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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313403
details
property
value
status
complete
benchmark
ExAppendixB_AEL03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.49535 seconds
cpu usage
17.7551
user time
16.6263
system time
1.1288
max virtual memory
1.8844256E7
max residence set size
3524100.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
17.40/5.39 WORST_CASE(Omega(n^2), O(n^2)) 17.40/5.40 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.40/5.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.40/5.40 17.40/5.40 17.40/5.40 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 17.40/5.40 17.40/5.40 (0) CpxTRS 17.40/5.40 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 17.40/5.40 (2) CdtProblem 17.40/5.40 (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 17.40/5.40 (4) CdtProblem 17.40/5.40 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (6) CdtProblem 17.40/5.40 (7) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (8) CdtProblem 17.40/5.40 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (10) CdtProblem 17.40/5.40 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 110 ms] 17.40/5.40 (12) CdtProblem 17.40/5.40 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 29 ms] 17.40/5.40 (14) CdtProblem 17.40/5.40 (15) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (16) CdtProblem 17.40/5.40 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 114 ms] 17.40/5.40 (18) CdtProblem 17.40/5.40 (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (20) BOUNDS(1, 1) 17.40/5.40 (21) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (22) CpxTRS 17.40/5.40 (23) SlicingProof [LOWER BOUND(ID), 0 ms] 17.40/5.40 (24) CpxTRS 17.40/5.40 (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 17.40/5.40 (26) typed CpxTrs 17.40/5.40 (27) OrderProof [LOWER BOUND(ID), 0 ms] 17.40/5.40 (28) typed CpxTrs 17.40/5.40 (29) RewriteLemmaProof [LOWER BOUND(ID), 294 ms] 17.40/5.40 (30) BEST 17.40/5.40 (31) proven lower bound 17.40/5.40 (32) LowerBoundPropagationProof [FINISHED, 0 ms] 17.40/5.40 (33) BOUNDS(n^1, INF) 17.40/5.40 (34) typed CpxTrs 17.40/5.40 (35) RewriteLemmaProof [LOWER BOUND(ID), 106 ms] 17.40/5.40 (36) BEST 17.40/5.40 (37) proven lower bound 17.40/5.40 (38) LowerBoundPropagationProof [FINISHED, 0 ms] 17.40/5.40 (39) BOUNDS(n^2, INF) 17.40/5.40 (40) typed CpxTrs 17.40/5.40 17.40/5.40 17.40/5.40 ---------------------------------------- 17.40/5.40 17.40/5.40 (0) 17.40/5.40 Obligation: 17.40/5.40 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 17.40/5.40 17.40/5.40 17.40/5.40 The TRS R consists of the following rules: 17.40/5.40 17.40/5.40 from(X) -> cons(X, n__from(s(X))) 17.40/5.40 2ndspos(0, Z) -> rnil 17.40/5.40 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 17.40/5.40 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 17.40/5.40 2ndsneg(0, Z) -> rnil 17.40/5.40 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 17.40/5.40 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, activate(Z))) 17.40/5.40 pi(X) -> 2ndspos(X, from(0)) 17.40/5.40 plus(0, Y) -> Y 17.40/5.40 plus(s(X), Y) -> s(plus(X, Y)) 17.40/5.40 times(0, Y) -> 0 17.40/5.40 times(s(X), Y) -> plus(Y, times(X, Y)) 17.40/5.40 square(X) -> times(X, X) 17.40/5.40 from(X) -> n__from(X) 17.40/5.40 activate(n__from(X)) -> from(X) 17.40/5.40 activate(X) -> X 17.40/5.40 17.40/5.40 S is empty. 17.40/5.40 Rewrite Strategy: INNERMOST 17.40/5.40 ---------------------------------------- 17.40/5.40 17.40/5.40 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 17.40/5.40 Converted Cpx (relative) TRS to CDT 17.40/5.40 ---------------------------------------- 17.40/5.40 17.40/5.40 (2) 17.40/5.40 Obligation: 17.40/5.40 Complexity Dependency Tuples Problem 17.40/5.40 17.40/5.40 Rules: 17.40/5.40 from(z0) -> cons(z0, n__from(s(z0))) 17.40/5.40 from(z0) -> n__from(z0) 17.40/5.40 2ndspos(0, z0) -> rnil 17.40/5.40 2ndspos(s(z0), cons(z1, z2)) -> 2ndspos(s(z0), cons2(z1, activate(z2))) 17.40/5.40 2ndspos(s(z0), cons2(z1, cons(z2, z3))) -> rcons(posrecip(z2), 2ndsneg(z0, activate(z3))) 17.40/5.40 2ndsneg(0, z0) -> rnil 17.40/5.40 2ndsneg(s(z0), cons(z1, z2)) -> 2ndsneg(s(z0), cons2(z1, activate(z2))) 17.40/5.40 2ndsneg(s(z0), cons2(z1, cons(z2, z3))) -> rcons(negrecip(z2), 2ndspos(z0, activate(z3))) 17.40/5.40 pi(z0) -> 2ndspos(z0, from(0)) 17.40/5.40 plus(0, z0) -> z0 17.40/5.40 plus(s(z0), z1) -> s(plus(z0, z1))
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