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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313506
details
property
value
status
complete
benchmark
PEANO_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.597 seconds
cpu usage
1077.52
user time
1066.14
system time
11.3887
max virtual memory
3.7312576E7
max residence set size
1.4797328E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1073.51/291.58 WORST_CASE(Omega(n^1), ?) 1077.11/292.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1077.11/292.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1077.11/292.47 1077.11/292.47 1077.11/292.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/292.47 1077.11/292.47 (0) CpxTRS 1077.11/292.47 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1077.11/292.47 (2) CpxTRS 1077.11/292.47 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1077.11/292.47 (4) typed CpxTrs 1077.11/292.47 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1077.11/292.47 (6) typed CpxTrs 1077.11/292.47 (7) RewriteLemmaProof [LOWER BOUND(ID), 23.4 s] 1077.11/292.47 (8) BEST 1077.11/292.47 (9) proven lower bound 1077.11/292.47 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1077.11/292.47 (11) BOUNDS(n^1, INF) 1077.11/292.47 (12) typed CpxTrs 1077.11/292.47 (13) RewriteLemmaProof [LOWER BOUND(ID), 197 ms] 1077.11/292.47 (14) typed CpxTrs 1077.11/292.47 (15) RewriteLemmaProof [LOWER BOUND(ID), 2667 ms] 1077.11/292.47 (16) typed CpxTrs 1077.11/292.47 1077.11/292.47 1077.11/292.47 ---------------------------------------- 1077.11/292.47 1077.11/292.47 (0) 1077.11/292.47 Obligation: 1077.11/292.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/292.47 1077.11/292.47 1077.11/292.47 The TRS R consists of the following rules: 1077.11/292.47 1077.11/292.47 a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) 1077.11/292.47 a__U12(tt, V2) -> a__U13(a__isNat(V2)) 1077.11/292.47 a__U13(tt) -> tt 1077.11/292.47 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 1077.11/292.47 a__U22(tt) -> tt 1077.11/292.47 a__U31(tt, N) -> mark(N) 1077.11/292.47 a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1077.11/292.47 a__and(tt, X) -> mark(X) 1077.11/292.47 a__isNat(0) -> tt 1077.11/292.47 a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) 1077.11/292.47 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 1077.11/292.47 a__isNatKind(0) -> tt 1077.11/292.47 a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) 1077.11/292.47 a__isNatKind(s(V1)) -> a__isNatKind(V1) 1077.11/292.47 a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) 1077.11/292.47 a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) 1077.11/292.47 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1077.11/292.47 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 1077.11/292.47 mark(isNat(X)) -> a__isNat(X) 1077.11/292.47 mark(U13(X)) -> a__U13(mark(X)) 1077.11/292.47 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1077.11/292.47 mark(U22(X)) -> a__U22(mark(X)) 1077.11/292.47 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1077.11/292.47 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1077.11/292.47 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1077.11/292.47 mark(and(X1, X2)) -> a__and(mark(X1), X2) 1077.11/292.47 mark(isNatKind(X)) -> a__isNatKind(X) 1077.11/292.47 mark(tt) -> tt 1077.11/292.47 mark(s(X)) -> s(mark(X)) 1077.11/292.47 mark(0) -> 0 1077.11/292.47 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1077.11/292.47 a__U12(X1, X2) -> U12(X1, X2) 1077.11/292.47 a__isNat(X) -> isNat(X) 1077.11/292.47 a__U13(X) -> U13(X) 1077.11/292.47 a__U21(X1, X2) -> U21(X1, X2) 1077.11/292.47 a__U22(X) -> U22(X) 1077.11/292.47 a__U31(X1, X2) -> U31(X1, X2) 1077.11/292.47 a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1077.11/292.47 a__plus(X1, X2) -> plus(X1, X2) 1077.11/292.47 a__and(X1, X2) -> and(X1, X2) 1077.11/292.47 a__isNatKind(X) -> isNatKind(X) 1077.11/292.47 1077.11/292.47 S is empty. 1077.11/292.47 Rewrite Strategy: INNERMOST 1077.11/292.47 ---------------------------------------- 1077.11/292.47 1077.11/292.47 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1077.11/292.47 Renamed function symbols to avoid clashes with predefined symbol. 1077.11/292.47 ---------------------------------------- 1077.11/292.47 1077.11/292.47 (2) 1077.11/292.47 Obligation: 1077.11/292.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1077.11/292.47 1077.11/292.47 1077.11/292.47 The TRS R consists of the following rules: 1077.11/292.47 1077.11/292.47 a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) 1077.11/292.47 a__U12(tt, V2) -> a__U13(a__isNat(V2)) 1077.11/292.47 a__U13(tt) -> tt 1077.11/292.47 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 1077.11/292.47 a__U22(tt) -> tt 1077.11/292.47 a__U31(tt, N) -> mark(N) 1077.11/292.47 a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1077.11/292.47 a__and(tt, X) -> mark(X)
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