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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313330
details
property
value
status
complete
benchmark
fib_llist.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.671 seconds
cpu usage
1116.43
user time
1103.5
system time
12.9244
max virtual memory
3.7989E7
max residence set size
1.4790868E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1116.16/291.52 WORST_CASE(Omega(n^1), ?) 1116.16/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1116.16/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1116.16/291.53 1116.16/291.53 1116.16/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1116.16/291.53 1116.16/291.53 (0) CpxTRS 1116.16/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1116.16/291.53 (2) TRS for Loop Detection 1116.16/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1116.16/291.53 (4) BEST 1116.16/291.53 (5) proven lower bound 1116.16/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1116.16/291.53 (7) BOUNDS(n^1, INF) 1116.16/291.53 (8) TRS for Loop Detection 1116.16/291.53 1116.16/291.53 1116.16/291.53 ---------------------------------------- 1116.16/291.53 1116.16/291.53 (0) 1116.16/291.53 Obligation: 1116.16/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1116.16/291.53 1116.16/291.53 1116.16/291.53 The TRS R consists of the following rules: 1116.16/291.53 1116.16/291.53 fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) 1116.16/291.53 cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil 1116.16/291.53 cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) 1116.16/291.53 cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) 1116.16/291.53 plus#2(0, x12) -> x12 1116.16/291.53 plus#2(S(x4), x2) -> S(plus#2(x4, x2)) 1116.16/291.53 cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) 1116.16/291.53 cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) 1116.16/291.53 cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) 1116.16/291.53 zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) 1116.16/291.53 main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) 1116.16/291.53 1116.16/291.53 S is empty. 1116.16/291.53 Rewrite Strategy: INNERMOST 1116.16/291.53 ---------------------------------------- 1116.16/291.53 1116.16/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1116.16/291.53 Transformed a relative TRS into a decreasing-loop problem. 1116.16/291.53 ---------------------------------------- 1116.16/291.53 1116.16/291.53 (2) 1116.16/291.53 Obligation: 1116.16/291.53 Analyzing the following TRS for decreasing loops: 1116.16/291.53 1116.16/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1116.16/291.53 1116.16/291.53 1116.16/291.53 The TRS R consists of the following rules: 1116.16/291.53 1116.16/291.53 fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) 1116.16/291.53 cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil 1116.16/291.53 cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) 1116.16/291.53 cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) 1116.16/291.53 plus#2(0, x12) -> x12 1116.16/291.53 plus#2(S(x4), x2) -> S(plus#2(x4, x2)) 1116.16/291.53 cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) 1116.16/291.53 cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) 1116.16/291.53 cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) 1116.16/291.53 zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) 1116.16/291.53 zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) 1116.16/291.53 main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) 1116.16/291.53 1116.16/291.53 S is empty. 1116.16/291.53 Rewrite Strategy: INNERMOST 1116.16/291.53 ---------------------------------------- 1116.16/291.53 1116.16/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1116.16/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1116.16/291.53 1116.16/291.53 The rewrite sequence 1116.16/291.53 1116.16/291.53 plus#2(S(x4), x2) ->^+ S(plus#2(x4, x2)) 1116.16/291.53 1116.16/291.53 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1116.16/291.53 1116.16/291.53 The pumping substitution is [x4 / S(x4)]. 1116.16/291.53 1116.16/291.53 The result substitution is [ ]. 1116.16/291.53 1116.16/291.53 1116.16/291.53 1116.16/291.53 1116.16/291.53 ---------------------------------------- 1116.16/291.53 1116.16/291.53 (4) 1116.16/291.53 Complex Obligation (BEST) 1116.16/291.53 1116.16/291.53 ----------------------------------------
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