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TRS Innermost pair #487093313
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
n137.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
47.3695 seconds
cpu usage
156.75
user time
147.48
system time
9.27
max virtual memory
8.3657216E7
max residence set size
1.1233624E7
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 67 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 12 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 17 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 45 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 23 ms] (12) CSR (13) CSRRRRProof [EQUIVALENT, 0 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, 169 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) AND (25) QDP (26) QDPOrderProof [EQUIVALENT, 0 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE (30) QDP (31) QDPOrderProof [EQUIVALENT, 158 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) active(U42(X1, X2)) -> U42(active(X1), X2) active(U43(X)) -> U43(active(X)) active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) active(U52(X1, X2)) -> U52(active(X1), X2) active(U53(X)) -> U53(active(X)) active(U61(X1, X2)) -> U61(active(X1), X2)
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