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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313499
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.121 seconds
cpu usage
1133.54
user time
1120.96
system time
12.5778
max virtual memory
1.8862888E7
max residence set size
1.5099764E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1122.71/292.35 WORST_CASE(Omega(n^1), ?) 1133.40/295.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1133.40/295.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1133.40/295.05 1133.40/295.05 1133.40/295.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1133.40/295.05 1133.40/295.05 (0) CpxTRS 1133.40/295.05 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1133.40/295.05 (2) TRS for Loop Detection 1133.40/295.05 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1133.40/295.05 (4) BEST 1133.40/295.05 (5) proven lower bound 1133.40/295.05 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1133.40/295.05 (7) BOUNDS(n^1, INF) 1133.40/295.05 (8) TRS for Loop Detection 1133.40/295.05 1133.40/295.05 1133.40/295.05 ---------------------------------------- 1133.40/295.05 1133.40/295.05 (0) 1133.40/295.05 Obligation: 1133.40/295.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1133.40/295.05 1133.40/295.05 1133.40/295.05 The TRS R consists of the following rules: 1133.40/295.05 1133.40/295.05 a__U11(tt, V2) -> a__U12(a__isNat(V2)) 1133.40/295.05 a__U12(tt) -> tt 1133.40/295.05 a__U21(tt) -> tt 1133.40/295.05 a__U31(tt, N) -> mark(N) 1133.40/295.05 a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) 1133.40/295.05 a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1133.40/295.05 a__isNat(0) -> tt 1133.40/295.05 a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 1133.40/295.05 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1133.40/295.05 a__plus(N, 0) -> a__U31(a__isNat(N), N) 1133.40/295.05 a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) 1133.40/295.05 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1133.40/295.05 mark(U12(X)) -> a__U12(mark(X)) 1133.40/295.05 mark(isNat(X)) -> a__isNat(X) 1133.40/295.05 mark(U21(X)) -> a__U21(mark(X)) 1133.40/295.05 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1133.40/295.05 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1133.40/295.05 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1133.40/295.05 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1133.40/295.05 mark(tt) -> tt 1133.40/295.05 mark(s(X)) -> s(mark(X)) 1133.40/295.05 mark(0) -> 0 1133.40/295.05 a__U11(X1, X2) -> U11(X1, X2) 1133.40/295.05 a__U12(X) -> U12(X) 1133.40/295.05 a__isNat(X) -> isNat(X) 1133.40/295.05 a__U21(X) -> U21(X) 1133.40/295.05 a__U31(X1, X2) -> U31(X1, X2) 1133.40/295.05 a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1133.40/295.05 a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1133.40/295.05 a__plus(X1, X2) -> plus(X1, X2) 1133.40/295.05 1133.40/295.05 S is empty. 1133.40/295.05 Rewrite Strategy: INNERMOST 1133.40/295.05 ---------------------------------------- 1133.40/295.05 1133.40/295.05 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1133.40/295.05 Transformed a relative TRS into a decreasing-loop problem. 1133.40/295.05 ---------------------------------------- 1133.40/295.05 1133.40/295.05 (2) 1133.40/295.05 Obligation: 1133.40/295.05 Analyzing the following TRS for decreasing loops: 1133.40/295.05 1133.40/295.05 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1133.40/295.05 1133.40/295.05 1133.40/295.05 The TRS R consists of the following rules: 1133.40/295.05 1133.40/295.05 a__U11(tt, V2) -> a__U12(a__isNat(V2)) 1133.40/295.05 a__U12(tt) -> tt 1133.40/295.05 a__U21(tt) -> tt 1133.40/295.05 a__U31(tt, N) -> mark(N) 1133.40/295.05 a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) 1133.40/295.05 a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) 1133.40/295.05 a__isNat(0) -> tt 1133.40/295.05 a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 1133.40/295.05 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1133.40/295.05 a__plus(N, 0) -> a__U31(a__isNat(N), N) 1133.40/295.05 a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) 1133.40/295.05 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1133.40/295.05 mark(U12(X)) -> a__U12(mark(X)) 1133.40/295.05 mark(isNat(X)) -> a__isNat(X) 1133.40/295.05 mark(U21(X)) -> a__U21(mark(X)) 1133.40/295.05 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1133.40/295.05 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1133.40/295.05 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1133.40/295.05 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1133.40/295.05 mark(tt) -> tt 1133.40/295.05 mark(s(X)) -> s(mark(X)) 1133.40/295.05 mark(0) -> 0 1133.40/295.05 a__U11(X1, X2) -> U11(X1, X2) 1133.40/295.05 a__U12(X) -> U12(X) 1133.40/295.05 a__isNat(X) -> isNat(X)
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