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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313803
details
property
value
status
complete
benchmark
duplicate.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.0434 seconds
cpu usage
11.772
user time
10.8534
system time
0.918634
max virtual memory
1.8544064E7
max residence set size
3061308.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
11.45/3.99 WORST_CASE(Omega(n^1), O(n^1)) 11.68/4.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.68/4.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.68/4.00 11.68/4.00 11.68/4.00 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.68/4.00 11.68/4.00 (0) CpxTRS 11.68/4.00 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 11.68/4.00 (2) CdtProblem 11.68/4.00 (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 11.68/4.00 (4) CdtProblem 11.68/4.00 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 11.68/4.00 (6) CdtProblem 11.68/4.00 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 3 ms] 11.68/4.00 (8) CdtProblem 11.68/4.00 (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 11.68/4.00 (10) BOUNDS(1, 1) 11.68/4.00 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 11.68/4.00 (12) CpxTRS 11.68/4.00 (13) SlicingProof [LOWER BOUND(ID), 0 ms] 11.68/4.00 (14) CpxTRS 11.68/4.00 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 11.68/4.00 (16) typed CpxTrs 11.68/4.00 (17) OrderProof [LOWER BOUND(ID), 0 ms] 11.68/4.00 (18) typed CpxTrs 11.68/4.00 (19) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] 11.68/4.00 (20) proven lower bound 11.68/4.00 (21) LowerBoundPropagationProof [FINISHED, 0 ms] 11.68/4.00 (22) BOUNDS(n^1, INF) 11.68/4.00 11.68/4.00 11.68/4.00 ---------------------------------------- 11.68/4.00 11.68/4.00 (0) 11.68/4.00 Obligation: 11.68/4.00 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.68/4.00 11.68/4.00 11.68/4.00 The TRS R consists of the following rules: 11.68/4.00 11.68/4.00 duplicate(Cons(x, xs)) -> Cons(x, Cons(x, duplicate(xs))) 11.68/4.00 duplicate(Nil) -> Nil 11.68/4.00 goal(x) -> duplicate(x) 11.68/4.00 11.68/4.00 S is empty. 11.68/4.00 Rewrite Strategy: INNERMOST 11.68/4.00 ---------------------------------------- 11.68/4.00 11.68/4.00 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 11.68/4.00 Converted Cpx (relative) TRS to CDT 11.68/4.00 ---------------------------------------- 11.68/4.00 11.68/4.00 (2) 11.68/4.00 Obligation: 11.68/4.00 Complexity Dependency Tuples Problem 11.68/4.00 11.68/4.00 Rules: 11.68/4.00 duplicate(Cons(z0, z1)) -> Cons(z0, Cons(z0, duplicate(z1))) 11.68/4.00 duplicate(Nil) -> Nil 11.68/4.00 goal(z0) -> duplicate(z0) 11.68/4.00 Tuples: 11.68/4.00 DUPLICATE(Cons(z0, z1)) -> c(DUPLICATE(z1)) 11.68/4.00 DUPLICATE(Nil) -> c1 11.68/4.00 GOAL(z0) -> c2(DUPLICATE(z0)) 11.68/4.00 S tuples: 11.68/4.00 DUPLICATE(Cons(z0, z1)) -> c(DUPLICATE(z1)) 11.68/4.00 DUPLICATE(Nil) -> c1 11.68/4.00 GOAL(z0) -> c2(DUPLICATE(z0)) 11.68/4.00 K tuples:none 11.68/4.00 Defined Rule Symbols: duplicate_1, goal_1 11.68/4.00 11.68/4.00 Defined Pair Symbols: DUPLICATE_1, GOAL_1 11.68/4.00 11.68/4.00 Compound Symbols: c_1, c1, c2_1 11.68/4.00 11.68/4.00 11.68/4.00 ---------------------------------------- 11.68/4.00 11.68/4.00 (3) CdtLeafRemovalProof (ComplexityIfPolyImplication) 11.68/4.00 Removed 1 leading nodes: 11.68/4.00 GOAL(z0) -> c2(DUPLICATE(z0)) 11.68/4.00 Removed 1 trailing nodes: 11.68/4.00 DUPLICATE(Nil) -> c1 11.68/4.00 11.68/4.00 ---------------------------------------- 11.68/4.00 11.68/4.00 (4) 11.68/4.00 Obligation: 11.68/4.00 Complexity Dependency Tuples Problem 11.68/4.00 11.68/4.00 Rules: 11.68/4.00 duplicate(Cons(z0, z1)) -> Cons(z0, Cons(z0, duplicate(z1))) 11.68/4.00 duplicate(Nil) -> Nil 11.68/4.00 goal(z0) -> duplicate(z0) 11.68/4.00 Tuples: 11.68/4.00 DUPLICATE(Cons(z0, z1)) -> c(DUPLICATE(z1)) 11.68/4.00 S tuples: 11.68/4.00 DUPLICATE(Cons(z0, z1)) -> c(DUPLICATE(z1)) 11.68/4.00 K tuples:none
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