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Runtime Complexity: TRS Innermost pair #487111822
details
property
value
status
complete
benchmark
JFP_Ex51.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
298.302 seconds
cpu usage
1141.63
user time
1127.77
system time
13.8623
max virtual memory
3.7778764E7
max residence set size
1.485486E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 284 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), 73 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (16) 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: minus_active(0, y) -> 0 mark(0) -> 0 minus_active(s(x), s(y)) -> minus_active(x, y) mark(s(x)) -> s(mark(x)) ge_active(x, 0) -> true mark(minus(x, y)) -> minus_active(x, y) ge_active(0, s(y)) -> false mark(ge(x, y)) -> ge_active(x, y) ge_active(s(x), s(y)) -> ge_active(x, y) mark(div(x, y)) -> div_active(mark(x), y) div_active(0, s(y)) -> 0 mark(if(x, y, z)) -> if_active(mark(x), y, z) div_active(s(x), s(y)) -> if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0) if_active(true, x, y) -> mark(x) minus_active(x, y) -> minus(x, y) if_active(false, x, y) -> mark(y) ge_active(x, y) -> ge(x, y) if_active(x, y, z) -> if(x, y, z) div_active(x, y) -> div(x, y) 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: minus_active(0', y) -> 0' mark(0') -> 0' minus_active(s(x), s(y)) -> minus_active(x, y) mark(s(x)) -> s(mark(x)) ge_active(x, 0') -> true mark(minus(x, y)) -> minus_active(x, y) ge_active(0', s(y)) -> false mark(ge(x, y)) -> ge_active(x, y) ge_active(s(x), s(y)) -> ge_active(x, y) mark(div(x, y)) -> div_active(mark(x), y) div_active(0', s(y)) -> 0' mark(if(x, y, z)) -> if_active(mark(x), y, z) div_active(s(x), s(y)) -> if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0') if_active(true, x, y) -> mark(x) minus_active(x, y) -> minus(x, y) if_active(false, x, y) -> mark(y) ge_active(x, y) -> ge(x, y) if_active(x, y, z) -> if(x, y, z) div_active(x, y) -> div(x, y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation:
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