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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308073
details
property
value
status
complete
benchmark
PEANO_complete_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.34055 seconds
cpu usage
17.705
user time
16.5197
system time
1.18534
max virtual memory
1.828572E7
max residence set size
3722704.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
17.45/5.25 WORST_CASE(NON_POLY, ?) 17.45/5.27 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.45/5.27 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.45/5.27 17.45/5.27 17.45/5.27 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 17.45/5.27 17.45/5.27 (0) CpxTRS 17.45/5.27 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 17.45/5.27 (2) TRS for Loop Detection 17.45/5.27 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 17.45/5.27 (4) BEST 17.45/5.27 (5) proven lower bound 17.45/5.27 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 17.45/5.27 (7) BOUNDS(n^1, INF) 17.45/5.27 (8) TRS for Loop Detection 17.45/5.27 (9) DecreasingLoopProof [FINISHED, 2195 ms] 17.45/5.27 (10) BOUNDS(EXP, INF) 17.45/5.27 17.45/5.27 17.45/5.27 ---------------------------------------- 17.45/5.27 17.45/5.27 (0) 17.45/5.27 Obligation: 17.45/5.27 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 17.45/5.27 17.45/5.27 17.45/5.27 The TRS R consists of the following rules: 17.45/5.27 17.45/5.27 a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) 17.45/5.27 a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) 17.45/5.27 a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) 17.45/5.27 a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) 17.45/5.27 a__U15(tt, V2) -> a__U16(a__isNat(V2)) 17.45/5.27 a__U16(tt) -> tt 17.45/5.27 a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) 17.45/5.27 a__U22(tt, V1) -> a__U23(a__isNat(V1)) 17.45/5.27 a__U23(tt) -> tt 17.45/5.27 a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) 17.45/5.27 a__U32(tt) -> tt 17.45/5.27 a__U41(tt) -> tt 17.45/5.27 a__U51(tt, N) -> a__U52(a__isNatKind(N), N) 17.45/5.27 a__U52(tt, N) -> mark(N) 17.45/5.27 a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) 17.45/5.27 a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) 17.45/5.27 a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) 17.45/5.27 a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) 17.45/5.27 a__isNat(0) -> tt 17.45/5.27 a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) 17.45/5.27 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 17.45/5.27 a__isNatKind(0) -> tt 17.45/5.27 a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) 17.45/5.27 a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) 17.45/5.27 a__plus(N, 0) -> a__U51(a__isNat(N), N) 17.45/5.27 a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) 17.45/5.27 mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 17.45/5.27 mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 17.45/5.27 mark(isNatKind(X)) -> a__isNatKind(X) 17.45/5.27 mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) 17.45/5.27 mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) 17.45/5.27 mark(U15(X1, X2)) -> a__U15(mark(X1), X2) 17.45/5.27 mark(isNat(X)) -> a__isNat(X) 17.45/5.27 mark(U16(X)) -> a__U16(mark(X)) 17.45/5.27 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 17.45/5.27 mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 17.45/5.27 mark(U23(X)) -> a__U23(mark(X)) 17.45/5.27 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 17.45/5.27 mark(U32(X)) -> a__U32(mark(X)) 17.45/5.27 mark(U41(X)) -> a__U41(mark(X)) 17.45/5.27 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 17.45/5.27 mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 17.45/5.27 mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) 17.45/5.27 mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) 17.45/5.27 mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) 17.45/5.27 mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3) 17.45/5.27 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 17.45/5.27 mark(tt) -> tt 17.45/5.27 mark(s(X)) -> s(mark(X)) 17.45/5.27 mark(0) -> 0 17.45/5.27 a__U11(X1, X2, X3) -> U11(X1, X2, X3) 17.45/5.27 a__U12(X1, X2, X3) -> U12(X1, X2, X3) 17.45/5.27 a__isNatKind(X) -> isNatKind(X) 17.45/5.27 a__U13(X1, X2, X3) -> U13(X1, X2, X3) 17.45/5.27 a__U14(X1, X2, X3) -> U14(X1, X2, X3) 17.45/5.27 a__U15(X1, X2) -> U15(X1, X2) 17.45/5.27 a__isNat(X) -> isNat(X) 17.45/5.27 a__U16(X) -> U16(X) 17.45/5.27 a__U21(X1, X2) -> U21(X1, X2) 17.45/5.27 a__U22(X1, X2) -> U22(X1, X2) 17.45/5.27 a__U23(X) -> U23(X) 17.45/5.27 a__U31(X1, X2) -> U31(X1, X2) 17.45/5.27 a__U32(X) -> U32(X) 17.45/5.27 a__U41(X) -> U41(X) 17.45/5.27 a__U51(X1, X2) -> U51(X1, X2) 17.45/5.27 a__U52(X1, X2) -> U52(X1, X2) 17.45/5.27 a__U61(X1, X2, X3) -> U61(X1, X2, X3) 17.45/5.27 a__U62(X1, X2, X3) -> U62(X1, X2, X3) 17.45/5.27 a__U63(X1, X2, X3) -> U63(X1, X2, X3) 17.45/5.27 a__U64(X1, X2, X3) -> U64(X1, X2, X3) 17.45/5.27 a__plus(X1, X2) -> plus(X1, X2)
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