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Derivational Complexity: TRS Innermost pair #487105200
details
property
value
status
complete
benchmark
thiemann38.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
293.948 seconds
cpu usage
1140.21
user time
1129.94
system time
10.2708
max virtual memory
1.9981444E7
max residence set size
1.491244E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 624 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 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: length(nil) -> 0 length(cons(x, l)) -> s(length(l)) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) head(cons(x, l)) -> x head(nil) -> undefined tail(nil) -> nil tail(cons(x, l)) -> l reverse(l) -> rev(0, l, nil, l) rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) if(false, x, l, accu, orig) -> accu 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(0) -> 0 encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(true) -> true encArg(undefined) -> undefined encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_reverse(x_1)) -> reverse(encArg(x_1)) encArg(cons_rev(x_1, x_2, x_3, x_4)) -> rev(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)) encode_length(x_1) -> length(encArg(x_1)) encode_nil -> nil encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_false -> false encode_true -> true encode_head(x_1) -> head(encArg(x_1)) encode_undefined -> undefined encode_tail(x_1) -> tail(encArg(x_1)) encode_reverse(x_1) -> reverse(encArg(x_1)) encode_rev(x_1, x_2, x_3, x_4) -> rev(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) 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)) ---------------------------------------- (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: length(nil) -> 0 length(cons(x, l)) -> s(length(l)) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) head(cons(x, l)) -> x head(nil) -> undefined tail(nil) -> nil tail(cons(x, l)) -> l
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