Runtime Complexity: TRS Innermost pair #487112552

details

property	value
status	complete
benchmark	sat.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	TCT_12

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.499 seconds
cpu usage	374.546
user time	370.198
system time	4.34771
max virtual memory	1.950844E7
max residence set size	6503164.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (10) CdtProblem
    (11) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CdtProblem
    (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CdtProblem
    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 77 ms]
    (16) CdtProblem
    (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 40 ms]
    (18) CdtProblem
    (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 28 ms]
    (20) CdtProblem
    (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1 ms]
    (22) CdtProblem
    (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) BOUNDS(1, 1)
(25) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(26) CpxTRS
    (27) SlicingProof [LOWER BOUND(ID), 0 ms]
    (28) CpxTRS
    (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) typed CpxTrs
    (31) OrderProof [LOWER BOUND(ID), 0 ms]
    (32) typed CpxTrs
    (33) RewriteLemmaProof [LOWER BOUND(ID), 1235 ms]
    (34) BEST
        (35) proven lower bound
            (36) LowerBoundPropagationProof [FINISHED, 0 ms]
            (37) BOUNDS(n^1, INF)
        (38) typed CpxTrs
            (39) RewriteLemmaProof [LOWER BOUND(ID), 80 ms]
            (40) typed CpxTrs
            (41) RewriteLemmaProof [LOWER BOUND(ID), 408 ms]
            (42) typed CpxTrs


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

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


The TRS R consists of the following rules:

   if(true, t, e) -> t
   if(false, t, e) -> e
   member(x, nil) -> false
   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys))
   eq(nil, nil) -> true
   eq(O(x), 0(y)) -> eq(x, y)
   eq(0(x), 1(y)) -> false
   eq(1(x), 0(y)) -> false
   eq(1(x), 1(y)) -> eq(x, y)
   negate(0(x)) -> 1(x)
   negate(1(x)) -> 0(x)
   choice(cons(x, xs)) -> x
   choice(cons(x, xs)) -> choice(xs)
   guess(nil) -> nil
   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf))
   verify(nil) -> true
   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls))
   sat(cnf) -> satck(cnf, guess(cnf))
   satck(cnf, assign) -> if(verify(assign), assign, unsat)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> if(eq(z0, z1), true, member(z0, z2))
   eq(nil, nil) -> true
   eq(O(z0), 0(z1)) -> eq(z0, z1)

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