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Runtime Complexity: TRS Innermost pair #487112298
details
property
value
status
complete
benchmark
ExConc_Zan97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.0339 seconds
cpu usage
5.08055
user time
4.86278
system time
0.217772
max virtual memory
1.8279408E7
max residence set size
509556.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (4) BOUNDS(1, n^1) (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTRS (7) SlicingProof [LOWER BOUND(ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 178 ms] (14) proven lower bound (15) LowerBoundPropagationProof [FINISHED, 0 ms] (16) BOUNDS(n^1, INF) ---------------------------------------- (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: a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) a__f(X) -> f(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) a__f(X) -> f(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. The certificate found is represented by the following graph. "[3, 4, 5, 6, 7, 8, 9, 10] {(3,4,[a__f_1|0, mark_1|0, f_1|1, g_1|1]), (3,5,[g_1|1]), (3,7,[a__f_1|1, f_1|2]), (3,8,[h_1|1]), (3,9,[g_1|2]), (4,4,[g_1|0, h_1|0, f_1|0]), (5,6,[h_1|1]), (6,4,[f_1|1]), (7,4,[mark_1|1, g_1|1]), (7,7,[a__f_1|1, f_1|2]), (7,8,[h_1|1]), (7,9,[g_1|2]), (8,4,[mark_1|1, g_1|1]), (8,7,[a__f_1|1, f_1|2]), (8,8,[h_1|1]), (8,9,[g_1|2]), (9,10,[h_1|2]), (10,7,[f_1|2])}" ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__f(X) -> g(h(f(X))) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> h(mark(X)) a__f(X) -> f(X) S is empty. Rewrite Strategy: INNERMOST ----------------------------------------
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