Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313794

details

property	value
status	complete
benchmark	mul_better.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n017.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.52671 seconds
cpu usage	21.1986
user time	19.6299
system time	1.56874
max virtual memory	1.9143484E7
max residence set size	3855964.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

output

20.92/7.46	WORST_CASE(Omega(n^3), O(n^3))
20.92/7.48	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
20.92/7.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.92/7.48	
20.92/7.48	
20.92/7.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).
20.92/7.48	
20.92/7.48	(0) CpxTRS
20.92/7.48	(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
20.92/7.48	(2) CdtProblem
20.92/7.48	    (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
20.92/7.48	    (4) CdtProblem
20.92/7.48	    (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
20.92/7.48	    (6) CdtProblem
20.92/7.48	    (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 39 ms]
20.92/7.48	    (8) CdtProblem
20.92/7.48	    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 150 ms]
20.92/7.48	    (10) CdtProblem
20.92/7.48	    (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
20.92/7.48	    (12) BOUNDS(1, 1)
20.92/7.48	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.92/7.48	(14) CpxTRS
20.92/7.48	    (15) SlicingProof [LOWER BOUND(ID), 0 ms]
20.92/7.48	    (16) CpxTRS
20.92/7.48	    (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.92/7.48	    (18) typed CpxTrs
20.92/7.48	    (19) OrderProof [LOWER BOUND(ID), 0 ms]
20.92/7.48	    (20) typed CpxTrs
20.92/7.48	    (21) RewriteLemmaProof [LOWER BOUND(ID), 290 ms]
20.92/7.48	    (22) BEST
20.92/7.48	        (23) proven lower bound
20.92/7.48	            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
20.92/7.48	            (25) BOUNDS(n^1, INF)
20.92/7.48	        (26) typed CpxTrs
20.92/7.48	            (27) RewriteLemmaProof [LOWER BOUND(ID), 64 ms]
20.92/7.48	            (28) proven lower bound
20.92/7.48	            (29) LowerBoundPropagationProof [FINISHED, 0 ms]
20.92/7.48	            (30) BOUNDS(n^3, INF)
20.92/7.48	
20.92/7.48	
20.92/7.48	----------------------------------------
20.92/7.48	
20.92/7.48	(0)
20.92/7.48	Obligation:
20.92/7.48	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).
20.92/7.48	
20.92/7.48	
20.92/7.48	The TRS R consists of the following rules:
20.92/7.48	
20.92/7.48	   mul0(C(x, y), y') -> add0(mul0(y, y'), y')
20.92/7.48	   mul0(Z, y) -> Z
20.92/7.48	   add0(C(x, y), y') -> add0(y, C(S, y'))
20.92/7.48	   add0(Z, y) -> y
20.92/7.48	   second(C(x, y)) -> y
20.92/7.48	   isZero(C(x, y)) -> False
20.92/7.48	   isZero(Z) -> True
20.92/7.48	   goal(xs, ys) -> mul0(xs, ys)
20.92/7.48	
20.92/7.48	S is empty.
20.92/7.48	Rewrite Strategy: INNERMOST
20.92/7.48	----------------------------------------
20.92/7.48	
20.92/7.48	(1) CpxTrsToCdtProof (UPPER BOUND(ID))
20.92/7.48	Converted Cpx (relative) TRS to CDT
20.92/7.48	----------------------------------------
20.92/7.48	
20.92/7.48	(2)
20.92/7.48	Obligation:
20.92/7.48	Complexity Dependency Tuples Problem
20.92/7.48	
20.92/7.48	Rules:
20.92/7.48	   mul0(C(z0, z1), z2) -> add0(mul0(z1, z2), z2)
20.92/7.48	   mul0(Z, z0) -> Z
20.92/7.48	   add0(C(z0, z1), z2) -> add0(z1, C(S, z2))
20.92/7.48	   add0(Z, z0) -> z0
20.92/7.48	   second(C(z0, z1)) -> z1
20.92/7.48	   isZero(C(z0, z1)) -> False
20.92/7.48	   isZero(Z) -> True
20.92/7.48	   goal(z0, z1) -> mul0(z0, z1)
20.92/7.48	Tuples:
20.92/7.48	   MUL0(C(z0, z1), z2) -> c(ADD0(mul0(z1, z2), z2), MUL0(z1, z2))
20.92/7.48	   MUL0(Z, z0) -> c1
20.92/7.48	   ADD0(C(z0, z1), z2) -> c2(ADD0(z1, C(S, z2)))
20.92/7.48	   ADD0(Z, z0) -> c3
20.92/7.48	   SECOND(C(z0, z1)) -> c4
20.92/7.48	   ISZERO(C(z0, z1)) -> c5
20.92/7.48	   ISZERO(Z) -> c6
20.92/7.48	   GOAL(z0, z1) -> c7(MUL0(z0, z1))
20.92/7.48	S tuples:
20.92/7.48	   MUL0(C(z0, z1), z2) -> c(ADD0(mul0(z1, z2), z2), MUL0(z1, z2))
20.92/7.48	   MUL0(Z, z0) -> c1
20.92/7.48	   ADD0(C(z0, z1), z2) -> c2(ADD0(z1, C(S, z2)))
20.92/7.48	   ADD0(Z, z0) -> c3
20.92/7.48	   SECOND(C(z0, z1)) -> c4
20.92/7.48	   ISZERO(C(z0, z1)) -> c5
20.92/7.48	   ISZERO(Z) -> c6
20.92/7.48	   GOAL(z0, z1) -> c7(MUL0(z0, z1))
20.92/7.48	K tuples:none
20.92/7.48	Defined Rule Symbols:   mul0_2, add0_2, second_1, isZero_1, goal_2
20.92/7.48

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40