Runti Compl Inner Rewri 22807 pair #381904759

details

property	value
status	complete
benchmark	#3.48.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.444670916 seconds
cpu usage	320.566327155
max memory	6.166339584E9

stage attributes

key	value
output-size	11443
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 31 ms]
    (10) CdtProblem
    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms]
    (12) CdtProblem
    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 0 ms]
    (14) CdtProblem
    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) BOUNDS(1, 1)
(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(18) TRS for Loop Detection
    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (20) BEST
        (21) proven lower bound
            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
            (23) BOUNDS(n^1, INF)
        (24) TRS for Loop Detection


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(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:

   f(0) -> true
   f(1) -> false
   f(s(x)) -> f(x)
   if(true, s(x), s(y)) -> s(x)
   if(false, s(x), s(y)) -> s(y)
   g(x, c(y)) -> c(g(x, y))
   g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y)))

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

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

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> true
   f(1) -> false
   f(s(z0)) -> f(z0)
   if(true, s(z0), s(z1)) -> s(z0)
   if(false, s(z0), s(z1)) -> s(z1)
   g(z0, c(z1)) -> c(g(z0, z1))
   g(z0, c(z1)) -> g(z0, if(f(z0), c(g(s(z0), z1)), c(z1)))
Tuples:
   F(0) -> c1
   F(1) -> c2
   F(s(z0)) -> c3(F(z0))
   IF(true, s(z0), s(z1)) -> c4
   IF(false, s(z0), s(z1)) -> c5
   G(z0, c(z1)) -> c6(G(z0, z1))
   G(z0, c(z1)) -> c7(G(z0, if(f(z0), c(g(s(z0), z1)), c(z1))), IF(f(z0), c(g(s(z0), z1)), c(z1)), F(z0), G(s(z0), z1))
S tuples:
   F(0) -> c1
   F(1) -> c2
   F(s(z0)) -> c3(F(z0))
   IF(true, s(z0), s(z1)) -> c4
   IF(false, s(z0), s(z1)) -> c5
   G(z0, c(z1)) -> c6(G(z0, z1))
   G(z0, c(z1)) -> c7(G(z0, if(f(z0), c(g(s(z0), z1)), c(z1))), IF(f(z0), c(g(s(z0), z1)), c(z1)), F(z0), G(s(z0), z1))
K tuples:none
Defined Rule Symbols:   f_1, if_3, g_2

Defined Pair Symbols:   F_1, IF_3, G_2

Compound Symbols:   c1, c2, c3_1, c4, c5, c6_1, c7_4

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