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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313364
details
property
value
status
complete
benchmark
subtrees.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.553 seconds
cpu usage
311.45
user time
309.6
system time
1.85
max virtual memory
1.8744048E7
max residence set size
5205788.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
311.45/291.49 WORST_CASE(Omega(n^1), O(n^2)) 311.45/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 311.45/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 311.45/291.51 311.45/291.51 311.45/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 311.45/291.51 311.45/291.51 (0) CpxTRS 311.45/291.51 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 311.45/291.51 (2) CdtProblem 311.45/291.51 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 311.45/291.51 (4) CdtProblem 311.45/291.51 (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 120 ms] 311.45/291.51 (6) CdtProblem 311.45/291.51 (7) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 311.45/291.51 (8) CdtProblem 311.45/291.51 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 106 ms] 311.45/291.51 (10) CdtProblem 311.45/291.51 (11) CdtKnowledgeProof [FINISHED, 0 ms] 311.45/291.51 (12) BOUNDS(1, 1) 311.45/291.51 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 311.45/291.51 (14) CpxTRS 311.45/291.51 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 311.45/291.51 (16) CpxTRS 311.45/291.51 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 311.45/291.51 (18) typed CpxTrs 311.45/291.51 (19) OrderProof [LOWER BOUND(ID), 0 ms] 311.45/291.51 (20) typed CpxTrs 311.45/291.51 (21) RewriteLemmaProof [LOWER BOUND(ID), 249 ms] 311.45/291.51 (22) BEST 311.45/291.51 (23) proven lower bound 311.45/291.51 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 311.45/291.51 (25) BOUNDS(n^1, INF) 311.45/291.51 (26) typed CpxTrs 311.45/291.51 (27) RewriteLemmaProof [LOWER BOUND(ID), 13 ms] 311.45/291.51 (28) typed CpxTrs 311.45/291.51 311.45/291.51 311.45/291.51 ---------------------------------------- 311.45/291.51 311.45/291.51 (0) 311.45/291.51 Obligation: 311.45/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 311.45/291.51 311.45/291.51 311.45/291.51 The TRS R consists of the following rules: 311.45/291.51 311.45/291.51 append(@l1, @l2) -> append#1(@l1, @l2) 311.45/291.51 append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) 311.45/291.51 append#1(nil, @l2) -> @l2 311.45/291.51 subtrees(@t) -> subtrees#1(@t) 311.45/291.51 subtrees#1(leaf) -> nil 311.45/291.51 subtrees#1(node(@x, @t1, @t2)) -> subtrees#2(subtrees(@t1), @t1, @t2, @x) 311.45/291.51 subtrees#2(@l1, @t1, @t2, @x) -> subtrees#3(subtrees(@t2), @l1, @t1, @t2, @x) 311.45/291.51 subtrees#3(@l2, @l1, @t1, @t2, @x) -> ::(node(@x, @t1, @t2), append(@l1, @l2)) 311.45/291.51 311.45/291.51 S is empty. 311.45/291.51 Rewrite Strategy: INNERMOST 311.45/291.51 ---------------------------------------- 311.45/291.51 311.45/291.51 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 311.45/291.51 Converted Cpx (relative) TRS to CDT 311.45/291.51 ---------------------------------------- 311.45/291.51 311.45/291.51 (2) 311.45/291.51 Obligation: 311.45/291.51 Complexity Dependency Tuples Problem 311.45/291.51 311.45/291.51 Rules: 311.45/291.51 append(z0, z1) -> append#1(z0, z1) 311.45/291.51 append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2)) 311.45/291.51 append#1(nil, z0) -> z0 311.45/291.51 subtrees(z0) -> subtrees#1(z0) 311.45/291.51 subtrees#1(leaf) -> nil 311.45/291.51 subtrees#1(node(z0, z1, z2)) -> subtrees#2(subtrees(z1), z1, z2, z0) 311.45/291.51 subtrees#2(z0, z1, z2, z3) -> subtrees#3(subtrees(z2), z0, z1, z2, z3) 311.45/291.51 subtrees#3(z0, z1, z2, z3, z4) -> ::(node(z4, z2, z3), append(z1, z0)) 311.45/291.51 Tuples: 311.45/291.51 APPEND(z0, z1) -> c(APPEND#1(z0, z1)) 311.45/291.51 APPEND#1(::(z0, z1), z2) -> c1(APPEND(z1, z2)) 311.45/291.51 APPEND#1(nil, z0) -> c2 311.45/291.51 SUBTREES(z0) -> c3(SUBTREES#1(z0)) 311.45/291.51 SUBTREES#1(leaf) -> c4 311.45/291.51 SUBTREES#1(node(z0, z1, z2)) -> c5(SUBTREES#2(subtrees(z1), z1, z2, z0), SUBTREES(z1)) 311.45/291.51 SUBTREES#2(z0, z1, z2, z3) -> c6(SUBTREES#3(subtrees(z2), z0, z1, z2, z3), SUBTREES(z2)) 311.45/291.51 SUBTREES#3(z0, z1, z2, z3, z4) -> c7(APPEND(z1, z0)) 311.45/291.51 S tuples: 311.45/291.51 APPEND(z0, z1) -> c(APPEND#1(z0, z1)) 311.45/291.51 APPEND#1(::(z0, z1), z2) -> c1(APPEND(z1, z2)) 311.45/291.51 APPEND#1(nil, z0) -> c2 311.45/291.51 SUBTREES(z0) -> c3(SUBTREES#1(z0)) 311.45/291.51 SUBTREES#1(leaf) -> c4 311.45/291.51 SUBTREES#1(node(z0, z1, z2)) -> c5(SUBTREES#2(subtrees(z1), z1, z2, z0), SUBTREES(z1)) 311.45/291.51 SUBTREES#2(z0, z1, z2, z3) -> c6(SUBTREES#3(subtrees(z2), z0, z1, z2, z3), SUBTREES(z2)) 311.45/291.51 SUBTREES#3(z0, z1, z2, z3, z4) -> c7(APPEND(z1, z0)) 311.45/291.51 K tuples:none 311.45/291.51 Defined Rule Symbols: append_2, append#1_2, subtrees_1, subtrees#1_1, subtrees#2_4, subtrees#3_5 311.45/291.51 311.45/291.51 Defined Pair Symbols: APPEND_2, APPEND#1_2, SUBTREES_1, SUBTREES#1_1, SUBTREES#2_4, SUBTREES#3_5 311.45/291.51
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