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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308231
details
property
value
status
complete
benchmark
OvConsOS_complete_GM.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
complexity
runtime (wallclock)
6.00354 seconds
cpu usage
20.251
user time
19.1428
system time
1.10823
max virtual memory
1.8279768E7
max residence set size
3973780.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
19.75/5.89 WORST_CASE(NON_POLY, ?) 19.98/5.92 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.98/5.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.98/5.92 19.98/5.92 19.98/5.92 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 19.98/5.92 19.98/5.92 (0) CpxTRS 19.98/5.92 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 19.98/5.92 (2) TRS for Loop Detection 19.98/5.92 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 19.98/5.92 (4) BEST 19.98/5.92 (5) proven lower bound 19.98/5.92 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 19.98/5.92 (7) BOUNDS(n^1, INF) 19.98/5.92 (8) TRS for Loop Detection 19.98/5.92 (9) DecreasingLoopProof [FINISHED, 2862 ms] 19.98/5.92 (10) BOUNDS(EXP, INF) 19.98/5.92 19.98/5.92 19.98/5.92 ---------------------------------------- 19.98/5.92 19.98/5.92 (0) 19.98/5.92 Obligation: 19.98/5.92 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 19.98/5.92 19.98/5.92 19.98/5.92 The TRS R consists of the following rules: 19.98/5.92 19.98/5.92 a__zeros -> cons(0, zeros) 19.98/5.92 a__U11(tt, V1) -> a__U12(a__isNatList(V1)) 19.98/5.92 a__U12(tt) -> tt 19.98/5.92 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 19.98/5.92 a__U22(tt) -> tt 19.98/5.92 a__U31(tt, V) -> a__U32(a__isNatList(V)) 19.98/5.92 a__U32(tt) -> tt 19.98/5.92 a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) 19.98/5.92 a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) 19.98/5.92 a__U43(tt) -> tt 19.98/5.92 a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) 19.98/5.92 a__U52(tt, V2) -> a__U53(a__isNatList(V2)) 19.98/5.92 a__U53(tt) -> tt 19.98/5.92 a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) 19.98/5.92 a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) 19.98/5.92 a__U63(tt) -> tt 19.98/5.92 a__U71(tt, L) -> s(a__length(mark(L))) 19.98/5.92 a__U81(tt) -> nil 19.98/5.92 a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 19.98/5.92 a__and(tt, X) -> mark(X) 19.98/5.92 a__isNat(0) -> tt 19.98/5.92 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 19.98/5.92 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 19.98/5.92 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 19.98/5.92 a__isNatIList(zeros) -> tt 19.98/5.92 a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 19.98/5.92 a__isNatIListKind(nil) -> tt 19.98/5.92 a__isNatIListKind(zeros) -> tt 19.98/5.92 a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) 19.98/5.92 a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) 19.98/5.92 a__isNatKind(0) -> tt 19.98/5.92 a__isNatKind(length(V1)) -> a__isNatIListKind(V1) 19.98/5.92 a__isNatKind(s(V1)) -> a__isNatKind(V1) 19.98/5.92 a__isNatList(nil) -> tt 19.98/5.92 a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 19.98/5.92 a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 19.98/5.92 a__length(nil) -> 0 19.98/5.92 a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 19.98/5.92 a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) 19.98/5.92 a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) 19.98/5.92 mark(zeros) -> a__zeros 19.98/5.92 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 19.98/5.92 mark(U12(X)) -> a__U12(mark(X)) 19.98/5.92 mark(isNatList(X)) -> a__isNatList(X) 19.98/5.92 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 19.98/5.92 mark(U22(X)) -> a__U22(mark(X)) 19.98/5.92 mark(isNat(X)) -> a__isNat(X) 19.98/5.92 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 19.98/5.92 mark(U32(X)) -> a__U32(mark(X)) 19.98/5.92 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 19.98/5.92 mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 19.98/5.92 mark(U43(X)) -> a__U43(mark(X)) 19.98/5.92 mark(isNatIList(X)) -> a__isNatIList(X) 19.98/5.92 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 19.98/5.92 mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 19.98/5.92 mark(U53(X)) -> a__U53(mark(X)) 19.98/5.92 mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) 19.98/5.92 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 19.98/5.92 mark(U63(X)) -> a__U63(mark(X)) 19.98/5.92 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 19.98/5.92 mark(length(X)) -> a__length(mark(X)) 19.98/5.92 mark(U81(X)) -> a__U81(mark(X)) 19.98/5.92 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 19.98/5.92 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 19.98/5.92 mark(and(X1, X2)) -> a__and(mark(X1), X2) 19.98/5.92 mark(isNatIListKind(X)) -> a__isNatIListKind(X) 19.98/5.92 mark(isNatKind(X)) -> a__isNatKind(X) 19.98/5.92 mark(cons(X1, X2)) -> cons(mark(X1), X2) 19.98/5.92 mark(0) -> 0 19.98/5.92 mark(tt) -> tt 19.98/5.92 mark(s(X)) -> s(mark(X))
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