Derivational Complexity: TRS Innermost pair #487108672

details

property	value
status	complete
benchmark	Ex6_15_AEL02_C.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	rcdcRelativeAlsoLower
runtime (wallclock)	292.385 seconds
cpu usage	1147.1
user time	1134.49
system time	12.6122
max virtual memory	1.9116264E7
max residence set size	1.502686E7

stage attributes

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

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 798 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) typed CpxTrs
(9) OrderProof [LOWER BOUND(ID), 9 ms]
(10) typed CpxTrs
(11) RewriteLemmaProof [LOWER BOUND(ID), 469 ms]
(12) BEST
    (13) proven lower bound
        (14) LowerBoundPropagationProof [FINISHED, 0 ms]
        (15) BOUNDS(n^1, INF)
    (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 151 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 188 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 122 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 132 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 185 ms]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 180 ms]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 178 ms]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 116 ms]
        (32) typed CpxTrs
        (33) RewriteLemmaProof [LOWER BOUND(ID), 129 ms]
        (34) typed CpxTrs
        (35) RewriteLemmaProof [LOWER BOUND(ID), 184 ms]
        (36) typed CpxTrs
        (37) RewriteLemmaProof [LOWER BOUND(ID), 89 ms]
        (38) typed CpxTrs


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

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


The TRS R consists of the following rules:

   active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
   active(sel(0, cons(X, Z))) -> mark(X)
   active(first(0, Z)) -> mark(nil)
   active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
   active(from(X)) -> mark(cons(X, from(s(X))))
   active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
   active(sel1(0, cons(X, Z))) -> mark(quote(X))
   active(first1(0, Z)) -> mark(nil1)
   active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
   active(quote(0)) -> mark(01)
   active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
   active(quote1(nil)) -> mark(nil1)
   active(quote(s(X))) -> mark(s1(quote(X)))
   active(quote(sel(X, Z))) -> mark(sel1(X, Z))
   active(quote1(first(X, Z))) -> mark(first1(X, Z))
   active(unquote(01)) -> mark(0)
   active(unquote(s1(X))) -> mark(s(unquote(X)))
   active(unquote1(nil1)) -> mark(nil)
   active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
   active(fcons(X, Z)) -> mark(cons(X, Z))
   active(sel(X1, X2)) -> sel(active(X1), X2)
   active(sel(X1, X2)) -> sel(X1, active(X2))
   active(s(X)) -> s(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(first(X1, X2)) -> first(active(X1), X2)
   active(first(X1, X2)) -> first(X1, active(X2))
   active(from(X)) -> from(active(X))
   active(sel1(X1, X2)) -> sel1(active(X1), X2)
   active(sel1(X1, X2)) -> sel1(X1, active(X2))
   active(first1(X1, X2)) -> first1(active(X1), X2)
   active(first1(X1, X2)) -> first1(X1, active(X2))
   active(cons1(X1, X2)) -> cons1(active(X1), X2)
   active(cons1(X1, X2)) -> cons1(X1, active(X2))
   active(s1(X)) -> s1(active(X))
   active(unquote(X)) -> unquote(active(X))
   active(unquote1(X)) -> unquote1(active(X))
   active(fcons(X1, X2)) -> fcons(active(X1), X2)
   active(fcons(X1, X2)) -> fcons(X1, active(X2))
   sel(mark(X1), X2) -> mark(sel(X1, X2))
   sel(X1, mark(X2)) -> mark(sel(X1, X2))
   s(mark(X)) -> mark(s(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   first(mark(X1), X2) -> mark(first(X1, X2))

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