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TRS Standard pair #487069713
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nokinds_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.34473 seconds
cpu usage
6.04142
user time
5.76737
system time
0.274045
max virtual memory
1.8609852E7
max residence set size
390648.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 47 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 16 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) CSRInnermostProof [EQUIVALENT, 0 ms] (10) CSR (11) CSDependencyPairsProof [EQUIVALENT, 0 ms] (12) QCSDP (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QCSDP (16) QCSDPSubtermProof [EQUIVALENT, 5 ms] (17) QCSDP (18) PIsEmptyProof [EQUIVALENT, 0 ms] (19) YES (20) QCSDP (21) QCSUsableRulesProof [EQUIVALENT, 0 ms] (22) QCSDP (23) QCSDPMuMonotonicPoloProof [EQUIVALENT, 11 ms] (24) QCSDP (25) PIsEmptyProof [EQUIVALENT, 0 ms] (26) YES (27) QCSDP (28) QCSDPReductionPairProof [EQUIVALENT, 23 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, L)) -> mark(s(length(L))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(isNatList(V1)) active(isNat(s(V1))) -> mark(isNat(V1)) active(isNatIList(V)) -> mark(isNatList(V)) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1, V2))) -> mark(and(isNat(V1), isNatList(V2))) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U11(and(isNatList(L), isNat(N)), L)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X1, X2)) -> U11(active(X1), X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) active(and(X1, X2)) -> and(active(X1), X2) cons(mark(X1), X2) -> mark(cons(X1, X2)) U11(mark(X1), X2) -> mark(U11(X1, X2)) s(mark(X)) -> mark(s(X)) length(mark(X)) -> mark(length(X)) and(mark(X1), X2) -> mark(and(X1, X2)) proper(zeros) -> ok(zeros) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(0) -> ok(0) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(isNat(X)) -> isNat(proper(X)) proper(isNatList(X)) -> isNatList(proper(X)) proper(isNatIList(X)) -> isNatIList(proper(X)) proper(nil) -> ok(nil) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) isNat(ok(X)) -> ok(isNat(X)) isNatList(ok(X)) -> ok(isNatList(X)) isNatIList(ok(X)) -> ok(isNatIList(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRSToCSRProof (EQUIVALENT) The following Q TRS is given: Q restricted rewrite system:
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