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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307996
details
property
value
status
complete
benchmark
PEANO_complete-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.592 seconds
cpu usage
314.779
user time
312.723
system time
2.05638
max virtual memory
1.8279384E7
max residence set size
5538136.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
314.66/291.55 WORST_CASE(Omega(n^1), ?) 314.66/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 314.66/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 314.66/291.56 314.66/291.56 314.66/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.66/291.56 314.66/291.56 (0) CpxTRS 314.66/291.56 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 314.66/291.56 (2) TRS for Loop Detection 314.66/291.56 (3) DecreasingLoopProof [LOWER BOUND(ID), 134 ms] 314.66/291.56 (4) BEST 314.66/291.56 (5) proven lower bound 314.66/291.56 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 314.66/291.56 (7) BOUNDS(n^1, INF) 314.66/291.56 (8) TRS for Loop Detection 314.66/291.56 314.66/291.56 314.66/291.56 ---------------------------------------- 314.66/291.56 314.66/291.56 (0) 314.66/291.56 Obligation: 314.66/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.66/291.56 314.66/291.56 314.66/291.56 The TRS R consists of the following rules: 314.66/291.56 314.66/291.56 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 314.66/291.56 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 314.66/291.56 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 314.66/291.56 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 314.66/291.56 U15(tt, V2) -> U16(isNat(activate(V2))) 314.66/291.56 U16(tt) -> tt 314.66/291.56 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 314.66/291.56 U22(tt, V1) -> U23(isNat(activate(V1))) 314.66/291.56 U23(tt) -> tt 314.66/291.56 U31(tt, V2) -> U32(isNatKind(activate(V2))) 314.66/291.56 U32(tt) -> tt 314.66/291.56 U41(tt) -> tt 314.66/291.56 U51(tt, N) -> U52(isNatKind(activate(N)), activate(N)) 314.66/291.56 U52(tt, N) -> activate(N) 314.66/291.56 U61(tt, M, N) -> U62(isNatKind(activate(M)), activate(M), activate(N)) 314.66/291.56 U62(tt, M, N) -> U63(isNat(activate(N)), activate(M), activate(N)) 314.66/291.56 U63(tt, M, N) -> U64(isNatKind(activate(N)), activate(M), activate(N)) 314.66/291.56 U64(tt, M, N) -> s(plus(activate(N), activate(M))) 314.66/291.56 isNat(n__0) -> tt 314.66/291.56 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 314.66/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 314.66/291.56 isNatKind(n__0) -> tt 314.66/291.56 isNatKind(n__plus(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V2)) 314.66/291.56 isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) 314.66/291.56 plus(N, 0) -> U51(isNat(N), N) 314.66/291.56 plus(N, s(M)) -> U61(isNat(M), M, N) 314.66/291.56 0 -> n__0 314.66/291.56 plus(X1, X2) -> n__plus(X1, X2) 314.66/291.56 s(X) -> n__s(X) 314.66/291.56 activate(n__0) -> 0 314.66/291.56 activate(n__plus(X1, X2)) -> plus(X1, X2) 314.66/291.56 activate(n__s(X)) -> s(X) 314.66/291.56 activate(X) -> X 314.66/291.56 314.66/291.56 S is empty. 314.66/291.56 Rewrite Strategy: FULL 314.66/291.56 ---------------------------------------- 314.66/291.56 314.66/291.56 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 314.66/291.56 Transformed a relative TRS into a decreasing-loop problem. 314.66/291.56 ---------------------------------------- 314.66/291.56 314.66/291.56 (2) 314.66/291.56 Obligation: 314.66/291.56 Analyzing the following TRS for decreasing loops: 314.66/291.56 314.66/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 314.66/291.56 314.66/291.56 314.66/291.56 The TRS R consists of the following rules: 314.66/291.56 314.66/291.56 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 314.66/291.56 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 314.66/291.56 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 314.66/291.56 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 314.66/291.56 U15(tt, V2) -> U16(isNat(activate(V2))) 314.66/291.56 U16(tt) -> tt 314.66/291.56 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 314.66/291.56 U22(tt, V1) -> U23(isNat(activate(V1))) 314.66/291.56 U23(tt) -> tt 314.66/291.56 U31(tt, V2) -> U32(isNatKind(activate(V2))) 314.66/291.56 U32(tt) -> tt 314.66/291.56 U41(tt) -> tt 314.66/291.56 U51(tt, N) -> U52(isNatKind(activate(N)), activate(N)) 314.66/291.56 U52(tt, N) -> activate(N) 314.66/291.56 U61(tt, M, N) -> U62(isNatKind(activate(M)), activate(M), activate(N)) 314.66/291.56 U62(tt, M, N) -> U63(isNat(activate(N)), activate(M), activate(N)) 314.66/291.56 U63(tt, M, N) -> U64(isNatKind(activate(N)), activate(M), activate(N)) 314.66/291.56 U64(tt, M, N) -> s(plus(activate(N), activate(M))) 314.66/291.56 isNat(n__0) -> tt 314.66/291.56 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 314.66/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 314.66/291.56 isNatKind(n__0) -> tt
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