(isNat(M), M, N)) active(x(N, 0)) -> mark(U61(isNat(N))) active(x(N, s(M))) -> mark(U71(isNat(M), M, N)) active(U11(X1, X2)) -> U11(active(X1), X2) active(U12(X)) -> U12(active(X)) active(U21(X)) -> U21(active(X)) active(U31(X1, X2)) -> U31(active(X1), X2) active(U32(X)) -> U32(active(X)) active(U41(X1, X2)) -> U41(active(X1), X2) active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) active(s(X)) -> s(active(X)) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(U61(X)) -> U61(active(X)) active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) active(U72(X1, X2, X3)) -> U72(active(X1), X2, X3) active(x(X1, X2)) -> x(active(X1), X2) active(x(X1, X2)) -> x(X1, active(X2)) U11(mark(X1), X2) -> mark(U11(X1, X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X)) -> mark(U21(X)) U31(mark(X1), X2) -> mark(U31(X1, X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1), X2) -> mark(U41(X1, X2)) U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) U72(mark(X1), X2, X3) -> mark(U72(X1, X2, X3)) x(mark(X1), X2) -> mark(x(X1, X2)) x(X1, mark(X2)) -> mark(x(X1, X2)) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(U12(X)) -> U12(proper(X)) proper(isNat(X)) -> isNat(proper(X)) proper(U21(X)) -> U21(proper(X))
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