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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313525
details
property
value
status
complete
benchmark
Ex2_Luc03b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n176.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.84601 seconds
cpu usage
15.1275
user time
13.8098
system time
1.31767
max virtual memory
1.8907092E7
max residence set size
3959272.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
14.67/4.78 WORST_CASE(Omega(n^1), O(n^1)) 15.05/4.79 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 15.05/4.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.05/4.79 15.05/4.79 15.05/4.79 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.05/4.79 15.05/4.79 (0) CpxTRS 15.05/4.79 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 15.05/4.79 (2) CdtProblem 15.05/4.79 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 15.05/4.79 (4) CdtProblem 15.05/4.79 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 15.05/4.79 (6) CdtProblem 15.05/4.79 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 94 ms] 15.05/4.79 (8) CdtProblem 15.05/4.79 (9) CdtKnowledgeProof [FINISHED, 0 ms] 15.05/4.79 (10) BOUNDS(1, 1) 15.05/4.79 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.05/4.79 (12) TRS for Loop Detection 15.05/4.79 (13) DecreasingLoopProof [LOWER BOUND(ID), 45 ms] 15.05/4.79 (14) BEST 15.05/4.79 (15) proven lower bound 15.05/4.79 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 15.05/4.79 (17) BOUNDS(n^1, INF) 15.05/4.79 (18) TRS for Loop Detection 15.05/4.79 15.05/4.79 15.05/4.79 ---------------------------------------- 15.05/4.79 15.05/4.79 (0) 15.05/4.79 Obligation: 15.05/4.79 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.05/4.79 15.05/4.79 15.05/4.79 The TRS R consists of the following rules: 15.05/4.79 15.05/4.79 fst(0, Z) -> nil 15.05/4.79 fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) 15.05/4.79 from(X) -> cons(X, n__from(s(X))) 15.05/4.79 add(0, X) -> X 15.05/4.79 add(s(X), Y) -> s(n__add(activate(X), Y)) 15.05/4.79 len(nil) -> 0 15.05/4.79 len(cons(X, Z)) -> s(n__len(activate(Z))) 15.05/4.79 fst(X1, X2) -> n__fst(X1, X2) 15.05/4.79 from(X) -> n__from(X) 15.05/4.79 add(X1, X2) -> n__add(X1, X2) 15.05/4.79 len(X) -> n__len(X) 15.05/4.79 activate(n__fst(X1, X2)) -> fst(X1, X2) 15.05/4.79 activate(n__from(X)) -> from(X) 15.05/4.79 activate(n__add(X1, X2)) -> add(X1, X2) 15.05/4.79 activate(n__len(X)) -> len(X) 15.05/4.79 activate(X) -> X 15.05/4.79 15.05/4.79 S is empty. 15.05/4.79 Rewrite Strategy: INNERMOST 15.05/4.79 ---------------------------------------- 15.05/4.79 15.05/4.79 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 15.05/4.79 Converted Cpx (relative) TRS to CDT 15.05/4.79 ---------------------------------------- 15.05/4.79 15.05/4.79 (2) 15.05/4.79 Obligation: 15.05/4.79 Complexity Dependency Tuples Problem 15.05/4.79 15.05/4.79 Rules: 15.05/4.79 fst(0, z0) -> nil 15.05/4.79 fst(s(z0), cons(z1, z2)) -> cons(z1, n__fst(activate(z0), activate(z2))) 15.05/4.79 fst(z0, z1) -> n__fst(z0, z1) 15.05/4.79 from(z0) -> cons(z0, n__from(s(z0))) 15.05/4.79 from(z0) -> n__from(z0) 15.05/4.79 add(0, z0) -> z0 15.05/4.79 add(s(z0), z1) -> s(n__add(activate(z0), z1)) 15.05/4.79 add(z0, z1) -> n__add(z0, z1) 15.05/4.79 len(nil) -> 0 15.05/4.79 len(cons(z0, z1)) -> s(n__len(activate(z1))) 15.05/4.79 len(z0) -> n__len(z0) 15.05/4.79 activate(n__fst(z0, z1)) -> fst(z0, z1) 15.05/4.79 activate(n__from(z0)) -> from(z0) 15.05/4.79 activate(n__add(z0, z1)) -> add(z0, z1) 15.05/4.79 activate(n__len(z0)) -> len(z0) 15.05/4.79 activate(z0) -> z0 15.05/4.79 Tuples: 15.05/4.79 FST(0, z0) -> c 15.05/4.79 FST(s(z0), cons(z1, z2)) -> c1(ACTIVATE(z0), ACTIVATE(z2)) 15.05/4.79 FST(z0, z1) -> c2 15.05/4.79 FROM(z0) -> c3 15.05/4.79 FROM(z0) -> c4 15.05/4.79 ADD(0, z0) -> c5 15.05/4.79 ADD(s(z0), z1) -> c6(ACTIVATE(z0)) 15.05/4.79 ADD(z0, z1) -> c7 15.05/4.79 LEN(nil) -> c8 15.05/4.79 LEN(cons(z0, z1)) -> c9(ACTIVATE(z1)) 15.05/4.79 LEN(z0) -> c10 15.05/4.79 ACTIVATE(n__fst(z0, z1)) -> c11(FST(z0, z1)) 15.05/4.79 ACTIVATE(n__from(z0)) -> c12(FROM(z0)) 15.05/4.79 ACTIVATE(n__add(z0, z1)) -> c13(ADD(z0, z1)) 15.05/4.79 ACTIVATE(n__len(z0)) -> c14(LEN(z0)) 15.05/4.79 ACTIVATE(z0) -> c15
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