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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313409
details
property
value
status
complete
benchmark
Ex6_9_Luc02c_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n161.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.532 seconds
cpu usage
353.587
user time
347.296
system time
6.29089
max virtual memory
1.9301324E7
max residence set size
9227512.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
353.41/291.46 WORST_CASE(Omega(n^1), O(n^2)) 353.49/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 353.49/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 353.49/291.47 353.49/291.47 353.49/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 353.49/291.47 353.49/291.47 (0) CpxTRS 353.49/291.47 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 353.49/291.47 (2) CdtProblem 353.49/291.47 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 353.49/291.47 (4) CdtProblem 353.49/291.47 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 353.49/291.47 (6) CdtProblem 353.49/291.47 (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 353.49/291.47 (8) CdtProblem 353.49/291.47 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 353.49/291.47 (10) CdtProblem 353.49/291.47 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 36 ms] 353.49/291.47 (12) CdtProblem 353.49/291.47 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] 353.49/291.47 (14) CdtProblem 353.49/291.47 (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 353.49/291.47 (16) BOUNDS(1, 1) 353.49/291.47 (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 353.49/291.47 (18) TRS for Loop Detection 353.49/291.47 (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 353.49/291.47 (20) BEST 353.49/291.47 (21) proven lower bound 353.49/291.47 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 353.49/291.47 (23) BOUNDS(n^1, INF) 353.49/291.47 (24) TRS for Loop Detection 353.49/291.47 353.49/291.47 353.49/291.47 ---------------------------------------- 353.49/291.47 353.49/291.47 (0) 353.49/291.47 Obligation: 353.49/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 353.49/291.47 353.49/291.47 353.49/291.47 The TRS R consists of the following rules: 353.49/291.47 353.49/291.47 2nd(cons1(X, cons(Y, Z))) -> Y 353.49/291.47 2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1))) 353.49/291.47 from(X) -> cons(X, n__from(n__s(X))) 353.49/291.47 from(X) -> n__from(X) 353.49/291.47 s(X) -> n__s(X) 353.49/291.47 activate(n__from(X)) -> from(activate(X)) 353.49/291.47 activate(n__s(X)) -> s(activate(X)) 353.49/291.47 activate(X) -> X 353.49/291.47 353.49/291.47 S is empty. 353.49/291.47 Rewrite Strategy: INNERMOST 353.49/291.47 ---------------------------------------- 353.49/291.47 353.49/291.47 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 353.49/291.47 Converted Cpx (relative) TRS to CDT 353.49/291.47 ---------------------------------------- 353.49/291.47 353.49/291.47 (2) 353.49/291.47 Obligation: 353.49/291.47 Complexity Dependency Tuples Problem 353.49/291.47 353.49/291.47 Rules: 353.49/291.47 2nd(cons1(z0, cons(z1, z2))) -> z1 353.49/291.47 2nd(cons(z0, z1)) -> 2nd(cons1(z0, activate(z1))) 353.49/291.47 from(z0) -> cons(z0, n__from(n__s(z0))) 353.49/291.48 from(z0) -> n__from(z0) 353.49/291.48 s(z0) -> n__s(z0) 353.49/291.48 activate(n__from(z0)) -> from(activate(z0)) 353.49/291.48 activate(n__s(z0)) -> s(activate(z0)) 353.49/291.48 activate(z0) -> z0 353.49/291.48 Tuples: 353.49/291.48 2ND(cons1(z0, cons(z1, z2))) -> c 353.49/291.48 2ND(cons(z0, z1)) -> c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) 353.49/291.48 FROM(z0) -> c2 353.49/291.48 FROM(z0) -> c3 353.49/291.48 S(z0) -> c4 353.49/291.48 ACTIVATE(n__from(z0)) -> c5(FROM(activate(z0)), ACTIVATE(z0)) 353.49/291.48 ACTIVATE(n__s(z0)) -> c6(S(activate(z0)), ACTIVATE(z0)) 353.49/291.48 ACTIVATE(z0) -> c7 353.49/291.48 S tuples: 353.49/291.48 2ND(cons1(z0, cons(z1, z2))) -> c 353.49/291.48 2ND(cons(z0, z1)) -> c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) 353.49/291.48 FROM(z0) -> c2 353.49/291.48 FROM(z0) -> c3 353.49/291.48 S(z0) -> c4 353.49/291.48 ACTIVATE(n__from(z0)) -> c5(FROM(activate(z0)), ACTIVATE(z0)) 353.49/291.48 ACTIVATE(n__s(z0)) -> c6(S(activate(z0)), ACTIVATE(z0)) 353.49/291.48 ACTIVATE(z0) -> c7 353.49/291.48 K tuples:none 353.49/291.48 Defined Rule Symbols: 2nd_1, from_1, s_1, activate_1 353.49/291.48 353.49/291.48 Defined Pair Symbols: 2ND_1, FROM_1, S_1, ACTIVATE_1 353.49/291.48 353.49/291.48 Compound Symbols: c, c1_2, c2, c3, c4, c5_2, c6_2, c7 353.49/291.48 353.49/291.48 353.49/291.48 ----------------------------------------
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