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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313335
details
property
value
status
complete
benchmark
isort-fold.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.529 seconds
cpu usage
332.496
user time
329.094
system time
3.40145
max virtual memory
1.9187688E7
max residence set size
5656380.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
332.36/291.47 WORST_CASE(Omega(n^1), O(n^2)) 332.36/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 332.36/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 332.36/291.49 332.36/291.49 332.36/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 332.36/291.49 332.36/291.49 (0) CpxTRS 332.36/291.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 332.36/291.49 (2) CpxWeightedTrs 332.36/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 332.36/291.49 (4) CpxTypedWeightedTrs 332.36/291.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (6) CpxTypedWeightedCompleteTrs 332.36/291.49 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 332.36/291.49 (8) CpxTypedWeightedCompleteTrs 332.36/291.49 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (10) CpxRNTS 332.36/291.49 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 332.36/291.49 (12) CpxRNTS 332.36/291.49 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 332.36/291.49 (14) CpxRNTS 332.36/291.49 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (16) CpxRNTS 332.36/291.49 (17) IntTrsBoundProof [UPPER BOUND(ID), 278 ms] 332.36/291.49 (18) CpxRNTS 332.36/291.49 (19) IntTrsBoundProof [UPPER BOUND(ID), 169 ms] 332.36/291.49 (20) CpxRNTS 332.36/291.49 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (22) CpxRNTS 332.36/291.49 (23) IntTrsBoundProof [UPPER BOUND(ID), 2085 ms] 332.36/291.49 (24) CpxRNTS 332.36/291.49 (25) IntTrsBoundProof [UPPER BOUND(ID), 718 ms] 332.36/291.49 (26) CpxRNTS 332.36/291.49 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (28) CpxRNTS 332.36/291.49 (29) IntTrsBoundProof [UPPER BOUND(ID), 704 ms] 332.36/291.49 (30) CpxRNTS 332.36/291.49 (31) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] 332.36/291.49 (32) CpxRNTS 332.36/291.49 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (34) CpxRNTS 332.36/291.49 (35) IntTrsBoundProof [UPPER BOUND(ID), 126 ms] 332.36/291.49 (36) CpxRNTS 332.36/291.49 (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 332.36/291.49 (38) CpxRNTS 332.36/291.49 (39) FinalProof [FINISHED, 0 ms] 332.36/291.49 (40) BOUNDS(1, n^2) 332.36/291.49 (41) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 332.36/291.49 (42) TRS for Loop Detection 332.36/291.49 (43) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 332.36/291.49 (44) BEST 332.36/291.49 (45) proven lower bound 332.36/291.49 (46) LowerBoundPropagationProof [FINISHED, 0 ms] 332.36/291.49 (47) BOUNDS(n^1, INF) 332.36/291.49 (48) TRS for Loop Detection 332.36/291.49 332.36/291.49 332.36/291.49 ---------------------------------------- 332.36/291.49 332.36/291.49 (0) 332.36/291.49 Obligation: 332.36/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 332.36/291.49 332.36/291.49 332.36/291.49 The TRS R consists of the following rules: 332.36/291.49 332.36/291.49 fold#3(insert_ord(x2), Nil) -> Nil 332.36/291.49 fold#3(insert_ord(x6), Cons(x4, x2)) -> insert_ord#2(x6, x4, fold#3(insert_ord(x6), x2)) 332.36/291.49 cond_insert_ord_x_ys_1(True, x3, x2, x1) -> Cons(x3, Cons(x2, x1)) 332.36/291.49 cond_insert_ord_x_ys_1(False, x0, x5, x2) -> Cons(x5, insert_ord#2(leq, x0, x2)) 332.36/291.49 insert_ord#2(leq, x2, Nil) -> Cons(x2, Nil) 332.36/291.49 insert_ord#2(leq, x6, Cons(x4, x2)) -> cond_insert_ord_x_ys_1(leq#2(x6, x4), x6, x4, x2) 332.36/291.49 leq#2(0, x8) -> True 332.36/291.49 leq#2(S(x12), 0) -> False 332.36/291.49 leq#2(S(x4), S(x2)) -> leq#2(x4, x2) 332.36/291.49 main(x3) -> fold#3(insert_ord(leq), x3) 332.36/291.49 332.36/291.49 S is empty. 332.36/291.49 Rewrite Strategy: INNERMOST 332.36/291.49 ---------------------------------------- 332.36/291.49 332.36/291.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 332.36/291.49 Transformed relative TRS to weighted TRS 332.36/291.49 ---------------------------------------- 332.36/291.49 332.36/291.49 (2) 332.36/291.49 Obligation: 332.36/291.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 332.36/291.49 332.36/291.49 332.36/291.49 The TRS R consists of the following rules: 332.36/291.49 332.36/291.49 fold#3(insert_ord(x2), Nil) -> Nil [1] 332.36/291.49 fold#3(insert_ord(x6), Cons(x4, x2)) -> insert_ord#2(x6, x4, fold#3(insert_ord(x6), x2)) [1] 332.36/291.49 cond_insert_ord_x_ys_1(True, x3, x2, x1) -> Cons(x3, Cons(x2, x1)) [1] 332.36/291.49 cond_insert_ord_x_ys_1(False, x0, x5, x2) -> Cons(x5, insert_ord#2(leq, x0, x2)) [1] 332.36/291.49 insert_ord#2(leq, x2, Nil) -> Cons(x2, Nil) [1] 332.36/291.49 insert_ord#2(leq, x6, Cons(x4, x2)) -> cond_insert_ord_x_ys_1(leq#2(x6, x4), x6, x4, x2) [1] 332.36/291.49 leq#2(0, x8) -> True [1]
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