Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308376

details

property	value
status	complete
benchmark	MYNAT_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n111.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.0028 seconds
cpu usage	36.4475
user time	34.4722
system time	1.97536
max virtual memory	1.961E7
max residence set size	4184164.0

stage attributes

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

output

36.12/10.89	WORST_CASE(Omega(n^1), O(n^1))
36.12/10.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
36.12/10.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
36.12/10.91	
36.12/10.91	
36.12/10.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
36.12/10.91	
36.12/10.91	(0) CpxTRS
36.12/10.91	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
36.12/10.91	(2) CpxTRS
36.12/10.91	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
36.12/10.91	    (4) CpxTRS
36.12/10.91	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 525 ms]
36.12/10.91	    (6) BOUNDS(1, n^1)
36.12/10.91	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
36.12/10.91	(8) CpxTRS
36.12/10.91	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
36.12/10.91	    (10) typed CpxTrs
36.12/10.91	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
36.12/10.91	    (12) typed CpxTrs
36.12/10.91	    (13) RewriteLemmaProof [LOWER BOUND(ID), 463 ms]
36.12/10.91	    (14) BEST
36.12/10.91	        (15) proven lower bound
36.12/10.91	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
36.12/10.91	            (17) BOUNDS(n^1, INF)
36.12/10.91	        (18) typed CpxTrs
36.12/10.91	            (19) RewriteLemmaProof [LOWER BOUND(ID), 115 ms]
36.12/10.91	            (20) typed CpxTrs
36.12/10.91	            (21) RewriteLemmaProof [LOWER BOUND(ID), 76 ms]
36.12/10.91	            (22) typed CpxTrs
36.12/10.91	            (23) RewriteLemmaProof [LOWER BOUND(ID), 102 ms]
36.12/10.91	            (24) typed CpxTrs
36.12/10.91	            (25) RewriteLemmaProof [LOWER BOUND(ID), 104 ms]
36.12/10.91	            (26) typed CpxTrs
36.12/10.91	            (27) RewriteLemmaProof [LOWER BOUND(ID), 94 ms]
36.12/10.91	            (28) typed CpxTrs
36.12/10.91	            (29) RewriteLemmaProof [LOWER BOUND(ID), 123 ms]
36.12/10.91	            (30) typed CpxTrs
36.12/10.91	            (31) RewriteLemmaProof [LOWER BOUND(ID), 126 ms]
36.12/10.91	            (32) typed CpxTrs
36.12/10.91	            (33) RewriteLemmaProof [LOWER BOUND(ID), 179 ms]
36.12/10.91	            (34) typed CpxTrs
36.12/10.91	            (35) RewriteLemmaProof [LOWER BOUND(ID), 113 ms]
36.12/10.91	            (36) typed CpxTrs
36.12/10.91	            (37) RewriteLemmaProof [LOWER BOUND(ID), 174 ms]
36.12/10.91	            (38) typed CpxTrs
36.12/10.91	            (39) RewriteLemmaProof [LOWER BOUND(ID), 157 ms]
36.12/10.91	            (40) typed CpxTrs
36.12/10.91	            (41) RewriteLemmaProof [LOWER BOUND(ID), 141 ms]
36.12/10.91	            (42) typed CpxTrs
36.12/10.91	            (43) RewriteLemmaProof [LOWER BOUND(ID), 144 ms]
36.12/10.91	            (44) typed CpxTrs
36.12/10.91	            (45) RewriteLemmaProof [LOWER BOUND(ID), 96 ms]
36.12/10.91	            (46) typed CpxTrs
36.12/10.91	            (47) RewriteLemmaProof [LOWER BOUND(ID), 143 ms]
36.12/10.91	            (48) typed CpxTrs
36.12/10.91	
36.12/10.91	
36.12/10.91	----------------------------------------
36.12/10.91	
36.12/10.91	(0)
36.12/10.91	Obligation:
36.12/10.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
36.12/10.91	
36.12/10.91	
36.12/10.91	The TRS R consists of the following rules:
36.12/10.91	
36.12/10.91	   active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
36.12/10.91	   active(U12(tt, V2)) -> mark(U13(isNat(V2)))
36.12/10.91	   active(U13(tt)) -> mark(tt)
36.12/10.91	   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
36.12/10.91	   active(U22(tt)) -> mark(tt)
36.12/10.91	   active(U31(tt, V1, V2)) -> mark(U32(isNat(V1), V2))
36.12/10.91	   active(U32(tt, V2)) -> mark(U33(isNat(V2)))
36.12/10.91	   active(U33(tt)) -> mark(tt)
36.12/10.91	   active(U41(tt, N)) -> mark(N)
36.12/10.91	   active(U51(tt, M, N)) -> mark(s(plus(N, M)))
36.12/10.91	   active(U61(tt)) -> mark(0)
36.12/10.91	   active(U71(tt, M, N)) -> mark(plus(x(N, M), N))
36.12/10.91	   active(and(tt, X)) -> mark(X)
36.12/10.91	   active(isNat(0)) -> mark(tt)
36.12/10.91	   active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
36.12/10.91	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
36.12/10.91	   active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2))
36.12/10.91	   active(isNatKind(0)) -> mark(tt)
36.12/10.91	   active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
36.12/10.91	   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
36.12/10.91	   active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
36.12/10.91	   active(plus(N, 0)) -> mark(U41(and(isNat(N), isNatKind(N)), N))
36.12/10.91	   active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
36.12/10.91	   active(x(N, 0)) -> mark(U61(and(isNat(N), isNatKind(N))))
36.12/10.91	   active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
36.12/10.91	   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
36.12/10.91	   active(U12(X1, X2)) -> U12(active(X1), X2)
36.12/10.91	   active(U13(X)) -> U13(active(X))
36.12/10.91	   active(U21(X1, X2)) -> U21(active(X1), X2)
36.12/10.91	   active(U22(X)) -> U22(active(X))
36.12/10.91	   active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3)
36.12/10.91	   active(U32(X1, X2)) -> U32(active(X1), X2)
36.12/10.91	   active(U33(X)) -> U33(active(X))

popout

output may be truncated. 'popout' for the full output.

job log

popout

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