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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313428
details
property
value
status
complete
benchmark
PEANO_complete_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.56 seconds
cpu usage
1149.02
user time
1139.1
system time
9.92399
max virtual memory
3.7804596E7
max residence set size
1.491274E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1148.66/292.46 WORST_CASE(Omega(n^1), ?) 1148.85/292.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1148.85/292.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1148.85/292.49 1148.85/292.49 1148.85/292.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.85/292.49 1148.85/292.49 (0) CpxTRS 1148.85/292.49 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1148.85/292.49 (2) TRS for Loop Detection 1148.85/292.49 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1148.85/292.49 (4) BEST 1148.85/292.49 (5) proven lower bound 1148.85/292.49 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1148.85/292.49 (7) BOUNDS(n^1, INF) 1148.85/292.49 (8) TRS for Loop Detection 1148.85/292.49 1148.85/292.49 1148.85/292.49 ---------------------------------------- 1148.85/292.49 1148.85/292.49 (0) 1148.85/292.49 Obligation: 1148.85/292.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.85/292.49 1148.85/292.49 1148.85/292.49 The TRS R consists of the following rules: 1148.85/292.49 1148.85/292.49 a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) 1148.85/292.49 a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) 1148.85/292.49 a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) 1148.85/292.49 a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) 1148.85/292.49 a__U15(tt, V2) -> a__U16(a__isNat(V2)) 1148.85/292.49 a__U16(tt) -> tt 1148.85/292.49 a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) 1148.85/292.49 a__U22(tt, V1) -> a__U23(a__isNat(V1)) 1148.85/292.49 a__U23(tt) -> tt 1148.85/292.49 a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) 1148.85/292.49 a__U32(tt) -> tt 1148.85/292.49 a__U41(tt) -> tt 1148.85/292.49 a__U51(tt, N) -> a__U52(a__isNatKind(N), N) 1148.85/292.49 a__U52(tt, N) -> mark(N) 1148.85/292.49 a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) 1148.85/292.49 a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) 1148.85/292.49 a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) 1148.85/292.49 a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1148.85/292.49 a__isNat(0) -> tt 1148.85/292.49 a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) 1148.85/292.49 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 1148.85/292.49 a__isNatKind(0) -> tt 1148.85/292.49 a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) 1148.85/292.49 a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) 1148.85/292.49 a__plus(N, 0) -> a__U51(a__isNat(N), N) 1148.85/292.49 a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) 1148.85/292.49 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1148.85/292.49 mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1148.85/292.49 mark(isNatKind(X)) -> a__isNatKind(X) 1148.85/292.49 mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) 1148.85/292.49 mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) 1148.85/292.49 mark(U15(X1, X2)) -> a__U15(mark(X1), X2) 1148.85/292.49 mark(isNat(X)) -> a__isNat(X) 1148.85/292.49 mark(U16(X)) -> a__U16(mark(X)) 1148.85/292.49 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1148.85/292.49 mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1148.85/292.49 mark(U23(X)) -> a__U23(mark(X)) 1148.85/292.49 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1148.85/292.49 mark(U32(X)) -> a__U32(mark(X)) 1148.85/292.49 mark(U41(X)) -> a__U41(mark(X)) 1148.85/292.49 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1148.85/292.49 mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 1148.85/292.49 mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) 1148.85/292.49 mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) 1148.85/292.49 mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) 1148.85/292.49 mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3) 1148.85/292.49 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1148.85/292.49 mark(tt) -> tt 1148.85/292.49 mark(s(X)) -> s(mark(X)) 1148.85/292.49 mark(0) -> 0 1148.85/292.49 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1148.85/292.49 a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1148.85/292.49 a__isNatKind(X) -> isNatKind(X) 1148.85/292.49 a__U13(X1, X2, X3) -> U13(X1, X2, X3) 1148.85/292.49 a__U14(X1, X2, X3) -> U14(X1, X2, X3) 1148.85/292.49 a__U15(X1, X2) -> U15(X1, X2) 1148.85/292.49 a__isNat(X) -> isNat(X) 1148.85/292.49 a__U16(X) -> U16(X) 1148.85/292.49 a__U21(X1, X2) -> U21(X1, X2) 1148.85/292.49 a__U22(X1, X2) -> U22(X1, X2) 1148.85/292.49 a__U23(X) -> U23(X) 1148.85/292.49 a__U31(X1, X2) -> U31(X1, X2) 1148.85/292.49 a__U32(X) -> U32(X) 1148.85/292.49 a__U41(X) -> U41(X) 1148.85/292.49 a__U51(X1, X2) -> U51(X1, X2) 1148.85/292.49 a__U52(X1, X2) -> U52(X1, X2) 1148.85/292.49 a__U61(X1, X2, X3) -> U61(X1, X2, X3) 1148.85/292.49 a__U62(X1, X2, X3) -> U62(X1, X2, X3) 1148.85/292.49 a__U63(X1, X2, X3) -> U63(X1, X2, X3) 1148.85/292.49 a__U64(X1, X2, X3) -> U64(X1, X2, X3) 1148.85/292.49 a__plus(X1, X2) -> plus(X1, X2) 1148.85/292.49 1148.85/292.49 S is empty.
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