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Derivational Complexity: TRS Innermost pair #487108364
details
property
value
status
complete
benchmark
Ex7_BLR02_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
293.038 seconds
cpu usage
1137.24
user time
1124.64
system time
12.6004
max virtual memory
3.7541936E7
max residence set size
1.502136E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 380 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: a__from(X) -> cons(mark(X), from(s(X))) a__head(cons(X, XS)) -> mark(X) a__2nd(cons(X, XS)) -> a__head(mark(XS)) a__take(0, XS) -> nil a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) a__sel(0, cons(X, XS)) -> mark(X) a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(2nd(X)) -> a__2nd(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(nil) -> nil a__from(X) -> from(X) a__head(X) -> head(X) a__2nd(X) -> 2nd(X) a__take(X1, X2) -> take(X1, X2) a__sel(X1, X2) -> sel(X1, X2) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(from(x_1)) -> from(encArg(x_1)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(nil) -> nil encArg(take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(head(x_1)) -> head(encArg(x_1)) encArg(2nd(x_1)) -> 2nd(encArg(x_1)) encArg(sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_a__from(x_1)) -> a__from(encArg(x_1)) encArg(cons_a__head(x_1)) -> a__head(encArg(x_1)) encArg(cons_a__2nd(x_1)) -> a__2nd(encArg(x_1)) encArg(cons_a__take(x_1, x_2)) -> a__take(encArg(x_1), encArg(x_2)) encArg(cons_a__sel(x_1, x_2)) -> a__sel(encArg(x_1), encArg(x_2)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__from(x_1) -> a__from(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_mark(x_1) -> mark(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_a__head(x_1) -> a__head(encArg(x_1)) encode_a__2nd(x_1) -> a__2nd(encArg(x_1)) encode_a__take(x_1, x_2) -> a__take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_nil -> nil encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_a__sel(x_1, x_2) -> a__sel(encArg(x_1), encArg(x_2)) encode_head(x_1) -> head(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) ---------------------------------------- (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:
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