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Runtime Complexity: TRS pair #487111040
details
property
value
status
complete
benchmark
wiehe06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.495 seconds
cpu usage
313.412
user time
311.028
system time
2.38475
max virtual memory
1.8281084E7
max residence set size
5429192.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 457 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: times(x, plus(y, 1)) -> plus(times(x, plus(y, times(1, 0))), x) times(x, 1) -> x times(x, 0) -> 0 plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) plus(zero, y) -> y plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) id(x) -> x if(true, x, y) -> x if(false, x, y) -> y not(x) -> if(x, false, true) gt(s(x), zero) -> true gt(zero, y) -> false gt(s(x), s(y)) -> gt(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: times(x, plus(y, 1')) -> plus(times(x, plus(y, times(1', 0'))), x) times(x, 1') -> x times(x, 0') -> 0' plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) plus(zero, y) -> y plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) id(x) -> x if(true, x, y) -> x if(false, x, y) -> y not(x) -> if(x, false, true) gt(s(x), zero) -> true gt(zero, y) -> false gt(s(x), s(y)) -> gt(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: times(x, plus(y, 1')) -> plus(times(x, plus(y, times(1', 0'))), x) times(x, 1') -> x times(x, 0') -> 0' plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) plus(zero, y) -> y plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) id(x) -> x if(true, x, y) -> x if(false, x, y) -> y not(x) -> if(x, false, true) gt(s(x), zero) -> true
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