Runtime Complexity: TRS pair #487110072

details

property	value
status	complete
benchmark	Ex2_Luc03b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.0461 seconds
cpu usage	27.8077
user time	26.0799
system time	1.72782
max virtual memory	1.9046564E7
max residence set size	3964044.0

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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (12) CpxRNTS
    (13) InliningProof [UPPER BOUND(ID), 99 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), 95 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 6 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 3428 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 432 ms]
    (30) CpxRNTS
    (31) FinalProof [FINISHED, 0 ms]
    (32) BOUNDS(1, n^1)
(33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(34) TRS for Loop Detection
    (35) DecreasingLoopProof [LOWER BOUND(ID), 34 ms]
    (36) BEST
        (37) proven lower bound
            (38) LowerBoundPropagationProof [FINISHED, 0 ms]
            (39) BOUNDS(n^1, INF)
        (40) 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:

   fst(0, Z) -> nil
   fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z)))
   from(X) -> cons(X, n__from(s(X)))
   add(0, X) -> X
   add(s(X), Y) -> s(n__add(activate(X), Y))
   len(nil) -> 0
   len(cons(X, Z)) -> s(n__len(activate(Z)))
   fst(X1, X2) -> n__fst(X1, X2)
   from(X) -> n__from(X)
   add(X1, X2) -> n__add(X1, X2)
   len(X) -> n__len(X)
   activate(n__fst(X1, X2)) -> fst(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__add(X1, X2)) -> add(X1, X2)
   activate(n__len(X)) -> len(X)
   activate(X) -> X

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

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

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

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


The TRS R consists of the following rules:

   fst(0, Z) -> nil
   fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z)))
   from(X) -> cons(X, n__from(s(X)))
   add(0, X) -> X
   add(s(X), Y) -> s(n__add(activate(X), Y))
   len(nil) -> 0
   len(cons(X, Z)) -> s(n__len(activate(Z)))

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