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Runtime Complexity: TRS Innermost pair #487111600
details
property
value
status
complete
benchmark
t013.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.593 seconds
cpu usage
1039.34
user time
1031.77
system time
7.57397
max virtual memory
1.9441496E7
max residence set size
1.0532788E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 1297 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 2722 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 3052 ms] (18) BOUNDS(1, INF) ---------------------------------------- (0) 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: -(x, 0) -> x -(0, s(y)) -> 0 -(s(x), s(y)) -> -(x, y) f(0) -> 0 f(s(x)) -> -(s(x), g(f(x))) g(0) -> s(0) g(s(x)) -> -(s(x), f(g(x))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) 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: -(x, 0') -> x -(0', s(y)) -> 0' -(s(x), s(y)) -> -(x, y) f(0') -> 0' f(s(x)) -> -(s(x), g(f(x))) g(0') -> s(0') g(s(x)) -> -(s(x), f(g(x))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: -(x, 0') -> x -(0', s(y)) -> 0' -(s(x), s(y)) -> -(x, y) f(0') -> 0' f(s(x)) -> -(s(x), g(f(x))) g(0') -> s(0') g(s(x)) -> -(s(x), f(g(x))) Types: - :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s f :: 0':s -> 0':s g :: 0':s -> 0':s hole_0':s1_0 :: 0':s gen_0':s2_0 :: Nat -> 0':s ---------------------------------------- (5) OrderProof (LOWER BOUND(ID))
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