Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308169
details
property
value
status
complete
benchmark
Ex3_2_Luc97_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.89727 seconds
cpu usage
28.5943
user time
26.715
system time
1.87923
max virtual memory
1.9169792E7
max residence set size
3889316.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
28.50/8.83 WORST_CASE(Omega(n^1), O(n^1)) 28.50/8.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 28.50/8.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.50/8.84 28.50/8.84 28.50/8.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.50/8.84 28.50/8.84 (0) CpxTRS 28.50/8.84 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 6 ms] 28.50/8.84 (2) CpxTRS 28.50/8.84 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 28.50/8.84 (4) CpxTRS 28.50/8.84 (5) CpxTrsMatchBoundsTAProof [FINISHED, 50 ms] 28.50/8.84 (6) BOUNDS(1, n^1) 28.50/8.84 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 28.50/8.84 (8) TRS for Loop Detection 28.50/8.84 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 28.50/8.84 (10) BEST 28.50/8.84 (11) proven lower bound 28.50/8.84 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 28.50/8.84 (13) BOUNDS(n^1, INF) 28.50/8.84 (14) TRS for Loop Detection 28.50/8.84 28.50/8.84 28.50/8.84 ---------------------------------------- 28.50/8.84 28.50/8.84 (0) 28.50/8.84 Obligation: 28.50/8.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.50/8.84 28.50/8.84 28.50/8.84 The TRS R consists of the following rules: 28.50/8.84 28.50/8.84 active(dbl(0)) -> mark(0) 28.50/8.84 active(dbl(s(X))) -> mark(s(s(dbl(X)))) 28.50/8.84 active(dbls(nil)) -> mark(nil) 28.50/8.84 active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))) 28.50/8.84 active(sel(0, cons(X, Y))) -> mark(X) 28.50/8.84 active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) 28.50/8.84 active(indx(nil, X)) -> mark(nil) 28.50/8.84 active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))) 28.50/8.84 active(from(X)) -> mark(cons(X, from(s(X)))) 28.50/8.84 active(dbl(X)) -> dbl(active(X)) 28.50/8.84 active(dbls(X)) -> dbls(active(X)) 28.50/8.84 active(sel(X1, X2)) -> sel(active(X1), X2) 28.50/8.84 active(sel(X1, X2)) -> sel(X1, active(X2)) 28.50/8.84 active(indx(X1, X2)) -> indx(active(X1), X2) 28.50/8.84 dbl(mark(X)) -> mark(dbl(X)) 28.50/8.84 dbls(mark(X)) -> mark(dbls(X)) 28.50/8.84 sel(mark(X1), X2) -> mark(sel(X1, X2)) 28.50/8.84 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 28.50/8.84 indx(mark(X1), X2) -> mark(indx(X1, X2)) 28.50/8.84 proper(dbl(X)) -> dbl(proper(X)) 28.50/8.84 proper(0) -> ok(0) 28.50/8.84 proper(s(X)) -> s(proper(X)) 28.50/8.84 proper(dbls(X)) -> dbls(proper(X)) 28.50/8.84 proper(nil) -> ok(nil) 28.50/8.84 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 28.50/8.84 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 28.50/8.84 proper(indx(X1, X2)) -> indx(proper(X1), proper(X2)) 28.50/8.84 proper(from(X)) -> from(proper(X)) 28.50/8.84 dbl(ok(X)) -> ok(dbl(X)) 28.50/8.84 s(ok(X)) -> ok(s(X)) 28.50/8.84 dbls(ok(X)) -> ok(dbls(X)) 28.50/8.84 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 28.50/8.84 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 28.50/8.84 indx(ok(X1), ok(X2)) -> ok(indx(X1, X2)) 28.50/8.84 from(ok(X)) -> ok(from(X)) 28.50/8.84 top(mark(X)) -> top(proper(X)) 28.50/8.84 top(ok(X)) -> top(active(X)) 28.50/8.84 28.50/8.84 S is empty. 28.50/8.84 Rewrite Strategy: FULL 28.50/8.84 ---------------------------------------- 28.50/8.84 28.50/8.84 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 28.50/8.84 The following defined symbols can occur below the 0th argument of top: proper, active 28.50/8.84 The following defined symbols can occur below the 0th argument of proper: proper, active 28.50/8.84 The following defined symbols can occur below the 0th argument of active: proper, active 28.50/8.84 28.50/8.84 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 28.50/8.84 active(dbl(0)) -> mark(0) 28.50/8.84 active(dbl(s(X))) -> mark(s(s(dbl(X)))) 28.50/8.84 active(dbls(nil)) -> mark(nil) 28.50/8.84 active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))) 28.50/8.84 active(sel(0, cons(X, Y))) -> mark(X) 28.50/8.84 active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) 28.50/8.84 active(indx(nil, X)) -> mark(nil) 28.50/8.84 active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))) 28.50/8.84 active(from(X)) -> mark(cons(X, from(s(X)))) 28.50/8.84 active(dbl(X)) -> dbl(active(X)) 28.50/8.84 active(dbls(X)) -> dbls(active(X)) 28.50/8.84 active(sel(X1, X2)) -> sel(active(X1), X2) 28.50/8.84 active(sel(X1, X2)) -> sel(X1, active(X2)) 28.50/8.84 active(indx(X1, X2)) -> indx(active(X1), X2) 28.50/8.84 proper(dbl(X)) -> dbl(proper(X)) 28.50/8.84 proper(s(X)) -> s(proper(X)) 28.50/8.84 proper(dbls(X)) -> dbls(proper(X)) 28.50/8.84 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 28.50/8.84 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11
