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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313480
details
property
value
status
complete
benchmark
ExIntrod_Zan97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.666 seconds
cpu usage
1137.93
user time
1126.04
system time
11.8851
max virtual memory
3.7443648E7
max residence set size
1.5079388E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1137.27/291.54 WORST_CASE(Omega(n^1), ?) 1137.68/291.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1137.68/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1137.68/291.58 1137.68/291.58 1137.68/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.68/291.58 1137.68/291.58 (0) CpxTRS 1137.68/291.58 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1137.68/291.58 (2) CpxTRS 1137.68/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1137.68/291.58 (4) typed CpxTrs 1137.68/291.58 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1137.68/291.58 (6) typed CpxTrs 1137.68/291.58 (7) RewriteLemmaProof [LOWER BOUND(ID), 528 ms] 1137.68/291.58 (8) BEST 1137.68/291.58 (9) proven lower bound 1137.68/291.58 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1137.68/291.58 (11) BOUNDS(n^1, INF) 1137.68/291.58 (12) typed CpxTrs 1137.68/291.58 1137.68/291.58 1137.68/291.58 ---------------------------------------- 1137.68/291.58 1137.68/291.58 (0) 1137.68/291.58 Obligation: 1137.68/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.68/291.58 1137.68/291.58 1137.68/291.58 The TRS R consists of the following rules: 1137.68/291.58 1137.68/291.58 a__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) 1137.68/291.58 a__add(0, X) -> mark(X) 1137.68/291.58 a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1137.68/291.58 a__prod(0, X) -> 0 1137.68/291.58 a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) 1137.68/291.58 a__if(true, X, Y) -> mark(X) 1137.68/291.58 a__if(false, X, Y) -> mark(Y) 1137.68/291.58 a__zero(0) -> true 1137.68/291.58 a__zero(s(X)) -> false 1137.68/291.58 a__p(s(X)) -> mark(X) 1137.68/291.58 mark(fact(X)) -> a__fact(mark(X)) 1137.68/291.58 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1137.68/291.58 mark(zero(X)) -> a__zero(mark(X)) 1137.68/291.58 mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) 1137.68/291.58 mark(p(X)) -> a__p(mark(X)) 1137.68/291.58 mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1137.68/291.58 mark(s(X)) -> s(mark(X)) 1137.68/291.58 mark(0) -> 0 1137.68/291.58 mark(true) -> true 1137.68/291.58 mark(false) -> false 1137.68/291.58 a__fact(X) -> fact(X) 1137.68/291.58 a__if(X1, X2, X3) -> if(X1, X2, X3) 1137.68/291.58 a__zero(X) -> zero(X) 1137.68/291.58 a__prod(X1, X2) -> prod(X1, X2) 1137.68/291.58 a__p(X) -> p(X) 1137.68/291.58 a__add(X1, X2) -> add(X1, X2) 1137.68/291.58 1137.68/291.58 S is empty. 1137.68/291.58 Rewrite Strategy: INNERMOST 1137.68/291.58 ---------------------------------------- 1137.68/291.58 1137.68/291.58 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1137.68/291.58 Renamed function symbols to avoid clashes with predefined symbol. 1137.68/291.58 ---------------------------------------- 1137.68/291.58 1137.68/291.58 (2) 1137.68/291.58 Obligation: 1137.68/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.68/291.58 1137.68/291.58 1137.68/291.58 The TRS R consists of the following rules: 1137.68/291.58 1137.68/291.58 a__fact(X) -> a__if(a__zero(mark(X)), s(0'), prod(X, fact(p(X)))) 1137.68/291.58 a__add(0', X) -> mark(X) 1137.68/291.58 a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) 1137.68/291.58 a__prod(0', X) -> 0' 1137.68/291.58 a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) 1137.68/291.58 a__if(true, X, Y) -> mark(X) 1137.68/291.58 a__if(false, X, Y) -> mark(Y) 1137.68/291.58 a__zero(0') -> true 1137.68/291.58 a__zero(s(X)) -> false 1137.68/291.58 a__p(s(X)) -> mark(X) 1137.68/291.58 mark(fact(X)) -> a__fact(mark(X)) 1137.68/291.58 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1137.68/291.58 mark(zero(X)) -> a__zero(mark(X)) 1137.68/291.58 mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) 1137.68/291.58 mark(p(X)) -> a__p(mark(X)) 1137.68/291.58 mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1137.68/291.58 mark(s(X)) -> s(mark(X)) 1137.68/291.58 mark(0') -> 0' 1137.68/291.58 mark(true) -> true 1137.68/291.58 mark(false) -> false 1137.68/291.58 a__fact(X) -> fact(X) 1137.68/291.58 a__if(X1, X2, X3) -> if(X1, X2, X3) 1137.68/291.58 a__zero(X) -> zero(X) 1137.68/291.58 a__prod(X1, X2) -> prod(X1, X2) 1137.68/291.58 a__p(X) -> p(X) 1137.68/291.58 a__add(X1, X2) -> add(X1, X2) 1137.68/291.58
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