Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313504
details
property
value
status
complete
benchmark
Ex1_2_AEL03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.665 seconds
cpu usage
1144.7
user time
1135.1
system time
9.59336
max virtual memory
3.8055824E7
max residence set size
1.4733252E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1144.28/291.52 WORST_CASE(Omega(n^1), ?) 1144.37/291.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1144.37/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1144.37/291.57 1144.37/291.57 1144.37/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1144.37/291.57 1144.37/291.57 (0) CpxTRS 1144.37/291.57 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1144.37/291.57 (2) TRS for Loop Detection 1144.37/291.57 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1144.37/291.57 (4) BEST 1144.37/291.57 (5) proven lower bound 1144.37/291.57 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1144.37/291.57 (7) BOUNDS(n^1, INF) 1144.37/291.57 (8) TRS for Loop Detection 1144.37/291.57 1144.37/291.57 1144.37/291.57 ---------------------------------------- 1144.37/291.57 1144.37/291.57 (0) 1144.37/291.57 Obligation: 1144.37/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1144.37/291.57 1144.37/291.57 1144.37/291.57 The TRS R consists of the following rules: 1144.37/291.57 1144.37/291.57 a__from(X) -> cons(mark(X), from(s(X))) 1144.37/291.57 a__2ndspos(0, Z) -> rnil 1144.37/291.57 a__2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1144.37/291.57 a__2ndsneg(0, Z) -> rnil 1144.37/291.57 a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1144.37/291.57 a__pi(X) -> a__2ndspos(mark(X), a__from(0)) 1144.37/291.57 a__plus(0, Y) -> mark(Y) 1144.37/291.57 a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1144.37/291.57 a__times(0, Y) -> 0 1144.37/291.57 a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1144.37/291.57 a__square(X) -> a__times(mark(X), mark(X)) 1144.37/291.57 mark(from(X)) -> a__from(mark(X)) 1144.37/291.57 mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1144.37/291.57 mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1144.37/291.57 mark(pi(X)) -> a__pi(mark(X)) 1144.37/291.57 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1144.37/291.57 mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1144.37/291.57 mark(square(X)) -> a__square(mark(X)) 1144.37/291.57 mark(0) -> 0 1144.37/291.57 mark(s(X)) -> s(mark(X)) 1144.37/291.57 mark(posrecip(X)) -> posrecip(mark(X)) 1144.37/291.57 mark(negrecip(X)) -> negrecip(mark(X)) 1144.37/291.57 mark(nil) -> nil 1144.37/291.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1144.37/291.57 mark(rnil) -> rnil 1144.37/291.57 mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1144.37/291.57 a__from(X) -> from(X) 1144.37/291.57 a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1144.37/291.57 a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1144.37/291.57 a__pi(X) -> pi(X) 1144.37/291.57 a__plus(X1, X2) -> plus(X1, X2) 1144.37/291.57 a__times(X1, X2) -> times(X1, X2) 1144.37/291.57 a__square(X) -> square(X) 1144.37/291.57 1144.37/291.57 S is empty. 1144.37/291.57 Rewrite Strategy: INNERMOST 1144.37/291.57 ---------------------------------------- 1144.37/291.57 1144.37/291.57 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1144.37/291.57 Transformed a relative TRS into a decreasing-loop problem. 1144.37/291.57 ---------------------------------------- 1144.37/291.57 1144.37/291.57 (2) 1144.37/291.57 Obligation: 1144.37/291.57 Analyzing the following TRS for decreasing loops: 1144.37/291.57 1144.37/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1144.37/291.57 1144.37/291.57 1144.37/291.57 The TRS R consists of the following rules: 1144.37/291.57 1144.37/291.57 a__from(X) -> cons(mark(X), from(s(X))) 1144.37/291.57 a__2ndspos(0, Z) -> rnil 1144.37/291.57 a__2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1144.37/291.57 a__2ndsneg(0, Z) -> rnil 1144.37/291.57 a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1144.37/291.57 a__pi(X) -> a__2ndspos(mark(X), a__from(0)) 1144.37/291.57 a__plus(0, Y) -> mark(Y) 1144.37/291.57 a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1144.37/291.57 a__times(0, Y) -> 0 1144.37/291.57 a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1144.37/291.57 a__square(X) -> a__times(mark(X), mark(X)) 1144.37/291.57 mark(from(X)) -> a__from(mark(X)) 1144.37/291.57 mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1144.37/291.57 mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1144.37/291.57 mark(pi(X)) -> a__pi(mark(X)) 1144.37/291.57 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1144.37/291.57 mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1144.37/291.57 mark(square(X)) -> a__square(mark(X)) 1144.37/291.57 mark(0) -> 0 1144.37/291.57 mark(s(X)) -> s(mark(X)) 1144.37/291.57 mark(posrecip(X)) -> posrecip(mark(X)) 1144.37/291.57 mark(negrecip(X)) -> negrecip(mark(X))
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