details

property	value
status	complete
benchmark	MYNAT_complete_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.562 seconds
cpu usage	320.803
user time	318.262
system time	2.54064
max virtual memory	1.8279408E7
max residence set size	6120152.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 128 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: U11(tt, V1, V2) -> U12(isNat(activate(V1)), activate(V2)) U12(tt, V2) -> U13(isNat(activate(V2))) U13(tt) -> tt U21(tt, V1) -> U22(isNat(activate(V1))) U22(tt) -> tt U31(tt, V1, V2) -> U32(isNat(activate(V1)), activate(V2)) U32(tt, V2) -> U33(isNat(activate(V2))) U33(tt) -> tt U41(tt, N) -> activate(N) U51(tt, M, N) -> s(plus(activate(N), activate(M))) U61(tt) -> 0 U71(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNat(n__x(V1, V2)) -> U31(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2)) isNatKind(n__0) -> tt isNatKind(n__plus(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatKind(n__x(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatKind(activate(V2))) plus(N, 0) -> U41(and(isNat(N), n__isNatKind(N)), N) plus(N, s(M)) -> U51(and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N))), M, N) x(N, 0) -> U61(and(isNat(N), n__isNatKind(N))) x(N, s(M)) -> U71(and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N))), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) x(X1, X2) -> n__x(X1, X2) and(X1, X2) -> n__and(X1, X2) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(X1, X2) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(X) activate(n__x(X1, X2)) -> x(X1, X2) activate(n__and(X1, X2)) -> and(X1, X2) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: U11(tt, V1, V2) -> U12(isNat(activate(V1)), activate(V2)) U12(tt, V2) -> U13(isNat(activate(V2))) U13(tt) -> tt U21(tt, V1) -> U22(isNat(activate(V1))) U22(tt) -> tt U31(tt, V1, V2) -> U32(isNat(activate(V1)), activate(V2)) U32(tt, V2) -> U33(isNat(activate(V2))) U33(tt) -> tt U41(tt, N) -> activate(N) U51(tt, M, N) -> s(plus(activate(N), activate(M))) U61(tt) -> 0 U71(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNat(n__x(V1, V2)) -> U31(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2)) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS