Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308357

details

property	value
status	complete
benchmark	PEANO_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n169.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.18884 seconds
cpu usage	28.4288
user time	26.931
system time	1.49779
max virtual memory	1.9502132E7
max residence set size	4040308.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

27.96/8.12	WORST_CASE(Omega(n^1), O(n^1))
28.34/8.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
28.34/8.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
28.34/8.13	
28.34/8.13	
28.34/8.13	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
28.34/8.13	
28.34/8.13	(0) CpxTRS
28.34/8.13	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 8 ms]
28.34/8.13	(2) CpxTRS
28.34/8.13	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
28.34/8.13	    (4) CpxTRS
28.34/8.13	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 339 ms]
28.34/8.13	    (6) BOUNDS(1, n^1)
28.34/8.13	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
28.34/8.13	(8) TRS for Loop Detection
28.34/8.13	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
28.34/8.13	    (10) BEST
28.34/8.13	        (11) proven lower bound
28.34/8.13	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
28.34/8.13	            (13) BOUNDS(n^1, INF)
28.34/8.13	        (14) TRS for Loop Detection
28.34/8.13	
28.34/8.13	
28.34/8.13	----------------------------------------
28.34/8.13	
28.34/8.13	(0)
28.34/8.13	Obligation:
28.34/8.13	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
28.34/8.13	
28.34/8.13	
28.34/8.13	The TRS R consists of the following rules:
28.34/8.13	
28.34/8.13	   active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
28.34/8.13	   active(U12(tt, V2)) -> mark(U13(isNat(V2)))
28.34/8.13	   active(U13(tt)) -> mark(tt)
28.34/8.13	   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
28.34/8.13	   active(U22(tt)) -> mark(tt)
28.34/8.13	   active(U31(tt, N)) -> mark(N)
28.34/8.13	   active(U41(tt, M, N)) -> mark(s(plus(N, M)))
28.34/8.13	   active(and(tt, X)) -> mark(X)
28.34/8.13	   active(isNat(0)) -> mark(tt)
28.34/8.13	   active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
28.34/8.13	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
28.34/8.13	   active(isNatKind(0)) -> mark(tt)
28.34/8.13	   active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
28.34/8.13	   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
28.34/8.13	   active(plus(N, 0)) -> mark(U31(and(isNat(N), isNatKind(N)), N))
28.34/8.13	   active(plus(N, s(M))) -> mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
28.34/8.13	   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
28.34/8.13	   active(U12(X1, X2)) -> U12(active(X1), X2)
28.34/8.13	   active(U13(X)) -> U13(active(X))
28.34/8.13	   active(U21(X1, X2)) -> U21(active(X1), X2)
28.34/8.13	   active(U22(X)) -> U22(active(X))
28.34/8.13	   active(U31(X1, X2)) -> U31(active(X1), X2)
28.34/8.13	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
28.34/8.13	   active(s(X)) -> s(active(X))
28.34/8.13	   active(plus(X1, X2)) -> plus(active(X1), X2)
28.34/8.13	   active(plus(X1, X2)) -> plus(X1, active(X2))
28.34/8.13	   active(and(X1, X2)) -> and(active(X1), X2)
28.34/8.13	   U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
28.34/8.13	   U12(mark(X1), X2) -> mark(U12(X1, X2))
28.34/8.13	   U13(mark(X)) -> mark(U13(X))
28.34/8.13	   U21(mark(X1), X2) -> mark(U21(X1, X2))
28.34/8.13	   U22(mark(X)) -> mark(U22(X))
28.34/8.13	   U31(mark(X1), X2) -> mark(U31(X1, X2))
28.34/8.13	   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
28.34/8.13	   s(mark(X)) -> mark(s(X))
28.34/8.13	   plus(mark(X1), X2) -> mark(plus(X1, X2))
28.34/8.13	   plus(X1, mark(X2)) -> mark(plus(X1, X2))
28.34/8.13	   and(mark(X1), X2) -> mark(and(X1, X2))
28.34/8.13	   proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
28.34/8.13	   proper(tt) -> ok(tt)
28.34/8.13	   proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
28.34/8.13	   proper(isNat(X)) -> isNat(proper(X))
28.34/8.13	   proper(U13(X)) -> U13(proper(X))
28.34/8.13	   proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
28.34/8.13	   proper(U22(X)) -> U22(proper(X))
28.34/8.13	   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
28.34/8.13	   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
28.34/8.13	   proper(s(X)) -> s(proper(X))
28.34/8.13	   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
28.34/8.13	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
28.34/8.13	   proper(0) -> ok(0)
28.34/8.13	   proper(isNatKind(X)) -> isNatKind(proper(X))
28.34/8.13	   U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
28.34/8.13	   U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
28.34/8.13	   isNat(ok(X)) -> ok(isNat(X))
28.34/8.13	   U13(ok(X)) -> ok(U13(X))
28.34/8.13	   U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
28.34/8.13	   U22(ok(X)) -> ok(U22(X))
28.34/8.13	   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
28.34/8.13	   U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
28.34/8.13	   s(ok(X)) -> ok(s(X))
28.34/8.13	   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
28.34/8.13	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
28.34/8.13	   isNatKind(ok(X)) -> ok(isNatKind(X))
28.34/8.13	   top(mark(X)) -> top(proper(X))
28.34/8.13	   top(ok(X)) -> top(active(X))
28.34/8.13

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11