details

property	value
status	complete
benchmark	PEANO_nokinds-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.509597063 seconds
cpu usage	307.852175956
max memory	6.232518656E9

stage attributes

key	value
output-size	5217
starexec-result	WORST_CASE(Omega(n^1), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 58 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: U11(tt, V2) -> U12(isNat(activate(V2))) U12(tt) -> tt U21(tt) -> tt U31(tt, N) -> activate(N) U41(tt, M, N) -> U42(isNat(activate(N)), activate(M), activate(N)) U42(tt, M, N) -> s(plus(activate(N), activate(M))) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) isNat(n__s(V1)) -> U21(isNat(activate(V1))) plus(N, 0) -> U31(isNat(N), N) plus(N, s(M)) -> U41(isNat(M), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(X1, X2) activate(n__s(X)) -> s(X) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: U11(tt, V2) -> U12(isNat(activate(V2))) U12(tt) -> tt U21(tt) -> tt U31(tt, N) -> activate(N) U41(tt, M, N) -> U42(isNat(activate(N)), activate(M), activate(N)) U42(tt, M, N) -> s(plus(activate(N), activate(M))) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) isNat(n__s(V1)) -> U21(isNat(activate(V1))) plus(N, 0) -> U31(isNat(N), N) plus(N, s(M)) -> U41(isNat(M), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(X1, X2) activate(n__s(X)) -> s(X) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence isNat(n__plus(V1, V2)) ->^+ U11(isNat(V1), activate(V2)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. popout

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actions

all output return to Runti Compl Full Rewri 10127