details

property	value
status	complete
benchmark	aprove04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.4 seconds
cpu usage	1142.02
user time	1131.39
system time	10.6291
max virtual memory	3.7887032E7
max residence set size	1.5004792E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 945 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 3 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 Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: lcm(x, y) -> lcmIter(x, y, 0, times(x, y)) lcmIter(x, y, z, u) -> if(or(ge(0, x), ge(z, u)), x, y, z, u) if(true, x, y, z, u) -> z if(false, x, y, z, u) -> if2(divisible(z, y), x, y, z, u) if2(true, x, y, z, u) -> z if2(false, x, y, z, u) -> lcmIter(x, y, plus(x, z), u) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> ifTimes(ge(0, x), x, y) ifTimes(true, x, y) -> 0 ifTimes(false, x, y) -> plus(y, times(y, p(x))) p(s(x)) -> x p(0) -> s(s(0)) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) or(true, y) -> true or(false, y) -> y divisible(0, s(y)) -> true divisible(s(x), s(y)) -> div(s(x), s(y), s(y)) div(x, y, 0) -> divisible(x, y) div(0, y, s(z)) -> false div(s(x), y, s(z)) -> div(x, y, z) a -> b a -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(b) -> b encArg(c) -> c encArg(cons_lcm(x_1, x_2)) -> lcm(encArg(x_1), encArg(x_2)) encArg(cons_lcmIter(x_1, x_2, x_3, x_4)) -> lcmIter(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_if(x_1, x_2, x_3, x_4, x_5)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encArg(cons_if2(x_1, x_2, x_3, x_4, x_5)) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_times(x_1, x_2)) -> times(encArg(x_1), encArg(x_2)) encArg(cons_ifTimes(x_1, x_2, x_3)) -> ifTimes(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_ge(x_1, x_2)) -> ge(encArg(x_1), encArg(x_2)) encArg(cons_or(x_1, x_2)) -> or(encArg(x_1), encArg(x_2)) encArg(cons_divisible(x_1, x_2)) -> divisible(encArg(x_1), encArg(x_2)) encArg(cons_div(x_1, x_2, x_3)) -> div(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a) -> a encode_lcm(x_1, x_2) -> lcm(encArg(x_1), encArg(x_2)) encode_lcmIter(x_1, x_2, x_3, x_4) -> lcmIter(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_0 -> 0 encode_times(x_1, x_2) -> times(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3, x_4, x_5) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encode_or(x_1, x_2) -> or(encArg(x_1), encArg(x_2)) encode_ge(x_1, x_2) -> ge(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_if2(x_1, x_2, x_3, x_4, x_5) -> if2(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5)) encode_divisible(x_1, x_2) -> divisible(encArg(x_1), encArg(x_2)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_ifTimes(x_1, x_2, x_3) -> ifTimes(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_div(x_1, x_2, x_3) -> div(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost