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Runtime Complexity: TRS Innermost pair #487112116
details
property
value
status
complete
benchmark
20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.319 seconds
cpu usage
52.0689
user time
49.6247
system time
2.44422
max virtual memory
3.70356E7
max residence set size
4281780.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) InliningProof [UPPER BOUND(ID), 250 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 209 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 77 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 287 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 196 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 140 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 23 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 132 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 1548 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 765 ms] (46) CpxRNTS (47) FinalProof [FINISHED, 0 ms] (48) BOUNDS(1, n^1) (49) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (50) TRS for Loop Detection (51) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (52) BEST (53) proven lower bound (54) LowerBoundPropagationProof [FINISHED, 0 ms] (55) BOUNDS(n^1, INF) (56) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(y, 0), x, y) cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(x)) -> false eq(s(x), s(y)) -> eq(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2)
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