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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313849
details
property
value
status
complete
benchmark
match.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n129.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.518 seconds
cpu usage
343.767
user time
340.244
system time
3.52271
max virtual memory
3.7444508E7
max residence set size
5852564.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
343.61/291.46 WORST_CASE(Omega(n^1), O(n^2)) 343.61/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 343.61/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 343.61/291.47 343.61/291.47 343.61/291.47 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 343.61/291.47 343.61/291.47 (0) CpxRelTRS 343.61/291.47 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 250 ms] 343.61/291.47 (2) CpxRelTRS 343.61/291.47 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 343.61/291.47 (4) CdtProblem 343.61/291.47 (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 343.61/291.47 (6) CdtProblem 343.61/291.47 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 343.61/291.47 (8) CdtProblem 343.61/291.47 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 33 ms] 343.61/291.47 (10) CdtProblem 343.61/291.47 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 127 ms] 343.61/291.47 (12) CdtProblem 343.61/291.47 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 343.61/291.47 (14) BOUNDS(1, 1) 343.61/291.47 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 343.61/291.47 (16) TRS for Loop Detection 343.61/291.47 (17) DecreasingLoopProof [LOWER BOUND(ID), 48 ms] 343.61/291.47 (18) BEST 343.61/291.47 (19) proven lower bound 343.61/291.47 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 343.61/291.47 (21) BOUNDS(n^1, INF) 343.61/291.47 (22) TRS for Loop Detection 343.61/291.47 343.61/291.47 343.61/291.47 ---------------------------------------- 343.61/291.47 343.61/291.47 (0) 343.61/291.47 Obligation: 343.61/291.47 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 343.61/291.47 343.61/291.47 343.61/291.47 The TRS R consists of the following rules: 343.61/291.47 343.61/291.47 loop(Cons(x, xs), Nil, pp, ss) -> False 343.61/291.47 loop(Cons(x', xs'), Cons(x, xs), pp, ss) -> loop[Ite](!EQ(x', x), Cons(x', xs'), Cons(x, xs), pp, ss) 343.61/291.47 loop(Nil, s, pp, ss) -> True 343.61/291.47 match1(p, s) -> loop(p, s, p, s) 343.61/291.47 343.61/291.47 The (relative) TRS S consists of the following rules: 343.61/291.47 343.61/291.47 !EQ(S(x), S(y)) -> !EQ(x, y) 343.61/291.47 !EQ(0, S(y)) -> False 343.61/291.47 !EQ(S(x), 0) -> False 343.61/291.47 !EQ(0, 0) -> True 343.61/291.47 loop[Ite](False, p, s, pp, Cons(x, xs)) -> loop(pp, xs, pp, xs) 343.61/291.47 loop[Ite](True, Cons(x', xs'), Cons(x, xs), pp, ss) -> loop(xs', xs, pp, ss) 343.61/291.47 343.61/291.47 Rewrite Strategy: INNERMOST 343.61/291.47 ---------------------------------------- 343.61/291.47 343.61/291.47 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 343.61/291.47 proved termination of relative rules 343.61/291.47 ---------------------------------------- 343.61/291.47 343.61/291.47 (2) 343.61/291.47 Obligation: 343.61/291.47 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 343.61/291.47 343.61/291.47 343.61/291.47 The TRS R consists of the following rules: 343.61/291.47 343.61/291.47 loop(Cons(x, xs), Nil, pp, ss) -> False 343.61/291.47 loop(Cons(x', xs'), Cons(x, xs), pp, ss) -> loop[Ite](!EQ(x', x), Cons(x', xs'), Cons(x, xs), pp, ss) 343.61/291.47 loop(Nil, s, pp, ss) -> True 343.61/291.47 match1(p, s) -> loop(p, s, p, s) 343.61/291.47 343.61/291.47 The (relative) TRS S consists of the following rules: 343.61/291.47 343.61/291.47 !EQ(S(x), S(y)) -> !EQ(x, y) 343.61/291.47 !EQ(0, S(y)) -> False 343.61/291.47 !EQ(S(x), 0) -> False 343.61/291.47 !EQ(0, 0) -> True 343.61/291.47 loop[Ite](False, p, s, pp, Cons(x, xs)) -> loop(pp, xs, pp, xs) 343.61/291.47 loop[Ite](True, Cons(x', xs'), Cons(x, xs), pp, ss) -> loop(xs', xs, pp, ss) 343.61/291.47 343.61/291.47 Rewrite Strategy: INNERMOST 343.61/291.47 ---------------------------------------- 343.61/291.47 343.61/291.47 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 343.61/291.47 Converted Cpx (relative) TRS to CDT 343.61/291.47 ---------------------------------------- 343.61/291.47 343.61/291.47 (4) 343.61/291.47 Obligation: 343.61/291.47 Complexity Dependency Tuples Problem 343.61/291.47 343.61/291.47 Rules: 343.61/291.47 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) 343.61/291.47 !EQ(0, S(z0)) -> False 343.61/291.47 !EQ(S(z0), 0) -> False 343.61/291.47 !EQ(0, 0) -> True 343.61/291.47 loop[Ite](False, z0, z1, z2, Cons(z3, z4)) -> loop(z2, z4, z2, z4)
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