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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308192
details
property
value
status
complete
benchmark
MYNAT_nokinds-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n129.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.739 seconds
cpu usage
309.373
user time
306.668
system time
2.7055
max virtual memory
1.8279384E7
max residence set size
6139020.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
308.99/291.60 WORST_CASE(Omega(n^1), ?) 309.27/291.70 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 309.27/291.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 309.27/291.70 309.27/291.70 309.27/291.70 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.27/291.70 309.27/291.70 (0) CpxTRS 309.27/291.70 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 309.27/291.70 (2) CpxTRS 309.27/291.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 309.27/291.70 (4) typed CpxTrs 309.27/291.70 (5) OrderProof [LOWER BOUND(ID), 0 ms] 309.27/291.70 (6) typed CpxTrs 309.27/291.70 (7) RewriteLemmaProof [LOWER BOUND(ID), 345 ms] 309.27/291.70 (8) BEST 309.27/291.70 (9) proven lower bound 309.27/291.70 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 309.27/291.70 (11) BOUNDS(n^1, INF) 309.27/291.70 (12) typed CpxTrs 309.27/291.70 309.27/291.70 309.27/291.70 ---------------------------------------- 309.27/291.70 309.27/291.70 (0) 309.27/291.70 Obligation: 309.27/291.70 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.27/291.70 309.27/291.70 309.27/291.70 The TRS R consists of the following rules: 309.27/291.70 309.27/291.70 U11(tt, V2) -> U12(isNat(activate(V2))) 309.27/291.70 U12(tt) -> tt 309.27/291.70 U21(tt) -> tt 309.27/291.70 U31(tt, V2) -> U32(isNat(activate(V2))) 309.27/291.70 U32(tt) -> tt 309.27/291.70 U41(tt, N) -> activate(N) 309.27/291.70 U51(tt, M, N) -> U52(isNat(activate(N)), activate(M), activate(N)) 309.27/291.70 U52(tt, M, N) -> s(plus(activate(N), activate(M))) 309.27/291.70 U61(tt) -> 0 309.27/291.70 U71(tt, M, N) -> U72(isNat(activate(N)), activate(M), activate(N)) 309.27/291.70 U72(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 309.27/291.70 isNat(n__0) -> tt 309.27/291.70 isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 309.27/291.70 isNat(n__s(V1)) -> U21(isNat(activate(V1))) 309.27/291.70 isNat(n__x(V1, V2)) -> U31(isNat(activate(V1)), activate(V2)) 309.27/291.70 plus(N, 0) -> U41(isNat(N), N) 309.27/291.70 plus(N, s(M)) -> U51(isNat(M), M, N) 309.27/291.70 x(N, 0) -> U61(isNat(N)) 309.27/291.70 x(N, s(M)) -> U71(isNat(M), M, N) 309.27/291.70 0 -> n__0 309.27/291.70 plus(X1, X2) -> n__plus(X1, X2) 309.27/291.70 s(X) -> n__s(X) 309.27/291.70 x(X1, X2) -> n__x(X1, X2) 309.27/291.70 activate(n__0) -> 0 309.27/291.70 activate(n__plus(X1, X2)) -> plus(X1, X2) 309.27/291.70 activate(n__s(X)) -> s(X) 309.27/291.70 activate(n__x(X1, X2)) -> x(X1, X2) 309.27/291.70 activate(X) -> X 309.27/291.70 309.27/291.70 S is empty. 309.27/291.70 Rewrite Strategy: FULL 309.27/291.70 ---------------------------------------- 309.27/291.70 309.27/291.70 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 309.27/291.70 Renamed function symbols to avoid clashes with predefined symbol. 309.27/291.70 ---------------------------------------- 309.27/291.70 309.27/291.70 (2) 309.27/291.70 Obligation: 309.27/291.70 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 309.27/291.70 309.27/291.70 309.27/291.70 The TRS R consists of the following rules: 309.27/291.70 309.27/291.70 U11(tt, V2) -> U12(isNat(activate(V2))) 309.27/291.70 U12(tt) -> tt 309.27/291.70 U21(tt) -> tt 309.27/291.70 U31(tt, V2) -> U32(isNat(activate(V2))) 309.27/291.70 U32(tt) -> tt 309.27/291.70 U41(tt, N) -> activate(N) 309.27/291.70 U51(tt, M, N) -> U52(isNat(activate(N)), activate(M), activate(N)) 309.27/291.70 U52(tt, M, N) -> s(plus(activate(N), activate(M))) 309.27/291.70 U61(tt) -> 0' 309.27/291.70 U71(tt, M, N) -> U72(isNat(activate(N)), activate(M), activate(N)) 309.27/291.70 U72(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 309.27/291.70 isNat(n__0) -> tt 309.27/291.70 isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 309.27/291.70 isNat(n__s(V1)) -> U21(isNat(activate(V1))) 309.27/291.70 isNat(n__x(V1, V2)) -> U31(isNat(activate(V1)), activate(V2)) 309.27/291.70 plus(N, 0') -> U41(isNat(N), N) 309.27/291.70 plus(N, s(M)) -> U51(isNat(M), M, N) 309.27/291.70 x(N, 0') -> U61(isNat(N)) 309.27/291.70 x(N, s(M)) -> U71(isNat(M), M, N) 309.27/291.70 0' -> n__0 309.27/291.70 plus(X1, X2) -> n__plus(X1, X2) 309.27/291.70 s(X) -> n__s(X) 309.27/291.70 x(X1, X2) -> n__x(X1, X2) 309.27/291.70 activate(n__0) -> 0' 309.27/291.70 activate(n__plus(X1, X2)) -> plus(X1, X2)
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