Runtime Complexity: TRS Innermost pair #487111900

details

property	value
status	complete
benchmark	gexgcd2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.587 seconds
cpu usage	329.433
user time	325.997
system time	3.43559
max virtual memory	1.9191672E7
max residence set size	5455748.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 256 ms]
(2) CpxRelTRS
(3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(4) CdtProblem
    (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CdtProblem
    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 75 ms]
    (14) CdtProblem
    (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CdtProblem
    (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CdtProblem
    (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 159 ms]
    (20) CdtProblem
    (21) CdtKnowledgeProof [FINISHED, 0 ms]
    (22) BOUNDS(1, 1)
(23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) CpxRelTRS
    (25) SlicingProof [LOWER BOUND(ID), 0 ms]
    (26) CpxRelTRS
    (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) typed CpxTrs
    (29) OrderProof [LOWER BOUND(ID), 0 ms]
    (30) typed CpxTrs
    (31) RewriteLemmaProof [LOWER BOUND(ID), 475 ms]
    (32) BEST
        (33) proven lower bound
            (34) LowerBoundPropagationProof [FINISHED, 0 ms]
            (35) BOUNDS(n^1, INF)
        (36) typed CpxTrs
            (37) RewriteLemmaProof [LOWER BOUND(ID), 42 ms]
            (38) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   monus(S(x'), S(x)) -> monus(x', x)
   gcd(x, y) -> gcd[Ite](equal0(x, y), x, y)
   equal0(a, b) -> equal0[Ite](<(a, b), a, b)

The (relative) TRS S consists of the following rules:

   <(S(x), S(y)) -> <(x, y)
   <(0, S(y)) -> True
   <(x, 0) -> False
   gcd[Ite](False, x, y) -> gcd[False][Ite](<(x, y), x, y)
   gcd[Ite](True, x, y) -> x
   gcd[False][Ite](False, x, y) -> gcd(y, monus(y, x))
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y)
   equal0[Ite](False, a, b) -> False
   equal0[Ite](True, a, b) -> equal0[True][Ite](<(b, a), a, b)
   equal0[True][Ite](False, a, b) -> False
   equal0[True][Ite](True, a, b) -> True

Rewrite Strategy: INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   monus(S(x'), S(x)) -> monus(x', x)
   gcd(x, y) -> gcd[Ite](equal0(x, y), x, y)
   equal0(a, b) -> equal0[Ite](<(a, b), a, b)

The (relative) TRS S consists of the following rules:

   <(S(x), S(y)) -> <(x, y)
   <(0, S(y)) -> True
   <(x, 0) -> False
   gcd[Ite](False, x, y) -> gcd[False][Ite](<(x, y), x, y)
   gcd[Ite](True, x, y) -> x

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