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TRS Stand 20472 pair #381716127
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_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)
51.2086770535 seconds
cpu usage
176.494855839
max memory
1.0845782016E10
stage attributes
key
value
output-size
91992
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 70 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 2 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 5 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 17 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 19 ms] (12) CSR (13) CSRRRRProof [EQUIVALENT, 20 ms] (14) CSR (15) Incomplete Giesl Middeldorp-Transformation [SOUND, 0 ms] (16) QTRS (17) DependencyPairsProof [EQUIVALENT, 0 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 148 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) AND (25) QDP (26) QDPOrderProof [EQUIVALENT, 28 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE (30) QDP (31) QDPOrderProof [EQUIVALENT, 41 ms] (32) QDP (33) DependencyGraphProof [EQUIVALENT, 0 ms] (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QDPSizeChangeProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(zeros) -> mark(cons(0, zeros)) active(U11(tt, V1)) -> mark(U12(isNatList(V1))) active(U12(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNat(V1))) active(U22(tt)) -> mark(tt) active(U31(tt, V)) -> mark(U32(isNatList(V))) active(U32(tt)) -> mark(tt) active(U41(tt, V1, V2)) -> mark(U42(isNat(V1), V2)) active(U42(tt, V2)) -> mark(U43(isNatIList(V2))) active(U43(tt)) -> mark(tt) active(U51(tt, V1, V2)) -> mark(U52(isNat(V1), V2)) active(U52(tt, V2)) -> mark(U53(isNatList(V2))) active(U53(tt)) -> mark(tt) active(U61(tt, L)) -> mark(s(length(L))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1, V2))) -> mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) active(isNatIListKind(nil)) -> mark(tt) active(isNatIListKind(zeros)) -> mark(tt) active(isNatIListKind(cons(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2))) active(isNatKind(0)) -> mark(tt) active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) active(isNatKind(s(V1))) -> mark(isNatKind(V1)) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1, V2))) -> mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U61(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X1, X2)) -> U11(active(X1), X2) active(U12(X)) -> U12(active(X)) active(U21(X1, X2)) -> U21(active(X1), X2) active(U22(X)) -> U22(active(X)) active(U31(X1, X2)) -> U31(active(X1), X2) active(U32(X)) -> U32(active(X)) active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
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