Runtime Complexity: TRS pair #487110182

details

property	value
status	complete
benchmark	ExAppendixB_AEL03_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.6281 seconds
cpu usage	36.5203
user time	34.4111
system time	2.10917
max virtual memory	1.928164E7
max residence set size	4158132.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
    (4) CpxTRS
    (5) CpxTrsMatchBoundsTAProof [FINISHED, 291 ms]
    (6) BOUNDS(1, n^1)
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 438 ms]
    (14) BEST
        (15) proven lower bound
            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
            (17) BOUNDS(n^1, INF)
        (18) typed CpxTrs
            (19) RewriteLemmaProof [LOWER BOUND(ID), 111 ms]
            (20) typed CpxTrs
            (21) RewriteLemmaProof [LOWER BOUND(ID), 100 ms]
            (22) typed CpxTrs
            (23) RewriteLemmaProof [LOWER BOUND(ID), 70 ms]
            (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 95 ms]
            (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 84 ms]
            (28) typed CpxTrs
            (29) RewriteLemmaProof [LOWER BOUND(ID), 98 ms]
            (30) typed CpxTrs
            (31) RewriteLemmaProof [LOWER BOUND(ID), 100 ms]
            (32) typed CpxTrs
            (33) RewriteLemmaProof [LOWER BOUND(ID), 108 ms]
            (34) typed CpxTrs
            (35) RewriteLemmaProof [LOWER BOUND(ID), 142 ms]
            (36) typed CpxTrs
            (37) RewriteLemmaProof [LOWER BOUND(ID), 120 ms]
            (38) typed CpxTrs
            (39) RewriteLemmaProof [LOWER BOUND(ID), 97 ms]
            (40) typed CpxTrs
            (41) RewriteLemmaProof [LOWER BOUND(ID), 132 ms]
            (42) typed CpxTrs


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

(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:

   active(from(X)) -> mark(cons(X, from(s(X))))
   active(2ndspos(0, Z)) -> mark(rnil)
   active(2ndspos(s(N), cons(X, Z))) -> mark(2ndspos(s(N), cons2(X, Z)))
   active(2ndspos(s(N), cons2(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
   active(2ndsneg(0, Z)) -> mark(rnil)
   active(2ndsneg(s(N), cons(X, Z))) -> mark(2ndsneg(s(N), cons2(X, Z)))
   active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z)))
   active(pi(X)) -> mark(2ndspos(X, from(0)))
   active(plus(0, Y)) -> mark(Y)
   active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
   active(times(0, Y)) -> mark(0)
   active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
   active(square(X)) -> mark(times(X, X))
   active(s(X)) -> s(active(X))
   active(posrecip(X)) -> posrecip(active(X))
   active(negrecip(X)) -> negrecip(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(cons2(X1, X2)) -> cons2(X1, active(X2))
   active(rcons(X1, X2)) -> rcons(active(X1), X2)
   active(rcons(X1, X2)) -> rcons(X1, active(X2))
   active(from(X)) -> from(active(X))
   active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
   active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
   active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
   active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
   active(pi(X)) -> pi(active(X))
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(times(X1, X2)) -> times(active(X1), X2)
   active(times(X1, X2)) -> times(X1, active(X2))
   active(square(X)) -> square(active(X))
   s(mark(X)) -> mark(s(X))
   posrecip(mark(X)) -> mark(posrecip(X))
   negrecip(mark(X)) -> mark(negrecip(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   cons2(X1, mark(X2)) -> mark(cons2(X1, X2))
   rcons(mark(X1), X2) -> mark(rcons(X1, X2))
   rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
   from(mark(X)) -> mark(from(X))

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