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Derivational Complexity: TRS Innermost pair #487105610
details
property
value
status
complete
benchmark
4.60.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
2.23892 seconds
cpu usage
4.2091
user time
4.00611
system time
0.202988
max virtual memory
1.8611452E7
max residence set size
330472.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF).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), 219 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 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 (13) DecreasingLoopProof [FINISHED, 0 ms] (14) 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: msort(nil) -> nil msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))) min(x, nil) -> x min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)) del(x, nil) -> nil del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, 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(=(x_1, x_2)) -> =(encArg(x_1), encArg(x_2)) encArg(cons_msort(x_1)) -> msort(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_del(x_1, x_2)) -> del(encArg(x_1), encArg(x_2)) encode_msort(x_1) -> msort(encArg(x_1)) encode_nil -> nil encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_del(x_1, x_2) -> del(encArg(x_1), encArg(x_2)) 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_=(x_1, x_2) -> =(encArg(x_1), encArg(x_2)) ---------------------------------------- (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: msort(nil) -> nil msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))) min(x, nil) -> x min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)) del(x, nil) -> nil del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, 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(=(x_1, x_2)) -> =(encArg(x_1), encArg(x_2)) encArg(cons_msort(x_1)) -> msort(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_del(x_1, x_2)) -> del(encArg(x_1), encArg(x_2)) encode_msort(x_1) -> msort(encArg(x_1)) encode_nil -> nil encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_del(x_1, x_2) -> del(encArg(x_1), encArg(x_2)) 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_=(x_1, x_2) -> =(encArg(x_1), encArg(x_2))
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