Runtime Complexity: TRS pair #487111556

details

property	value
status	complete
benchmark	2.07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.45256 seconds
cpu usage	21.3042
user time	20.1972
system time	1.10701
max virtual memory	1.9143536E7
max residence set size	2976912.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).

(0) CpxTRS
(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTRS
    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 939 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 160 ms]
    (24) CpxRNTS
    (25) FinalProof [FINISHED, 0 ms]
    (26) BOUNDS(1, n^1)
(27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(28) TRS for Loop Detection
    (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (30) BEST
        (31) proven lower bound
            (32) LowerBoundPropagationProof [FINISHED, 0 ms]
            (33) BOUNDS(n^1, INF)
        (34) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   f(0, y) -> y
   f(x, 0) -> x
   f(i(x), y) -> i(x)
   f(f(x, y), z) -> f(x, f(y, z))
   f(g(x, y), z) -> g(f(x, z), f(y, z))
   f(1, g(x, y)) -> x
   f(2, g(x, y)) -> y

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

(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
The TRS does not nest defined symbols.
Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
f(f(x, y), z) -> f(x, f(y, z))

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

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


The TRS R consists of the following rules:

   f(0, y) -> y
   f(x, 0) -> x
   f(i(x), y) -> i(x)
   f(g(x, y), z) -> g(f(x, z), f(y, z))
   f(1, g(x, y)) -> x
   f(2, g(x, y)) -> y

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

(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

As the TRS does not nest defined symbols, we have rc = irc.
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Runtime Complexity: TRS