details

property	value
status	complete
benchmark	assrewrite.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.588 seconds
cpu usage	362.109
user time	359.316
system time	2.79285
max virtual memory	1.9121104E7
max residence set size	5431312.0

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 269 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (6) BEST (7) proven lower bound (8) LowerBoundPropagationProof [FINISHED, 0 ms] (9) BOUNDS(n^1, INF) (10) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: rewrite(Op(Val(n), y)) -> Op(rewrite(y), Val(n)) rewrite(Op(Op(x, y), y')) -> rewrite[Let](Op(Op(x, y), y'), Op(x, y), rewrite(x)) rewrite(Val(n)) -> Val(n) second(Op(x, y)) -> y isOp(Val(n)) -> False isOp(Op(x, y)) -> True first(Val(n)) -> Val(n) first(Op(x, y)) -> x assrewrite(exp) -> rewrite(exp) The (relative) TRS S consists of the following rules: rewrite[Let](exp, Op(x, y), a1) -> rewrite[Let][Let](exp, Op(x, y), a1, rewrite(y)) rewrite[Let][Let](Op(x, y), opab, a1, b1) -> rewrite[Let][Let][Let](Op(x, y), a1, b1, rewrite(y)) rewrite[Let][Let][Let](exp, a1, b1, c1) -> rewrite(Op(a1, Op(b1, rewrite(c1)))) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: rewrite(Op(Val(n), y)) -> Op(rewrite(y), Val(n)) rewrite(Op(Op(x, y), y')) -> rewrite[Let](Op(Op(x, y), y'), Op(x, y), rewrite(x)) rewrite(Val(n)) -> Val(n) second(Op(x, y)) -> y isOp(Val(n)) -> False isOp(Op(x, y)) -> True first(Val(n)) -> Val(n) first(Op(x, y)) -> x assrewrite(exp) -> rewrite(exp) The (relative) TRS S consists of the following rules: rewrite[Let](exp, Op(x, y), a1) -> rewrite[Let][Let](exp, Op(x, y), a1, rewrite(y)) rewrite[Let][Let](Op(x, y), opab, a1, b1) -> rewrite[Let][Let][Let](Op(x, y), a1, b1, rewrite(y)) rewrite[Let][Let][Let](exp, a1, b1, c1) -> rewrite(Op(a1, Op(b1, rewrite(c1)))) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (4) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: rewrite(Op(Val(n), y)) -> Op(rewrite(y), Val(n)) rewrite(Op(Op(x, y), y')) -> rewrite[Let](Op(Op(x, y), y'), Op(x, y), rewrite(x)) rewrite(Val(n)) -> Val(n) second(Op(x, y)) -> y isOp(Val(n)) -> False isOp(Op(x, y)) -> True first(Val(n)) -> Val(n) first(Op(x, y)) -> x assrewrite(exp) -> rewrite(exp) popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost