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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313680
details
property
value
status
complete
benchmark
AAECC.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n164.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.096 seconds
cpu usage
1150.06
user time
1135.6
system time
14.4518
max virtual memory
5.6701792E7
max residence set size
1.4828688E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1149.55/291.99 WORST_CASE(Omega(n^1), O(n^2)) 1149.55/292.01 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1149.55/292.01 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1149.55/292.01 1149.55/292.01 1149.55/292.01 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1149.55/292.01 1149.55/292.01 (0) CpxTRS 1149.55/292.01 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms] 1149.55/292.01 (2) CpxWeightedTrs 1149.55/292.01 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1149.55/292.01 (4) CpxTypedWeightedTrs 1149.55/292.01 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1149.55/292.01 (6) CpxTypedWeightedCompleteTrs 1149.55/292.01 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 1149.55/292.01 (8) CpxRNTS 1149.55/292.01 (9) CompleteCoflocoProof [FINISHED, 1283 ms] 1149.55/292.01 (10) BOUNDS(1, n^2) 1149.55/292.01 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1149.55/292.01 (12) TRS for Loop Detection 1149.55/292.01 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1149.55/292.01 (14) BEST 1149.55/292.01 (15) proven lower bound 1149.55/292.01 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1149.55/292.01 (17) BOUNDS(n^1, INF) 1149.55/292.01 (18) TRS for Loop Detection 1149.55/292.01 1149.55/292.01 1149.55/292.01 ---------------------------------------- 1149.55/292.01 1149.55/292.01 (0) 1149.55/292.01 Obligation: 1149.55/292.01 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1149.55/292.01 1149.55/292.01 1149.55/292.01 The TRS R consists of the following rules: 1149.55/292.01 1149.55/292.01 fstsplit(0, x) -> nil 1149.55/292.01 fstsplit(s(n), nil) -> nil 1149.55/292.01 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) 1149.55/292.01 sndsplit(0, x) -> x 1149.55/292.01 sndsplit(s(n), nil) -> nil 1149.55/292.01 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) 1149.55/292.01 empty(nil) -> true 1149.55/292.01 empty(cons(h, t)) -> false 1149.55/292.01 leq(0, m) -> true 1149.55/292.01 leq(s(n), 0) -> false 1149.55/292.01 leq(s(n), s(m)) -> leq(n, m) 1149.55/292.01 length(nil) -> 0 1149.55/292.01 length(cons(h, t)) -> s(length(t)) 1149.55/292.01 app(nil, x) -> x 1149.55/292.01 app(cons(h, t), x) -> cons(h, app(t, x)) 1149.55/292.01 map_f(pid, nil) -> nil 1149.55/292.01 map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) 1149.55/292.01 process(store, m) -> if1(store, m, leq(m, length(store))) 1149.55/292.01 if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store))) 1149.55/292.01 if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store)))) 1149.55/292.01 if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m) 1149.55/292.01 if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m) 1149.55/292.01 1149.55/292.01 S is empty. 1149.55/292.01 Rewrite Strategy: INNERMOST 1149.55/292.01 ---------------------------------------- 1149.55/292.01 1149.55/292.01 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1149.55/292.01 Transformed relative TRS to weighted TRS 1149.55/292.01 ---------------------------------------- 1149.55/292.01 1149.55/292.01 (2) 1149.55/292.01 Obligation: 1149.55/292.01 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1149.55/292.01 1149.55/292.01 1149.55/292.01 The TRS R consists of the following rules: 1149.55/292.01 1149.55/292.01 fstsplit(0, x) -> nil [1] 1149.55/292.01 fstsplit(s(n), nil) -> nil [1] 1149.55/292.01 fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) [1] 1149.55/292.01 sndsplit(0, x) -> x [1] 1149.55/292.01 sndsplit(s(n), nil) -> nil [1] 1149.55/292.01 sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) [1] 1149.55/292.01 empty(nil) -> true [1] 1149.55/292.01 empty(cons(h, t)) -> false [1] 1149.55/292.01 leq(0, m) -> true [1] 1149.55/292.01 leq(s(n), 0) -> false [1] 1149.55/292.01 leq(s(n), s(m)) -> leq(n, m) [1] 1149.55/292.01 length(nil) -> 0 [1] 1149.55/292.01 length(cons(h, t)) -> s(length(t)) [1] 1149.55/292.01 app(nil, x) -> x [1] 1149.55/292.01 app(cons(h, t), x) -> cons(h, app(t, x)) [1] 1149.55/292.01 map_f(pid, nil) -> nil [1] 1149.55/292.01 map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) [1] 1149.55/292.01 process(store, m) -> if1(store, m, leq(m, length(store))) [1] 1149.55/292.01 if1(store, m, true) -> if2(store, m, empty(fstsplit(m, store))) [1] 1149.55/292.01 if1(store, m, false) -> if3(store, m, empty(fstsplit(m, app(map_f(self, nil), store)))) [1] 1149.55/292.01 if2(store, m, false) -> process(app(map_f(self, nil), sndsplit(m, store)), m) [1] 1149.55/292.01 if3(store, m, false) -> process(sndsplit(m, app(map_f(self, nil), store)), m) [1] 1149.55/292.01 1149.55/292.01 Rewrite Strategy: INNERMOST 1149.55/292.01 ----------------------------------------
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