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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308168
details
property
value
status
complete
benchmark
PALINDROME_complete_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.784 seconds
cpu usage
898.735
user time
892.557
system time
6.17885
max virtual memory
1.8281636E7
max residence set size
9887308.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
898.23/291.63 WORST_CASE(Omega(n^2), ?) 898.39/291.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 898.39/291.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 898.39/291.67 898.39/291.67 898.39/291.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 898.39/291.67 898.39/291.67 (0) CpxTRS 898.39/291.67 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 898.39/291.67 (2) CpxTRS 898.39/291.67 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 898.39/291.67 (4) typed CpxTrs 898.39/291.67 (5) OrderProof [LOWER BOUND(ID), 9 ms] 898.39/291.67 (6) typed CpxTrs 898.39/291.67 (7) RewriteLemmaProof [LOWER BOUND(ID), 522 ms] 898.39/291.67 (8) BEST 898.39/291.67 (9) proven lower bound 898.39/291.67 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 898.39/291.67 (11) BOUNDS(n^1, INF) 898.39/291.67 (12) typed CpxTrs 898.39/291.67 (13) RewriteLemmaProof [LOWER BOUND(ID), 54.5 s] 898.39/291.67 (14) BEST 898.39/291.67 (15) proven lower bound 898.39/291.67 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 898.39/291.67 (17) BOUNDS(n^2, INF) 898.39/291.67 (18) typed CpxTrs 898.39/291.67 898.39/291.67 898.39/291.67 ---------------------------------------- 898.39/291.67 898.39/291.67 (0) 898.39/291.67 Obligation: 898.39/291.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 898.39/291.67 898.39/291.67 898.39/291.67 The TRS R consists of the following rules: 898.39/291.67 898.39/291.67 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 898.39/291.67 a____(X, nil) -> mark(X) 898.39/291.67 a____(nil, X) -> mark(X) 898.39/291.67 a__U11(tt, V) -> a__U12(a__isPalListKind(V), V) 898.39/291.67 a__U12(tt, V) -> a__U13(a__isNeList(V)) 898.39/291.67 a__U13(tt) -> tt 898.39/291.67 a__U21(tt, V1, V2) -> a__U22(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__U22(tt, V1, V2) -> a__U23(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U23(tt, V1, V2) -> a__U24(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U24(tt, V1, V2) -> a__U25(a__isList(V1), V2) 898.39/291.67 a__U25(tt, V2) -> a__U26(a__isList(V2)) 898.39/291.67 a__U26(tt) -> tt 898.39/291.67 a__U31(tt, V) -> a__U32(a__isPalListKind(V), V) 898.39/291.67 a__U32(tt, V) -> a__U33(a__isQid(V)) 898.39/291.67 a__U33(tt) -> tt 898.39/291.67 a__U41(tt, V1, V2) -> a__U42(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__U42(tt, V1, V2) -> a__U43(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U43(tt, V1, V2) -> a__U44(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U44(tt, V1, V2) -> a__U45(a__isList(V1), V2) 898.39/291.67 a__U45(tt, V2) -> a__U46(a__isNeList(V2)) 898.39/291.67 a__U46(tt) -> tt 898.39/291.67 a__U51(tt, V1, V2) -> a__U52(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__U52(tt, V1, V2) -> a__U53(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U53(tt, V1, V2) -> a__U54(a__isPalListKind(V2), V1, V2) 898.39/291.67 a__U54(tt, V1, V2) -> a__U55(a__isNeList(V1), V2) 898.39/291.67 a__U55(tt, V2) -> a__U56(a__isList(V2)) 898.39/291.67 a__U56(tt) -> tt 898.39/291.67 a__U61(tt, V) -> a__U62(a__isPalListKind(V), V) 898.39/291.67 a__U62(tt, V) -> a__U63(a__isQid(V)) 898.39/291.67 a__U63(tt) -> tt 898.39/291.67 a__U71(tt, I, P) -> a__U72(a__isPalListKind(I), P) 898.39/291.67 a__U72(tt, P) -> a__U73(a__isPal(P), P) 898.39/291.67 a__U73(tt, P) -> a__U74(a__isPalListKind(P)) 898.39/291.67 a__U74(tt) -> tt 898.39/291.67 a__U81(tt, V) -> a__U82(a__isPalListKind(V), V) 898.39/291.67 a__U82(tt, V) -> a__U83(a__isNePal(V)) 898.39/291.67 a__U83(tt) -> tt 898.39/291.67 a__U91(tt, V2) -> a__U92(a__isPalListKind(V2)) 898.39/291.67 a__U92(tt) -> tt 898.39/291.67 a__isList(V) -> a__U11(a__isPalListKind(V), V) 898.39/291.67 a__isList(nil) -> tt 898.39/291.67 a__isList(__(V1, V2)) -> a__U21(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__isNeList(V) -> a__U31(a__isPalListKind(V), V) 898.39/291.67 a__isNeList(__(V1, V2)) -> a__U41(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__isNeList(__(V1, V2)) -> a__U51(a__isPalListKind(V1), V1, V2) 898.39/291.67 a__isNePal(V) -> a__U61(a__isPalListKind(V), V) 898.39/291.67 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), I, P) 898.39/291.67 a__isPal(V) -> a__U81(a__isPalListKind(V), V) 898.39/291.67 a__isPal(nil) -> tt 898.39/291.67 a__isPalListKind(a) -> tt 898.39/291.67 a__isPalListKind(e) -> tt 898.39/291.67 a__isPalListKind(i) -> tt 898.39/291.67 a__isPalListKind(nil) -> tt 898.39/291.67 a__isPalListKind(o) -> tt 898.39/291.67 a__isPalListKind(u) -> tt 898.39/291.67 a__isPalListKind(__(V1, V2)) -> a__U91(a__isPalListKind(V1), V2) 898.39/291.67 a__isQid(a) -> tt 898.39/291.67 a__isQid(e) -> tt 898.39/291.67 a__isQid(i) -> tt 898.39/291.67 a__isQid(o) -> tt 898.39/291.67 a__isQid(u) -> tt 898.39/291.67 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 898.39/291.67 mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
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