Derivational Complexity: TRS Innermost pair #487107420

details

property	value
status	complete
benchmark	z065.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	Zantema_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	299.998 seconds
cpu usage	1095.22
user time	1081.85
system time	13.3684
max virtual memory	1.8883564E7
max residence set size	1.5059052E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 41 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms]
(8) typed CpxTrs
(9) OrderProof [LOWER BOUND(ID), 0 ms]
(10) typed CpxTrs
(11) RewriteLemmaProof [LOWER BOUND(ID), 1258 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), 452 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 535 ms]
        (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 69 ms]
        (22) BOUNDS(1, INF)


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(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:

   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
   #(*(x1)) -> *(x1)

S is empty.
Rewrite Strategy: INNERMOST
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(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(*(x_1)) -> *(encArg(x_1))
   encArg($(x_1)) -> $(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_#(x_1)) -> #(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_*(x_1) -> *(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_#(x_1) -> #(encArg(x_1))
   encode_$(x_1) -> $(encArg(x_1))


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

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


The TRS R consists of the following rules:

   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
   #(*(x1)) -> *(x1)

The (relative) TRS S consists of the following rules:

   encArg(*(x_1)) -> *(encArg(x_1))
   encArg($(x_1)) -> $(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_#(x_1)) -> #(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_*(x_1) -> *(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_#(x_1) -> #(encArg(x_1))
   encode_$(x_1) -> $(encArg(x_1))

Rewrite Strategy: INNERMOST
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