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TRS Innermost pair #487093189
details
property
value
status
complete
benchmark
OvConsOS_complete_noand_GM.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)
14.6797 seconds
cpu usage
43.5507
user time
41.7353
system time
1.8154
max virtual memory
3.6704636E7
max residence set size
4014968.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 370 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) QDPOrderProof [EQUIVALENT, 907 ms] (21) QDP (22) DependencyGraphProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPOrderProof [EQUIVALENT, 611 ms] (25) QDP (26) DependencyGraphProof [EQUIVALENT, 0 ms] (27) AND (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES (35) QDP (36) QDPOrderProof [EQUIVALENT, 871 ms] (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U101(tt, V1, V2) -> a__U102(a__isNatKind(V1), V1, V2) a__U102(tt, V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2) a__U103(tt, V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2) a__U104(tt, V1, V2) -> a__U105(a__isNat(V1), V2) a__U105(tt, V2) -> a__U106(a__isNatIList(V2)) a__U106(tt) -> tt a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1) a__U111(tt, L, N) -> a__U112(a__isNatIListKind(L), L, N) a__U112(tt, L, N) -> a__U113(a__isNat(N), L, N) a__U113(tt, L, N) -> a__U114(a__isNatKind(N), L) a__U114(tt, L) -> s(a__length(mark(L))) a__U12(tt, V1) -> a__U13(a__isNatList(V1)) a__U121(tt, IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt) -> nil a__U13(tt) -> tt a__U131(tt, IL, M, N) -> a__U132(a__isNatIListKind(IL), IL, M, N) a__U132(tt, IL, M, N) -> a__U133(a__isNat(M), IL, M, N) a__U133(tt, IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N) a__U134(tt, IL, M, N) -> a__U135(a__isNat(N), IL, M, N) a__U135(tt, IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N) a__U136(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) a__U22(tt, V1) -> a__U23(a__isNat(V1)) a__U23(tt) -> tt a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V) a__U32(tt, V) -> a__U33(a__isNatList(V)) a__U33(tt) -> tt a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2) a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2) a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2) a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2) a__U45(tt, V2) -> a__U46(a__isNatIList(V2)) a__U46(tt) -> tt a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt) -> tt a__U61(tt, V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt) -> tt a__U71(tt) -> tt a__U81(tt) -> tt a__U91(tt, V1, V2) -> a__U92(a__isNatKind(V1), V1, V2) a__U92(tt, V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2) a__U93(tt, V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2) a__U94(tt, V1, V2) -> a__U95(a__isNat(V1), V2)
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