Runti Compl Inner Rewri 22807 pair #381904226

details

property	value
status	complete
benchmark	enno.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.703768015 seconds
cpu usage	356.137812642
max memory	5.518659584E9

stage attributes

key	value
output-size	32272
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

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


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 134 ms]
    (8) CdtProblem
    (9) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 919 ms]
    (12) CdtProblem
    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 700 ms]
    (14) CdtProblem
    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 729 ms]
    (16) CdtProblem
    (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 513 ms]
    (18) CdtProblem
    (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) BOUNDS(1, 1)
(21) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(22) TRS for Loop Detection
    (23) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (24) BEST
        (25) proven lower bound
            (26) LowerBoundPropagationProof [FINISHED, 0 ms]
            (27) BOUNDS(n^1, INF)
        (28) 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:

   lt(0, s(X)) -> true
   lt(s(X), 0) -> false
   lt(s(X), s(Y)) -> lt(X, Y)
   append(nil, Y) -> Y
   append(add(N, X), Y) -> add(N, append(X, Y))
   split(N, nil) -> pair(nil, nil)
   split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y)
   f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z)
   f_2(true, N, M, Y, X, Z) -> pair(X, add(M, Z))
   f_2(false, N, M, Y, X, Z) -> pair(add(M, X), Z)
   qsort(nil) -> nil
   qsort(add(N, X)) -> f_3(split(N, X), N, X)
   f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z)))

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

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

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   lt(0, s(z0)) -> true
   lt(s(z0), 0) -> false
   lt(s(z0), s(z1)) -> lt(z0, z1)
   append(nil, z0) -> z0
   append(add(z0, z1), z2) -> add(z0, append(z1, z2))
   split(z0, nil) -> pair(nil, nil)
   split(z0, add(z1, z2)) -> f_1(split(z0, z2), z0, z1, z2)
   f_1(pair(z0, z1), z2, z3, z4) -> f_2(lt(z2, z3), z2, z3, z4, z0, z1)
   f_2(true, z0, z1, z2, z3, z4) -> pair(z3, add(z1, z4))
   f_2(false, z0, z1, z2, z3, z4) -> pair(add(z1, z3), z4)
   qsort(nil) -> nil
   qsort(add(z0, z1)) -> f_3(split(z0, z1), z0, z1)
   f_3(pair(z0, z1), z2, z3) -> append(qsort(z0), add(z3, qsort(z1)))
Tuples:
   LT(0, s(z0)) -> c
   LT(s(z0), 0) -> c1
   LT(s(z0), s(z1)) -> c2(LT(z0, z1))
   APPEND(nil, z0) -> c3
   APPEND(add(z0, z1), z2) -> c4(APPEND(z1, z2))
   SPLIT(z0, nil) -> c5

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