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Runti Compl Full Rewri 10127 pair #381902952
details
property
value
status
complete
benchmark
PEANO_complete-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.475300074 seconds
cpu usage
319.996786091
max memory
5.62665472E9
stage attributes
key
value
output-size
8749
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 94 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(isNatKind(activate(V1)), activate(V1), activate(V2)) U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) U15(tt, V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) U22(tt, V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt, V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt, N) -> U52(isNatKind(activate(N)), activate(N)) U52(tt, N) -> activate(N) U61(tt, M, N) -> U62(isNatKind(activate(M)), activate(M), activate(N)) U62(tt, M, N) -> U63(isNat(activate(N)), activate(M), activate(N)) U63(tt, M, N) -> U64(isNatKind(activate(N)), activate(M), activate(N)) U64(tt, M, N) -> s(plus(activate(N), activate(M))) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N, 0) -> U51(isNat(N), N) plus(N, s(M)) -> U61(isNat(M), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(X1, X2) activate(n__s(X)) -> s(X) 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(isNatKind(activate(V1)), activate(V1), activate(V2)) U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) U15(tt, V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) U22(tt, V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt, V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt, N) -> U52(isNatKind(activate(N)), activate(N)) U52(tt, N) -> activate(N) U61(tt, M, N) -> U62(isNatKind(activate(M)), activate(M), activate(N)) U62(tt, M, N) -> U63(isNat(activate(N)), activate(M), activate(N))
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