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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313927
details
property
value
status
complete
benchmark
32.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n159.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.52 seconds
cpu usage
325.25
user time
322.216
system time
3.03394
max virtual memory
5.5938816E7
max residence set size
5689388.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
325.11/291.46 WORST_CASE(Omega(n^1), O(n^2)) 325.11/291.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 325.11/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 325.11/291.47 325.11/291.47 325.11/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 325.11/291.47 325.11/291.47 (0) CpxTRS 325.11/291.47 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 3 ms] 325.11/291.47 (2) CdtProblem 325.11/291.47 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 325.11/291.47 (4) CdtProblem 325.11/291.47 (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 108 ms] 325.11/291.47 (6) CdtProblem 325.11/291.47 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 67 ms] 325.11/291.47 (8) CdtProblem 325.11/291.47 (9) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 325.11/291.47 (10) CdtProblem 325.11/291.47 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 73 ms] 325.11/291.47 (12) CdtProblem 325.11/291.47 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 325.11/291.47 (14) BOUNDS(1, 1) 325.11/291.47 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 325.11/291.47 (16) CpxTRS 325.11/291.47 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 325.11/291.47 (18) typed CpxTrs 325.11/291.47 (19) OrderProof [LOWER BOUND(ID), 0 ms] 325.11/291.47 (20) typed CpxTrs 325.11/291.47 (21) RewriteLemmaProof [LOWER BOUND(ID), 457 ms] 325.11/291.47 (22) BEST 325.11/291.47 (23) proven lower bound 325.11/291.47 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 325.11/291.47 (25) BOUNDS(n^1, INF) 325.11/291.47 (26) typed CpxTrs 325.11/291.47 (27) RewriteLemmaProof [LOWER BOUND(ID), 361 ms] 325.11/291.47 (28) BOUNDS(1, INF) 325.11/291.47 325.11/291.47 325.11/291.47 ---------------------------------------- 325.11/291.47 325.11/291.47 (0) 325.11/291.47 Obligation: 325.11/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 325.11/291.47 325.11/291.47 325.11/291.47 The TRS R consists of the following rules: 325.11/291.47 325.11/291.47 sort(nil) -> nil 325.11/291.47 sort(cons(x, y)) -> insert(x, sort(y)) 325.11/291.47 insert(x, nil) -> cons(x, nil) 325.11/291.47 insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v) 325.11/291.47 choose(x, cons(v, w), y, 0) -> cons(x, cons(v, w)) 325.11/291.47 choose(x, cons(v, w), 0, s(z)) -> cons(v, insert(x, w)) 325.11/291.47 choose(x, cons(v, w), s(y), s(z)) -> choose(x, cons(v, w), y, z) 325.11/291.47 325.11/291.47 S is empty. 325.11/291.47 Rewrite Strategy: INNERMOST 325.11/291.47 ---------------------------------------- 325.11/291.47 325.11/291.47 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 325.11/291.47 Converted Cpx (relative) TRS to CDT 325.11/291.47 ---------------------------------------- 325.11/291.47 325.11/291.47 (2) 325.11/291.47 Obligation: 325.11/291.47 Complexity Dependency Tuples Problem 325.11/291.47 325.11/291.47 Rules: 325.11/291.47 sort(nil) -> nil 325.11/291.47 sort(cons(z0, z1)) -> insert(z0, sort(z1)) 325.11/291.47 insert(z0, nil) -> cons(z0, nil) 325.11/291.47 insert(z0, cons(z1, z2)) -> choose(z0, cons(z1, z2), z0, z1) 325.11/291.47 choose(z0, cons(z1, z2), z3, 0) -> cons(z0, cons(z1, z2)) 325.11/291.47 choose(z0, cons(z1, z2), 0, s(z3)) -> cons(z1, insert(z0, z2)) 325.11/291.47 choose(z0, cons(z1, z2), s(z3), s(z4)) -> choose(z0, cons(z1, z2), z3, z4) 325.11/291.47 Tuples: 325.11/291.47 SORT(nil) -> c 325.11/291.47 SORT(cons(z0, z1)) -> c1(INSERT(z0, sort(z1)), SORT(z1)) 325.11/291.47 INSERT(z0, nil) -> c2 325.11/291.47 INSERT(z0, cons(z1, z2)) -> c3(CHOOSE(z0, cons(z1, z2), z0, z1)) 325.11/291.47 CHOOSE(z0, cons(z1, z2), z3, 0) -> c4 325.11/291.47 CHOOSE(z0, cons(z1, z2), 0, s(z3)) -> c5(INSERT(z0, z2)) 325.11/291.47 CHOOSE(z0, cons(z1, z2), s(z3), s(z4)) -> c6(CHOOSE(z0, cons(z1, z2), z3, z4)) 325.11/291.47 S tuples: 325.11/291.47 SORT(nil) -> c 325.11/291.47 SORT(cons(z0, z1)) -> c1(INSERT(z0, sort(z1)), SORT(z1)) 325.11/291.47 INSERT(z0, nil) -> c2 325.11/291.47 INSERT(z0, cons(z1, z2)) -> c3(CHOOSE(z0, cons(z1, z2), z0, z1)) 325.11/291.47 CHOOSE(z0, cons(z1, z2), z3, 0) -> c4 325.11/291.47 CHOOSE(z0, cons(z1, z2), 0, s(z3)) -> c5(INSERT(z0, z2)) 325.11/291.47 CHOOSE(z0, cons(z1, z2), s(z3), s(z4)) -> c6(CHOOSE(z0, cons(z1, z2), z3, z4)) 325.11/291.47 K tuples:none 325.11/291.47 Defined Rule Symbols: sort_1, insert_2, choose_4 325.11/291.47 325.11/291.47 Defined Pair Symbols: SORT_1, INSERT_2, CHOOSE_4 325.11/291.47 325.11/291.47 Compound Symbols: c, c1_2, c2, c3_1, c4, c5_1, c6_1 325.11/291.47 325.11/291.47 325.11/291.47 ----------------------------------------
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