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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307988
details
property
value
status
complete
benchmark
MYNAT_nokinds_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.1904 seconds
cpu usage
35.6314
user time
33.7308
system time
1.9006
max virtual memory
1.9407324E7
max residence set size
4151144.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
35.46/10.12 WORST_CASE(Omega(n^1), O(n^1)) 35.46/10.12 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 35.46/10.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 35.46/10.12 35.46/10.12 35.46/10.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 35.46/10.12 35.46/10.12 (0) CpxTRS 35.46/10.12 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 35.46/10.12 (2) CpxTRS 35.46/10.12 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 35.46/10.12 (4) CpxTRS 35.46/10.12 (5) CpxTrsMatchBoundsTAProof [FINISHED, 387 ms] 35.46/10.12 (6) BOUNDS(1, n^1) 35.46/10.12 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 35.46/10.12 (8) TRS for Loop Detection 35.46/10.12 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 35.46/10.12 (10) BEST 35.46/10.12 (11) proven lower bound 35.46/10.12 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 35.46/10.12 (13) BOUNDS(n^1, INF) 35.46/10.12 (14) TRS for Loop Detection 35.46/10.12 35.46/10.12 35.46/10.12 ---------------------------------------- 35.46/10.12 35.46/10.12 (0) 35.46/10.12 Obligation: 35.46/10.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 35.46/10.12 35.46/10.12 35.46/10.12 The TRS R consists of the following rules: 35.46/10.12 35.46/10.12 active(U11(tt, V2)) -> mark(U12(isNat(V2))) 35.46/10.12 active(U12(tt)) -> mark(tt) 35.46/10.12 active(U21(tt)) -> mark(tt) 35.46/10.12 active(U31(tt, V2)) -> mark(U32(isNat(V2))) 35.46/10.12 active(U32(tt)) -> mark(tt) 35.46/10.12 active(U41(tt, N)) -> mark(N) 35.46/10.12 active(U51(tt, M, N)) -> mark(U52(isNat(N), M, N)) 35.46/10.12 active(U52(tt, M, N)) -> mark(s(plus(N, M))) 35.46/10.12 active(U61(tt)) -> mark(0) 35.46/10.12 active(U71(tt, M, N)) -> mark(U72(isNat(N), M, N)) 35.46/10.12 active(U72(tt, M, N)) -> mark(plus(x(N, M), N)) 35.46/10.12 active(isNat(0)) -> mark(tt) 35.46/10.12 active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) 35.46/10.12 active(isNat(s(V1))) -> mark(U21(isNat(V1))) 35.46/10.12 active(isNat(x(V1, V2))) -> mark(U31(isNat(V1), V2)) 35.46/10.12 active(plus(N, 0)) -> mark(U41(isNat(N), N)) 35.46/10.12 active(plus(N, s(M))) -> mark(U51(isNat(M), M, N)) 35.46/10.12 active(x(N, 0)) -> mark(U61(isNat(N))) 35.46/10.12 active(x(N, s(M))) -> mark(U71(isNat(M), M, N)) 35.46/10.12 active(U11(X1, X2)) -> U11(active(X1), X2) 35.46/10.12 active(U12(X)) -> U12(active(X)) 35.46/10.12 active(U21(X)) -> U21(active(X)) 35.46/10.12 active(U31(X1, X2)) -> U31(active(X1), X2) 35.46/10.12 active(U32(X)) -> U32(active(X)) 35.46/10.12 active(U41(X1, X2)) -> U41(active(X1), X2) 35.46/10.12 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 35.46/10.12 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 35.46/10.12 active(s(X)) -> s(active(X)) 35.46/10.12 active(plus(X1, X2)) -> plus(active(X1), X2) 35.46/10.12 active(plus(X1, X2)) -> plus(X1, active(X2)) 35.46/10.12 active(U61(X)) -> U61(active(X)) 35.46/10.12 active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3) 35.46/10.12 active(U72(X1, X2, X3)) -> U72(active(X1), X2, X3) 35.46/10.12 active(x(X1, X2)) -> x(active(X1), X2) 35.46/10.12 active(x(X1, X2)) -> x(X1, active(X2)) 35.46/10.12 U11(mark(X1), X2) -> mark(U11(X1, X2)) 35.46/10.12 U12(mark(X)) -> mark(U12(X)) 35.46/10.12 U21(mark(X)) -> mark(U21(X)) 35.46/10.12 U31(mark(X1), X2) -> mark(U31(X1, X2)) 35.46/10.12 U32(mark(X)) -> mark(U32(X)) 35.46/10.12 U41(mark(X1), X2) -> mark(U41(X1, X2)) 35.46/10.12 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 35.46/10.12 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 35.46/10.12 s(mark(X)) -> mark(s(X)) 35.46/10.12 plus(mark(X1), X2) -> mark(plus(X1, X2)) 35.46/10.12 plus(X1, mark(X2)) -> mark(plus(X1, X2)) 35.46/10.12 U61(mark(X)) -> mark(U61(X)) 35.46/10.12 U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3)) 35.46/10.12 U72(mark(X1), X2, X3) -> mark(U72(X1, X2, X3)) 35.46/10.12 x(mark(X1), X2) -> mark(x(X1, X2)) 35.46/10.12 x(X1, mark(X2)) -> mark(x(X1, X2)) 35.46/10.12 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 35.46/10.12 proper(tt) -> ok(tt) 35.46/10.12 proper(U12(X)) -> U12(proper(X)) 35.46/10.12 proper(isNat(X)) -> isNat(proper(X)) 35.46/10.12 proper(U21(X)) -> U21(proper(X)) 35.46/10.12 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 35.46/10.12 proper(U32(X)) -> U32(proper(X)) 35.46/10.12 proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) 35.46/10.12 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 35.46/10.12 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 35.46/10.12 proper(s(X)) -> s(proper(X)) 35.46/10.12 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 35.46/10.12 proper(U61(X)) -> U61(proper(X)) 35.46/10.12 proper(0) -> ok(0) 35.46/10.12 proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3)) 35.46/10.12 proper(U72(X1, X2, X3)) -> U72(proper(X1), proper(X2), proper(X3))
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