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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313793
details
property
value
status
complete
benchmark
power.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.708 seconds
cpu usage
746.613
user time
741.112
system time
5.50179
max virtual memory
1.9088148E7
max residence set size
7471636.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
746.47/291.64 WORST_CASE(Omega(n^3), ?) 746.47/291.65 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 746.47/291.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 746.47/291.65 746.47/291.65 746.47/291.65 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 746.47/291.65 746.47/291.65 (0) CpxTRS 746.47/291.65 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 746.47/291.65 (2) CpxTRS 746.47/291.65 (3) SlicingProof [LOWER BOUND(ID), 0 ms] 746.47/291.65 (4) CpxTRS 746.47/291.65 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 746.47/291.65 (6) typed CpxTrs 746.47/291.65 (7) OrderProof [LOWER BOUND(ID), 0 ms] 746.47/291.65 (8) typed CpxTrs 746.47/291.65 (9) RewriteLemmaProof [LOWER BOUND(ID), 321 ms] 746.47/291.65 (10) BEST 746.47/291.65 (11) proven lower bound 746.47/291.65 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 746.47/291.65 (13) BOUNDS(n^1, INF) 746.47/291.65 (14) typed CpxTrs 746.47/291.65 (15) RewriteLemmaProof [LOWER BOUND(ID), 113 ms] 746.47/291.65 (16) BEST 746.47/291.65 (17) proven lower bound 746.47/291.65 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 746.47/291.65 (19) BOUNDS(n^3, INF) 746.47/291.65 (20) typed CpxTrs 746.47/291.65 (21) RewriteLemmaProof [LOWER BOUND(ID), 610 ms] 746.47/291.65 (22) BOUNDS(1, INF) 746.47/291.65 746.47/291.65 746.47/291.65 ---------------------------------------- 746.47/291.65 746.47/291.65 (0) 746.47/291.65 Obligation: 746.47/291.65 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 746.47/291.65 746.47/291.65 746.47/291.65 The TRS R consists of the following rules: 746.47/291.65 746.47/291.65 power(x', Cons(x, xs)) -> mult(x', power(x', xs)) 746.47/291.65 mult(x', Cons(x, xs)) -> add0(x', mult(x', xs)) 746.47/291.65 add0(x', Cons(x, xs)) -> Cons(Cons(Nil, Nil), add0(x', xs)) 746.47/291.65 power(x, Nil) -> Cons(Nil, Nil) 746.47/291.65 mult(x, Nil) -> Nil 746.47/291.65 add0(x, Nil) -> x 746.47/291.65 goal(x, y) -> power(x, y) 746.47/291.65 746.47/291.65 S is empty. 746.47/291.65 Rewrite Strategy: INNERMOST 746.47/291.65 ---------------------------------------- 746.47/291.65 746.47/291.65 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 746.47/291.65 Renamed function symbols to avoid clashes with predefined symbol. 746.47/291.65 ---------------------------------------- 746.47/291.65 746.47/291.65 (2) 746.47/291.65 Obligation: 746.47/291.65 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 746.47/291.65 746.47/291.65 746.47/291.65 The TRS R consists of the following rules: 746.47/291.65 746.47/291.65 power(x', Cons(x, xs)) -> mult(x', power(x', xs)) 746.47/291.65 mult(x', Cons(x, xs)) -> add0(x', mult(x', xs)) 746.47/291.65 add0(x', Cons(x, xs)) -> Cons(Cons(Nil, Nil), add0(x', xs)) 746.47/291.65 power(x, Nil) -> Cons(Nil, Nil) 746.47/291.65 mult(x, Nil) -> Nil 746.47/291.65 add0(x, Nil) -> x 746.47/291.65 goal(x, y) -> power(x, y) 746.47/291.65 746.47/291.65 S is empty. 746.47/291.65 Rewrite Strategy: INNERMOST 746.47/291.65 ---------------------------------------- 746.47/291.65 746.47/291.65 (3) SlicingProof (LOWER BOUND(ID)) 746.47/291.65 Sliced the following arguments: 746.47/291.65 Cons/0 746.47/291.65 746.47/291.65 ---------------------------------------- 746.47/291.65 746.47/291.65 (4) 746.47/291.65 Obligation: 746.47/291.65 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). 746.47/291.65 746.47/291.65 746.47/291.65 The TRS R consists of the following rules: 746.47/291.65 746.47/291.65 power(x', Cons(xs)) -> mult(x', power(x', xs)) 746.47/291.65 mult(x', Cons(xs)) -> add0(x', mult(x', xs)) 746.47/291.65 add0(x', Cons(xs)) -> Cons(add0(x', xs)) 746.47/291.65 power(x, Nil) -> Cons(Nil) 746.47/291.65 mult(x, Nil) -> Nil 746.47/291.65 add0(x, Nil) -> x 746.47/291.65 goal(x, y) -> power(x, y) 746.47/291.65 746.47/291.65 S is empty. 746.47/291.65 Rewrite Strategy: INNERMOST 746.47/291.65 ----------------------------------------
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