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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307974
details
property
value
status
complete
benchmark
MYNAT_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.12686 seconds
cpu usage
13.0887
user time
11.8759
system time
1.21285
max virtual memory
1.8277336E7
max residence set size
3746416.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
12.86/4.08 WORST_CASE(NON_POLY, ?) 12.86/4.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.86/4.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.86/4.08 12.86/4.08 12.86/4.08 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 12.86/4.08 12.86/4.08 (0) CpxTRS 12.86/4.08 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 12.86/4.08 (2) TRS for Loop Detection 12.86/4.08 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 12.86/4.08 (4) BEST 12.86/4.08 (5) proven lower bound 12.86/4.08 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 12.86/4.08 (7) BOUNDS(n^1, INF) 12.86/4.08 (8) TRS for Loop Detection 12.86/4.08 (9) DecreasingLoopProof [FINISHED, 1847 ms] 12.86/4.08 (10) BOUNDS(EXP, INF) 12.86/4.08 12.86/4.08 12.86/4.08 ---------------------------------------- 12.86/4.08 12.86/4.08 (0) 12.86/4.08 Obligation: 12.86/4.08 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 12.86/4.08 12.86/4.08 12.86/4.08 The TRS R consists of the following rules: 12.86/4.08 12.86/4.08 a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) 12.86/4.08 a__U12(tt, V2) -> a__U13(a__isNat(V2)) 12.86/4.08 a__U13(tt) -> tt 12.86/4.08 a__U21(tt, V1) -> a__U22(a__isNat(V1)) 12.86/4.08 a__U22(tt) -> tt 12.86/4.08 a__U31(tt, V1, V2) -> a__U32(a__isNat(V1), V2) 12.86/4.08 a__U32(tt, V2) -> a__U33(a__isNat(V2)) 12.86/4.08 a__U33(tt) -> tt 12.86/4.08 a__U41(tt, N) -> mark(N) 12.86/4.08 a__U51(tt, M, N) -> s(a__plus(mark(N), mark(M))) 12.86/4.08 a__U61(tt) -> 0 12.86/4.08 a__U71(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 12.86/4.08 a__and(tt, X) -> mark(X) 12.86/4.08 a__isNat(0) -> tt 12.86/4.08 a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) 12.86/4.08 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 12.86/4.08 a__isNat(x(V1, V2)) -> a__U31(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) 12.86/4.08 a__isNatKind(0) -> tt 12.86/4.08 a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) 12.86/4.08 a__isNatKind(s(V1)) -> a__isNatKind(V1) 12.86/4.08 a__isNatKind(x(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) 12.86/4.08 a__plus(N, 0) -> a__U41(a__and(a__isNat(N), isNatKind(N)), N) 12.86/4.08 a__plus(N, s(M)) -> a__U51(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) 12.86/4.08 a__x(N, 0) -> a__U61(a__and(a__isNat(N), isNatKind(N))) 12.86/4.08 a__x(N, s(M)) -> a__U71(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) 12.86/4.08 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 12.86/4.08 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 12.86/4.08 mark(isNat(X)) -> a__isNat(X) 12.86/4.08 mark(U13(X)) -> a__U13(mark(X)) 12.86/4.08 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 12.86/4.08 mark(U22(X)) -> a__U22(mark(X)) 12.86/4.08 mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3) 12.86/4.08 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 12.86/4.08 mark(U33(X)) -> a__U33(mark(X)) 12.86/4.08 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 12.86/4.08 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 12.86/4.08 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 12.86/4.08 mark(U61(X)) -> a__U61(mark(X)) 12.86/4.08 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 12.86/4.08 mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 12.86/4.08 mark(and(X1, X2)) -> a__and(mark(X1), X2) 12.86/4.08 mark(isNatKind(X)) -> a__isNatKind(X) 12.86/4.08 mark(tt) -> tt 12.86/4.08 mark(s(X)) -> s(mark(X)) 12.86/4.08 mark(0) -> 0 12.86/4.08 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 12.86/4.08 a__U12(X1, X2) -> U12(X1, X2) 12.86/4.08 a__isNat(X) -> isNat(X) 12.86/4.08 a__U13(X) -> U13(X) 12.86/4.08 a__U21(X1, X2) -> U21(X1, X2) 12.86/4.08 a__U22(X) -> U22(X) 12.86/4.08 a__U31(X1, X2, X3) -> U31(X1, X2, X3) 12.86/4.08 a__U32(X1, X2) -> U32(X1, X2) 12.86/4.08 a__U33(X) -> U33(X) 12.86/4.08 a__U41(X1, X2) -> U41(X1, X2) 12.86/4.08 a__U51(X1, X2, X3) -> U51(X1, X2, X3) 12.86/4.08 a__plus(X1, X2) -> plus(X1, X2) 12.86/4.08 a__U61(X) -> U61(X) 12.86/4.08 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 12.86/4.08 a__x(X1, X2) -> x(X1, X2) 12.86/4.08 a__and(X1, X2) -> and(X1, X2) 12.86/4.08 a__isNatKind(X) -> isNatKind(X) 12.86/4.08 12.86/4.08 S is empty. 12.86/4.08 Rewrite Strategy: FULL 12.86/4.08 ---------------------------------------- 12.86/4.08 12.86/4.08 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 12.86/4.08 Transformed a relative TRS into a decreasing-loop problem. 12.86/4.08 ---------------------------------------- 12.86/4.08
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return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11