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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313765
details
property
value
status
complete
benchmark
#3.48.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.544 seconds
cpu usage
320.053
user time
317.497
system time
2.55605
max virtual memory
1.89787E7
max residence set size
5978596.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
319.96/291.50 WORST_CASE(Omega(n^1), O(n^3)) 319.99/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 319.99/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 319.99/291.51 319.99/291.51 319.99/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 319.99/291.51 319.99/291.51 (0) CpxTRS 319.99/291.51 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 319.99/291.51 (2) CdtProblem 319.99/291.51 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 319.99/291.51 (4) CdtProblem 319.99/291.51 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 319.99/291.51 (6) CdtProblem 319.99/291.51 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 319.99/291.51 (8) CdtProblem 319.99/291.51 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 17 ms] 319.99/291.51 (10) CdtProblem 319.99/291.51 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 0 ms] 319.99/291.51 (12) CdtProblem 319.99/291.51 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 319.99/291.51 (14) BOUNDS(1, 1) 319.99/291.51 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 319.99/291.51 (16) TRS for Loop Detection 319.99/291.51 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 319.99/291.51 (18) BEST 319.99/291.51 (19) proven lower bound 319.99/291.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 319.99/291.51 (21) BOUNDS(n^1, INF) 319.99/291.51 (22) TRS for Loop Detection 319.99/291.51 319.99/291.51 319.99/291.51 ---------------------------------------- 319.99/291.51 319.99/291.51 (0) 319.99/291.51 Obligation: 319.99/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 319.99/291.51 319.99/291.51 319.99/291.51 The TRS R consists of the following rules: 319.99/291.51 319.99/291.51 f(0) -> true 319.99/291.51 f(1) -> false 319.99/291.51 f(s(x)) -> f(x) 319.99/291.51 if(true, s(x), s(y)) -> s(x) 319.99/291.51 if(false, s(x), s(y)) -> s(y) 319.99/291.51 g(x, c(y)) -> c(g(x, y)) 319.99/291.51 g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 319.99/291.51 319.99/291.51 S is empty. 319.99/291.51 Rewrite Strategy: INNERMOST 319.99/291.51 ---------------------------------------- 319.99/291.51 319.99/291.51 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 319.99/291.51 Converted Cpx (relative) TRS to CDT 319.99/291.51 ---------------------------------------- 319.99/291.51 319.99/291.51 (2) 319.99/291.51 Obligation: 319.99/291.51 Complexity Dependency Tuples Problem 319.99/291.51 319.99/291.51 Rules: 319.99/291.51 f(0) -> true 319.99/291.51 f(1) -> false 319.99/291.51 f(s(z0)) -> f(z0) 319.99/291.51 if(true, s(z0), s(z1)) -> s(z0) 319.99/291.51 if(false, s(z0), s(z1)) -> s(z1) 319.99/291.51 g(z0, c(z1)) -> c(g(z0, z1)) 319.99/291.51 g(z0, c(z1)) -> g(z0, if(f(z0), c(g(s(z0), z1)), c(z1))) 319.99/291.51 Tuples: 319.99/291.51 F(0) -> c1 319.99/291.51 F(1) -> c2 319.99/291.51 F(s(z0)) -> c3(F(z0)) 319.99/291.51 IF(true, s(z0), s(z1)) -> c4 319.99/291.51 IF(false, s(z0), s(z1)) -> c5 319.99/291.51 G(z0, c(z1)) -> c6(G(z0, z1)) 319.99/291.51 G(z0, c(z1)) -> c7(G(z0, if(f(z0), c(g(s(z0), z1)), c(z1))), IF(f(z0), c(g(s(z0), z1)), c(z1)), F(z0), G(s(z0), z1)) 319.99/291.51 S tuples: 319.99/291.51 F(0) -> c1 319.99/291.51 F(1) -> c2 319.99/291.51 F(s(z0)) -> c3(F(z0)) 319.99/291.51 IF(true, s(z0), s(z1)) -> c4 319.99/291.51 IF(false, s(z0), s(z1)) -> c5 319.99/291.51 G(z0, c(z1)) -> c6(G(z0, z1)) 319.99/291.51 G(z0, c(z1)) -> c7(G(z0, if(f(z0), c(g(s(z0), z1)), c(z1))), IF(f(z0), c(g(s(z0), z1)), c(z1)), F(z0), G(s(z0), z1)) 319.99/291.51 K tuples:none 319.99/291.51 Defined Rule Symbols: f_1, if_3, g_2 319.99/291.51 319.99/291.51 Defined Pair Symbols: F_1, IF_3, G_2 319.99/291.51 319.99/291.51 Compound Symbols: c1, c2, c3_1, c4, c5, c6_1, c7_4 319.99/291.51 319.99/291.51 319.99/291.51 ---------------------------------------- 319.99/291.51 319.99/291.51 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 319.99/291.51 Removed 4 trailing nodes: 319.99/291.51 IF(false, s(z0), s(z1)) -> c5 319.99/291.51 F(1) -> c2 319.99/291.51 F(0) -> c1
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