details

property	value
status	complete
benchmark	cime2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.93167 seconds
cpu usage	21.2058
user time	19.9386
system time	1.26717
max virtual memory	1.9177468E7
max residence set size	3569952.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 36 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 184 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 138 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 909 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 239 ms] (38) CpxRNTS (39) FinalProof [FINISHED, 0 ms] (40) BOUNDS(1, n^1) (41) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (42) TRS for Loop Detection (43) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (44) BEST (45) proven lower bound (46) LowerBoundPropagationProof [FINISHED, 0 ms] (47) BOUNDS(n^1, INF) (48) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)) circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t)) circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t)) circ(circ(s, t), u) -> circ(s, circ(t, u)) circ(s, id) -> s circ(id, s) -> s circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u) subst(a, id) -> a msubst(a, id) -> a msubst(msubst(a, s), t) -> msubst(a, circ(s, t)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: circ(circ(s, t), u) -> circ(s, circ(t, u)) circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u) msubst(msubst(a, s), t) -> msubst(a, circ(s, t)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)) circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t)) popout

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actions

all output return to Runtime Complexity: TRS