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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308327
details
property
value
status
complete
benchmark
MYNAT_nokinds_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.531 seconds
cpu usage
322.343
user time
319.179
system time
3.16415
max virtual memory
1.8279384E7
max residence set size
6535184.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
322.24/291.49 WORST_CASE(Omega(n^1), ?) 322.24/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 322.24/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 322.24/291.50 322.24/291.50 322.24/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 322.24/291.50 322.24/291.50 (0) CpxTRS 322.24/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 322.24/291.50 (2) TRS for Loop Detection 322.24/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 46 ms] 322.24/291.50 (4) BEST 322.24/291.50 (5) proven lower bound 322.24/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 322.24/291.50 (7) BOUNDS(n^1, INF) 322.24/291.50 (8) TRS for Loop Detection 322.24/291.50 322.24/291.50 322.24/291.50 ---------------------------------------- 322.24/291.50 322.24/291.50 (0) 322.24/291.50 Obligation: 322.24/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 322.24/291.50 322.24/291.50 322.24/291.50 The TRS R consists of the following rules: 322.24/291.50 322.24/291.50 U11(tt, N) -> activate(N) 322.24/291.50 U21(tt, M, N) -> s(plus(activate(N), activate(M))) 322.24/291.50 U31(tt) -> 0 322.24/291.50 U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 322.24/291.50 and(tt, X) -> activate(X) 322.24/291.50 isNat(n__0) -> tt 322.24/291.50 isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 322.24/291.50 isNat(n__s(V1)) -> isNat(activate(V1)) 322.24/291.50 isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 322.24/291.50 plus(N, 0) -> U11(isNat(N), N) 322.24/291.50 plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 322.24/291.50 x(N, 0) -> U31(isNat(N)) 322.24/291.50 x(N, s(M)) -> U41(and(isNat(M), n__isNat(N)), M, N) 322.24/291.50 0 -> n__0 322.24/291.50 plus(X1, X2) -> n__plus(X1, X2) 322.24/291.50 isNat(X) -> n__isNat(X) 322.24/291.50 s(X) -> n__s(X) 322.24/291.50 x(X1, X2) -> n__x(X1, X2) 322.24/291.50 activate(n__0) -> 0 322.24/291.50 activate(n__plus(X1, X2)) -> plus(X1, X2) 322.24/291.50 activate(n__isNat(X)) -> isNat(X) 322.24/291.50 activate(n__s(X)) -> s(X) 322.24/291.50 activate(n__x(X1, X2)) -> x(X1, X2) 322.24/291.50 activate(X) -> X 322.24/291.50 322.24/291.50 S is empty. 322.24/291.50 Rewrite Strategy: FULL 322.24/291.50 ---------------------------------------- 322.24/291.50 322.24/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 322.24/291.50 Transformed a relative TRS into a decreasing-loop problem. 322.24/291.50 ---------------------------------------- 322.24/291.50 322.24/291.50 (2) 322.24/291.50 Obligation: 322.24/291.50 Analyzing the following TRS for decreasing loops: 322.24/291.50 322.24/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 322.24/291.50 322.24/291.50 322.24/291.50 The TRS R consists of the following rules: 322.24/291.50 322.24/291.50 U11(tt, N) -> activate(N) 322.24/291.50 U21(tt, M, N) -> s(plus(activate(N), activate(M))) 322.24/291.50 U31(tt) -> 0 322.24/291.50 U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 322.24/291.50 and(tt, X) -> activate(X) 322.24/291.50 isNat(n__0) -> tt 322.24/291.50 isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 322.24/291.50 isNat(n__s(V1)) -> isNat(activate(V1)) 322.24/291.50 isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 322.24/291.50 plus(N, 0) -> U11(isNat(N), N) 322.24/291.50 plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 322.24/291.50 x(N, 0) -> U31(isNat(N)) 322.24/291.50 x(N, s(M)) -> U41(and(isNat(M), n__isNat(N)), M, N) 322.24/291.50 0 -> n__0 322.24/291.50 plus(X1, X2) -> n__plus(X1, X2) 322.24/291.50 isNat(X) -> n__isNat(X) 322.24/291.50 s(X) -> n__s(X) 322.24/291.50 x(X1, X2) -> n__x(X1, X2) 322.24/291.50 activate(n__0) -> 0 322.24/291.50 activate(n__plus(X1, X2)) -> plus(X1, X2) 322.24/291.50 activate(n__isNat(X)) -> isNat(X) 322.24/291.50 activate(n__s(X)) -> s(X) 322.24/291.50 activate(n__x(X1, X2)) -> x(X1, X2) 322.24/291.50 activate(X) -> X 322.24/291.50 322.24/291.50 S is empty. 322.24/291.50 Rewrite Strategy: FULL 322.24/291.50 ---------------------------------------- 322.24/291.50 322.24/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 322.24/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1):
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