details

property	value
status	complete
benchmark	foldsum.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	hoca

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.81791710854 seconds
cpu usage	6.197921976
max memory	5.54786816E8

stage attributes

key	value
output-size	7604
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 264 ms] (4) BOUNDS(1, n^1) (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: comp_f_g#1(plus_x(x3), comp_f_g(x1, x2), 0) -> plus_x#1(x3, comp_f_g#1(x1, x2, 0)) comp_f_g#1(plus_x(x3), id, 0) -> plus_x#1(x3, 0) map#2(Nil) -> Nil map#2(Cons(x16, x6)) -> Cons(plus_x(x16), map#2(x6)) plus_x#1(0, x6) -> x6 plus_x#1(S(x8), x10) -> S(plus_x#1(x8, x10)) foldr_f#3(Nil, 0) -> 0 foldr_f#3(Cons(x16, x5), x24) -> comp_f_g#1(x16, foldr#3(x5), x24) foldr#3(Nil) -> id foldr#3(Cons(x32, x6)) -> comp_f_g(x32, foldr#3(x6)) main(x3) -> foldr_f#3(map#2(x3), 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: comp_f_g#1(plus_x(x3), comp_f_g(x1, x2), 0) -> plus_x#1(x3, comp_f_g#1(x1, x2, 0)) comp_f_g#1(plus_x(x3), id, 0) -> plus_x#1(x3, 0) map#2(Nil) -> Nil map#2(Cons(x16, x6)) -> Cons(plus_x(x16), map#2(x6)) plus_x#1(0, x6) -> x6 plus_x#1(S(x8), x10) -> S(plus_x#1(x8, x10)) foldr_f#3(Nil, 0) -> 0 foldr_f#3(Cons(x16, x5), x24) -> comp_f_g#1(x16, foldr#3(x5), x24) foldr#3(Nil) -> id foldr#3(Cons(x32, x6)) -> comp_f_g(x32, foldr#3(x6)) main(x3) -> foldr_f#3(map#2(x3), 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3, 4, 5, 6] transitions: plus_x0(0) -> 0 comp_f_g0(0, 0) -> 0 00() -> 0 id0() -> 0 Nil0() -> 0 Cons0(0, 0) -> 0 S0(0) -> 0 comp_f_g#10(0, 0, 0) -> 1 map#20(0) -> 2 plus_x#10(0, 0) -> 3 foldr_f#30(0, 0) -> 4 foldr#30(0) -> 5 main0(0) -> 6 01() -> 8 popout

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job log

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actions

all output return to Runti Compl Inner Rewri 22807