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TRS Innermost pair #487524389
details
property
value
status
complete
benchmark
OvConsOS_nokinds_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.49673390388 seconds
cpu usage
6.788723851
max memory
4.54893568E8
stage attributes
key
value
output-size
49275
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 90 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 42 ms] (6) CSR (7) CSDependencyPairsProof [EQUIVALENT, 0 ms] (8) QCSDP (9) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (10) AND (11) QCSDP (12) QCSUsableRulesProof [EQUIVALENT, 0 ms] (13) QCSDP (14) QCSDPMuMonotonicPoloProof [EQUIVALENT, 22 ms] (15) QCSDP (16) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (17) QCSDP (18) QCSDPSubtermProof [EQUIVALENT, 0 ms] (19) QCSDP (20) PIsEmptyProof [EQUIVALENT, 0 ms] (21) YES (22) QCSDP (23) QCSDPSubtermProof [EQUIVALENT, 1 ms] (24) QCSDP (25) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (26) TRUE (27) QCSDP (28) QCSDPReductionPairProof [EQUIVALENT, 42 ms] (29) QCSDP (30) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (31) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(zeros) -> mark(cons(0, zeros)) active(U11(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt)) -> mark(tt) active(U41(tt, V2)) -> mark(U42(isNatIList(V2))) active(U42(tt)) -> mark(tt) active(U51(tt, V2)) -> mark(U52(isNatList(V2))) active(U52(tt)) -> mark(tt) active(U61(tt, V2)) -> mark(U62(isNatIList(V2))) active(U62(tt)) -> mark(tt) active(U71(tt, L, N)) -> mark(U72(isNat(N), L)) active(U72(tt, L)) -> mark(s(length(L))) active(U81(tt)) -> mark(nil) active(U91(tt, IL, M, N)) -> mark(U92(isNat(M), IL, M, N)) active(U92(tt, IL, M, N)) -> mark(U93(isNat(N), IL, M, N)) active(U93(tt, IL, M, N)) -> mark(cons(N, take(M, IL))) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2)) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2)) active(isNatList(take(V1, V2))) -> mark(U61(isNat(V1), V2)) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U71(isNatList(L), L, N)) active(take(0, IL)) -> mark(U81(isNatIList(IL))) active(take(s(M), cons(N, IL))) -> mark(U91(isNatIList(IL), IL, M, N)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X)) -> U11(active(X)) active(U21(X)) -> U21(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1, X2)) -> U41(active(X1), X2) active(U42(X)) -> U42(active(X)) active(U51(X1, X2)) -> U51(active(X1), X2) active(U52(X)) -> U52(active(X)) active(U61(X1, X2)) -> U61(active(X1), X2) active(U62(X)) -> U62(active(X)) active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) active(U72(X1, X2)) -> U72(active(X1), X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) active(U81(X)) -> U81(active(X)) active(U91(X1, X2, X3, X4)) -> U91(active(X1), X2, X3, X4) active(U92(X1, X2, X3, X4)) -> U92(active(X1), X2, X3, X4)
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