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Runtime Complexity: TRS Innermost pair #487112610
details
property
value
status
complete
benchmark
mergesort-dc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.7 seconds
cpu usage
1111.72
user time
1098.57
system time
13.1513
max virtual memory
3.7649968E7
max residence set size
1.4841996E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) merge#2(Nil, x2) -> x2 merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) drop#2(0, x2) -> x2 drop#2(S(0), Nil) -> bot[1] drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) take#2(0, x2) -> Nil take#2(S(0), Nil) -> Cons(bot[0], Nil) take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) halve#1(0) -> 0 halve#1(S(0)) -> S(0) halve#1(S(S(x14))) -> S(halve#1(x14)) const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) leq#2(0, x16) -> True leq#2(S(x20), 0) -> False leq#2(S(x4), S(x2)) -> leq#2(x4, x2) length#1(Nil) -> 0 length#1(Cons(x6, x8)) -> S(length#1(x8)) map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) merge#2(Nil, x2) -> x2 merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) drop#2(0, x2) -> x2 drop#2(S(0), Nil) -> bot[1] drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) take#2(0, x2) -> Nil take#2(S(0), Nil) -> Cons(bot[0], Nil) take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) halve#1(0) -> 0 halve#1(S(0)) -> S(0) halve#1(S(S(x14))) -> S(halve#1(x14)) const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) leq#2(0, x16) -> True leq#2(S(x20), 0) -> False leq#2(S(x4), S(x2)) -> leq#2(x4, x2) length#1(Nil) -> 0 length#1(Cons(x6, x8)) -> S(length#1(x8)) map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113)
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