details

property	value
status	complete
benchmark	LengthOfFiniteLists_complete_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.6173 seconds
cpu usage	31.2856
user time	30.0824
system time	1.20326
max virtual memory	5.63995E7
max residence set size	2681904.0

stage attributes

key	value
starexec-result	YES

output

30.58/11.44 YES 30.91/11.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.91/11.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.91/11.49 30.91/11.49 30.91/11.49 Termination w.r.t. Q of the given QTRS could be proven: 30.91/11.49 30.91/11.49 (0) QTRS 30.91/11.49 (1) DependencyPairsProof [EQUIVALENT, 107 ms] 30.91/11.49 (2) QDP 30.91/11.49 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 30.91/11.49 (4) QDP 30.91/11.49 (5) QDPOrderProof [EQUIVALENT, 353 ms] 30.91/11.49 (6) QDP 30.91/11.49 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 30.91/11.49 (8) AND 30.91/11.49 (9) QDP 30.91/11.49 (10) QDPOrderProof [EQUIVALENT, 198 ms] 30.91/11.49 (11) QDP 30.91/11.49 (12) QDPOrderProof [EQUIVALENT, 242 ms] 30.91/11.49 (13) QDP 30.91/11.49 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 30.91/11.49 (15) QDP 30.91/11.49 (16) UsableRulesProof [EQUIVALENT, 0 ms] 30.91/11.49 (17) QDP 30.91/11.49 (18) QReductionProof [EQUIVALENT, 0 ms] 30.91/11.49 (19) QDP 30.91/11.49 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.91/11.49 (21) YES 30.91/11.49 (22) QDP 30.91/11.49 (23) QDPQMonotonicMRRProof [EQUIVALENT, 205 ms] 30.91/11.49 (24) QDP 30.91/11.49 (25) UsableRulesProof [EQUIVALENT, 0 ms] 30.91/11.49 (26) QDP 30.91/11.49 (27) QReductionProof [EQUIVALENT, 0 ms] 30.91/11.49 (28) QDP 30.91/11.49 (29) QDPQMonotonicMRRProof [EQUIVALENT, 107 ms] 30.91/11.49 (30) QDP 30.91/11.49 (31) DependencyGraphProof [EQUIVALENT, 0 ms] 30.91/11.49 (32) TRUE 30.91/11.49 30.91/11.49 30.91/11.49 ---------------------------------------- 30.91/11.49 30.91/11.49 (0) 30.91/11.49 Obligation: 30.91/11.49 Q restricted rewrite system: 30.91/11.49 The TRS R consists of the following rules: 30.91/11.49 30.91/11.49 a__zeros -> cons(0, zeros) 30.91/11.49 a__U11(tt, V1) -> a__U12(a__isNatList(V1)) 30.91/11.49 a__U12(tt) -> tt 30.91/11.49 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 30.91/11.49 a__U22(tt) -> tt 30.91/11.49 a__U31(tt, V) -> a__U32(a__isNatList(V)) 30.91/11.49 a__U32(tt) -> tt 30.91/11.49 a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) 30.91/11.49 a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) 30.91/11.49 a__U43(tt) -> tt 30.91/11.49 a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) 30.91/11.49 a__U52(tt, V2) -> a__U53(a__isNatList(V2)) 30.91/11.49 a__U53(tt) -> tt 30.91/11.49 a__U61(tt, L) -> s(a__length(mark(L))) 30.91/11.49 a__and(tt, X) -> mark(X) 30.91/11.49 a__isNat(0) -> tt 30.91/11.49 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 30.91/11.49 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 30.91/11.49 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 30.91/11.49 a__isNatIList(zeros) -> tt 30.91/11.49 a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 30.91/11.49 a__isNatIListKind(nil) -> tt 30.91/11.49 a__isNatIListKind(zeros) -> tt 30.91/11.49 a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) 30.91/11.49 a__isNatKind(0) -> tt 30.91/11.49 a__isNatKind(length(V1)) -> a__isNatIListKind(V1) 30.91/11.49 a__isNatKind(s(V1)) -> a__isNatKind(V1) 30.91/11.49 a__isNatList(nil) -> tt 30.91/11.49 a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 30.91/11.49 a__length(nil) -> 0 30.91/11.49 a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 30.91/11.49 mark(zeros) -> a__zeros 30.91/11.49 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 30.91/11.49 mark(U12(X)) -> a__U12(mark(X)) 30.91/11.49 mark(isNatList(X)) -> a__isNatList(X) 30.91/11.49 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 30.91/11.49 mark(U22(X)) -> a__U22(mark(X)) 30.91/11.49 mark(isNat(X)) -> a__isNat(X) 30.91/11.49 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 30.91/11.49 mark(U32(X)) -> a__U32(mark(X)) 30.91/11.49 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 30.91/11.49 mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 30.91/11.49 mark(U43(X)) -> a__U43(mark(X)) 30.91/11.49 mark(isNatIList(X)) -> a__isNatIList(X) 30.91/11.49 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 30.91/11.49 mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 30.91/11.49 mark(U53(X)) -> a__U53(mark(X)) 30.91/11.49 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 30.91/11.49 mark(length(X)) -> a__length(mark(X)) 30.91/11.49 mark(and(X1, X2)) -> a__and(mark(X1), X2) 30.91/11.49 mark(isNatIListKind(X)) -> a__isNatIListKind(X) popout

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actions

all output return to TRS_Innermost 2019-03-28 22.12