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TRS Stand 20472 pair #381716147
details
property
value
status
complete
benchmark
MYNAT_complete_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.42250609398 seconds
cpu usage
6.600115605
max memory
5.41556736E8
stage attributes
key
value
output-size
57602
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 56 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QCSDP (8) QCSDPSubtermProof [EQUIVALENT, 0 ms] (9) QCSDP (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (11) TRUE (12) QCSDP (13) QCSUsableRulesProof [EQUIVALENT, 0 ms] (14) QCSDP (15) QCSDPMuMonotonicPoloProof [EQUIVALENT, 61 ms] (16) QCSDP (17) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (18) TRUE (19) QCSDP (20) QCSDPSubtermProof [EQUIVALENT, 0 ms] (21) QCSDP (22) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (23) TRUE (24) QCSDP (25) QCSDPSubtermProof [EQUIVALENT, 0 ms] (26) QCSDP (27) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (28) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N)) active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N)) active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N)) active(U104(tt, M, N)) -> mark(plus(x(N, M), N)) active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2)) active(U15(tt, V2)) -> mark(U16(isNat(V2))) active(U16(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1)) active(U22(tt, V1)) -> mark(U23(isNat(V1))) active(U23(tt)) -> mark(tt) active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2)) active(U35(tt, V2)) -> mark(U36(isNat(V2))) active(U36(tt)) -> mark(tt) active(U41(tt, V2)) -> mark(U42(isNatKind(V2))) active(U42(tt)) -> mark(tt) active(U51(tt)) -> mark(tt) active(U61(tt, V2)) -> mark(U62(isNatKind(V2))) active(U62(tt)) -> mark(tt) active(U71(tt, N)) -> mark(U72(isNatKind(N), N)) active(U72(tt, N)) -> mark(N) active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N)) active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N)) active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N)) active(U84(tt, M, N)) -> mark(s(plus(N, M))) active(U91(tt, N)) -> mark(U92(isNatKind(N))) active(U92(tt)) -> mark(0) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) active(isNatKind(0)) -> mark(tt) active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) active(plus(N, 0)) -> mark(U71(isNat(N), N)) active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) active(x(N, 0)) -> mark(U91(isNat(N), N)) active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) active(plus(X1, X2)) -> plus(active(X1), X2)
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