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Derivational Complexity: TRS Innermost pair #487105582
details
property
value
status
complete
benchmark
4.31.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)
1.71194 seconds
cpu usage
3.68125
user time
3.49761
system time
0.18364
max virtual memory
1.8475476E7
max residence set size
244012.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF).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), 165 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: purge(nil) -> nil purge(.(x, y)) -> .(x, purge(remove(x, y))) remove(x, nil) -> nil remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(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(cons_purge(x_1)) -> purge(encArg(x_1)) encArg(cons_remove(x_1, x_2)) -> remove(encArg(x_1), encArg(x_2)) encode_purge(x_1) -> purge(encArg(x_1)) encode_nil -> nil encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_remove(x_1, x_2) -> remove(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)) ---------------------------------------- (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: purge(nil) -> nil purge(.(x, y)) -> .(x, purge(remove(x, y))) remove(x, nil) -> nil remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(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(cons_purge(x_1)) -> purge(encArg(x_1)) encArg(cons_remove(x_1, x_2)) -> remove(encArg(x_1), encArg(x_2)) encode_purge(x_1) -> purge(encArg(x_1)) encode_nil -> nil encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_remove(x_1, x_2) -> remove(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)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) 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: purge(nil) -> nil purge(.(x, y)) -> .(x, purge(remove(x, y))) remove(x, nil) -> nil remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))
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