Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313424
details
property
value
status
complete
benchmark
Ex1_GM03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.053 seconds
cpu usage
1114.2
user time
1101.77
system time
12.4286
max virtual memory
1.8839892E7
max residence set size
1.5085592E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1112.20/291.50 WORST_CASE(Omega(n^2), ?) 1113.81/291.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1113.81/291.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1113.81/291.97 1113.81/291.97 1113.81/291.97 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1113.81/291.97 1113.81/291.97 (0) CpxTRS 1113.81/291.97 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.81/291.97 (2) CpxTRS 1113.81/291.97 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.81/291.97 (4) typed CpxTrs 1113.81/291.97 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1113.81/291.97 (6) typed CpxTrs 1113.81/291.97 (7) RewriteLemmaProof [LOWER BOUND(ID), 358 ms] 1113.81/291.97 (8) BEST 1113.81/291.97 (9) proven lower bound 1113.81/291.97 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1113.81/291.97 (11) BOUNDS(n^1, INF) 1113.81/291.97 (12) typed CpxTrs 1113.81/291.97 (13) RewriteLemmaProof [LOWER BOUND(ID), 40 ms] 1113.81/291.97 (14) BEST 1113.81/291.97 (15) proven lower bound 1113.81/291.97 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1113.81/291.97 (17) BOUNDS(n^2, INF) 1113.81/291.97 (18) typed CpxTrs 1113.81/291.97 (19) RewriteLemmaProof [LOWER BOUND(ID), 81 ms] 1113.81/291.97 (20) typed CpxTrs 1113.81/291.97 1113.81/291.97 1113.81/291.97 ---------------------------------------- 1113.81/291.97 1113.81/291.97 (0) 1113.81/291.97 Obligation: 1113.81/291.97 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1113.81/291.97 1113.81/291.97 1113.81/291.97 The TRS R consists of the following rules: 1113.81/291.97 1113.81/291.97 a__p(0) -> 0 1113.81/291.97 a__p(s(X)) -> mark(X) 1113.81/291.97 a__leq(0, Y) -> true 1113.81/291.97 a__leq(s(X), 0) -> false 1113.81/291.97 a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) 1113.81/291.97 a__if(true, X, Y) -> mark(X) 1113.81/291.97 a__if(false, X, Y) -> mark(Y) 1113.81/291.97 a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) 1113.81/291.97 mark(p(X)) -> a__p(mark(X)) 1113.81/291.97 mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) 1113.81/291.97 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1113.81/291.97 mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) 1113.81/291.97 mark(0) -> 0 1113.81/291.97 mark(s(X)) -> s(mark(X)) 1113.81/291.97 mark(true) -> true 1113.81/291.97 mark(false) -> false 1113.81/291.97 a__p(X) -> p(X) 1113.81/291.97 a__leq(X1, X2) -> leq(X1, X2) 1113.81/291.97 a__if(X1, X2, X3) -> if(X1, X2, X3) 1113.81/291.97 a__diff(X1, X2) -> diff(X1, X2) 1113.81/291.97 1113.81/291.97 S is empty. 1113.81/291.97 Rewrite Strategy: INNERMOST 1113.81/291.97 ---------------------------------------- 1113.81/291.97 1113.81/291.97 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1113.81/291.97 Renamed function symbols to avoid clashes with predefined symbol. 1113.81/291.97 ---------------------------------------- 1113.81/291.97 1113.81/291.97 (2) 1113.81/291.97 Obligation: 1113.81/291.97 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1113.81/291.97 1113.81/291.97 1113.81/291.97 The TRS R consists of the following rules: 1113.81/291.97 1113.81/291.97 a__p(0') -> 0' 1113.81/291.97 a__p(s(X)) -> mark(X) 1113.81/291.97 a__leq(0', Y) -> true 1113.81/291.97 a__leq(s(X), 0') -> false 1113.81/291.97 a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) 1113.81/291.97 a__if(true, X, Y) -> mark(X) 1113.81/291.97 a__if(false, X, Y) -> mark(Y) 1113.81/291.97 a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0', s(diff(p(X), Y))) 1113.81/291.97 mark(p(X)) -> a__p(mark(X)) 1113.81/291.97 mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) 1113.81/291.97 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 1113.81/291.97 mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) 1113.81/291.97 mark(0') -> 0' 1113.81/291.97 mark(s(X)) -> s(mark(X)) 1113.81/291.97 mark(true) -> true 1113.81/291.97 mark(false) -> false 1113.81/291.97 a__p(X) -> p(X) 1113.81/291.97 a__leq(X1, X2) -> leq(X1, X2) 1113.81/291.97 a__if(X1, X2, X3) -> if(X1, X2, X3) 1113.81/291.97 a__diff(X1, X2) -> diff(X1, X2) 1113.81/291.97 1113.81/291.97 S is empty. 1113.81/291.97 Rewrite Strategy: INNERMOST 1113.81/291.97 ---------------------------------------- 1113.81/291.97
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40