details

property	value
status	complete
benchmark	4.61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	1.75687 seconds
cpu usage	4.09045
user time	3.91692
system time	0.173526
max virtual memory	1.8408912E7
max residence set size	252144.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 327 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [FINISHED, 0 ms] (8) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: bsort(nil) -> nil bsort(.(x, y)) -> last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y)))))) bubble(nil) -> nil bubble(.(x, nil)) -> .(x, nil) bubble(.(x, .(y, z))) -> if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z)))) last(nil) -> 0 last(.(x, nil)) -> x last(.(x, .(y, z))) -> last(.(y, z)) butlast(nil) -> nil butlast(.(x, nil)) -> nil butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z))) 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(nil) -> nil encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(<=(x_1, x_2)) -> <=(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_bsort(x_1)) -> bsort(encArg(x_1)) encArg(cons_bubble(x_1)) -> bubble(encArg(x_1)) encArg(cons_last(x_1)) -> last(encArg(x_1)) encArg(cons_butlast(x_1)) -> butlast(encArg(x_1)) encode_bsort(x_1) -> bsort(encArg(x_1)) encode_nil -> nil encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_last(x_1) -> last(encArg(x_1)) encode_bubble(x_1) -> bubble(encArg(x_1)) encode_butlast(x_1) -> butlast(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_<=(x_1, x_2) -> <=(encArg(x_1), encArg(x_2)) encode_0 -> 0 ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: bsort(nil) -> nil bsort(.(x, y)) -> last(.(bubble(.(x, y)), bsort(butlast(bubble(.(x, y)))))) bubble(nil) -> nil bubble(.(x, nil)) -> .(x, nil) bubble(.(x, .(y, z))) -> if(<=(x, y), .(y, bubble(.(x, z))), .(x, bubble(.(y, z)))) last(nil) -> 0 last(.(x, nil)) -> x last(.(x, .(y, z))) -> last(.(y, z)) butlast(nil) -> nil butlast(.(x, nil)) -> nil butlast(.(x, .(y, z))) -> .(x, butlast(.(y, z))) The (relative) TRS S consists of the following rules: encArg(nil) -> nil encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(<=(x_1, x_2)) -> <=(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_bsort(x_1)) -> bsort(encArg(x_1)) encArg(cons_bubble(x_1)) -> bubble(encArg(x_1)) encArg(cons_last(x_1)) -> last(encArg(x_1)) encArg(cons_butlast(x_1)) -> butlast(encArg(x_1)) encode_bsort(x_1) -> bsort(encArg(x_1)) encode_nil -> nil popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost