Runti Compl Inner Rewri 22807 pair #381904154

details

property	value
status	complete
benchmark	22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.06777906418 seconds
cpu usage	19.205393323
max memory	4.271620096E9

stage attributes

key	value
output-size	12454
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

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^1))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^1).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 61 ms]
    (8) CdtProblem
    (9) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CdtProblem
    (13) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CdtProblem
    (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (16) CdtProblem
    (17) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CdtProblem
    (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 5 ms]
    (20) CdtProblem
    (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) BOUNDS(1, 1)
(23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) CpxTRS
    (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) typed CpxTrs
    (27) OrderProof [LOWER BOUND(ID), 0 ms]
    (28) typed CpxTrs
    (29) RewriteLemmaProof [LOWER BOUND(ID), 306 ms]
    (30) BEST
        (31) proven lower bound
            (32) LowerBoundPropagationProof [FINISHED, 0 ms]
            (33) BOUNDS(n^1, INF)
        (34) typed CpxTrs


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


The TRS R consists of the following rules:

   f(x, 0) -> s(0)
   f(s(x), s(y)) -> s(f(x, y))
   g(0, x) -> g(f(x, x), x)

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(z0, 0) -> s(0)
   f(s(z0), s(z1)) -> s(f(z0, z1))
   g(0, z0) -> g(f(z0, z0), z0)
Tuples:
   F(z0, 0) -> c
   F(s(z0), s(z1)) -> c1(F(z0, z1))
   G(0, z0) -> c2(G(f(z0, z0), z0), F(z0, z0))
S tuples:
   F(z0, 0) -> c
   F(s(z0), s(z1)) -> c1(F(z0, z1))
   G(0, z0) -> c2(G(f(z0, z0), z0), F(z0, z0))
K tuples:none
Defined Rule Symbols:   f_2, g_2

Defined Pair Symbols:   F_2, G_2

Compound Symbols:   c, c1_1, c2_2


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(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   F(z0, 0) -> c

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