Derivational Complexity: TRS pair #487102774

details
property	value
status	complete
benchmark	43603.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.676 seconds
cpu usage	1122.62
user time	1118.35
system time	4.269
max virtual memory	1.8956696E7
max residence set size	6099516.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 51 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) CpxTrsMatchBoundsProof [FINISHED, 178 ms]
(8) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   0(0(1(2(0(3(3(1(2(2(4(0(4(2(2(4(1(4(2(0(1(0(2(4(3(0(0(1(3(5(2(2(5(4(1(0(2(4(3(2(2(1(3(2(1(0(4(3(4(5(4(3(1(0(3(1(3(4(4(3(2(2(0(3(2(5(4(0(5(0(2(0(3(0(4(0(3(3(5(5(1(0(5(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(4(3(0(0(1(5(2(5(5(0(4(2(0(3(5(2(5(1(4(4(0(4(5(3(1(4(0(1(3(3(1(4(4(1(1(0(5(3(3(3(5(0(2(0(2(1(5(5(5(5(1(4(4(0(0(5(2(2(5(5(0(5(0(4(4(1(0(3(4(0(0(5(5(5(1(2(4(1(4(1(0(4(3(2(0(5(5(4(1(4(0(1(2(1(3(4(0(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   0(2(4(2(2(5(4(2(0(3(0(1(2(4(1(4(1(3(1(2(4(2(0(4(0(3(2(2(1(3(5(4(0(3(0(1(0(3(1(2(3(4(1(2(1(4(4(2(3(2(4(3(4(0(4(5(2(0(2(0(4(1(3(3(1(2(5(0(5(4(4(5(5(3(1(0(1(1(3(5(4(0(2(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(4(5(3(2(4(4(5(4(0(2(3(1(5(4(3(4(2(1(0(1(2(1(4(1(3(0(1(3(2(2(0(1(0(2(5(3(2(3(5(0(5(1(3(0(4(0(2(0(4(4(0(1(2(5(1(0(3(0(1(1(0(5(0(5(1(1(5(0(5(4(4(1(4(3(4(4(2(3(4(5(5(1(0(3(4(1(2(3(5(4(5(4(4(5(2(0(3(0(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   0(3(5(0(4(5(3(4(0(2(0(3(4(2(2(2(1(4(2(2(3(4(3(2(4(5(5(1(0(2(0(3(1(2(2(5(4(4(4(3(4(5(2(3(0(3(0(1(3(0(4(2(2(4(3(0(3(4(5(1(2(0(4(2(2(5(4(2(2(3(1(0(3(5(0(0(4(4(3(1(2(5(3(1(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(0(2(1(4(2(5(5(3(1(4(3(2(5(1(5(3(2(2(5(3(3(5(4(0(5(0(1(0(0(4(0(0(0(2(0(0(5(0(0(5(0(1(1(1(0(5(0(2(5(5(0(0(4(4(3(5(1(1(5(4(4(0(4(0(0(1(5(4(5(1(0(4(4(3(0(2(5(3(2(4(4(4(2(5(2(2(0(5(4(2(2(0(3(2(2(1(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(2(4(3(0(2(4(2(1(0(1(4(0(4(3(0(4(0(4(4(5(4(0(0(5(1(5(2(4(5(4(4(5(2(3(3(1(3(3(5(2(3(3(0(1(4(1(5(0(1(2(0(2(2(0(2(5(4(5(3(3(1(3(2(5(2(3(0(3(4(1(3(1(5(4(2(2(0(4(3(4(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(0(1(5(2(2(3(4(1(4(4(2(0(0(2(4(4(5(0(0(4(5(3(1(0(0(1(3(4(0(0(2(3(2(5(5(0(0(3(0(4(2(1(0(0(0(5(5(0(0(5(3(0(3(1(5(5(1(4(1(0(1(1(1(0(3(1(0(4(0(2(2(4(4(1(5(0(5(0(1(2(3(2(1(4(5(1(3(5(3(5(1(0(4(3(5(0(0(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(4(3(1(4(5(4(2(2(4(5(3(5(2(2(0(1(1(3(5(2(1(1(1(3(0(2(1(1(4(4(1(1(4(3(2(3(0(4(5(2(3(1(4(3(5(4(2(0(1(2(0(5(2(2(3(1(3(4(0(3(5(0(4(3(5(4(2(5(1(0(1(5(5(2(4(5(1(1(5(1(4(2(2(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(4(3(4(2(0(5(0(5(3(5(0(3(0(0(2(4(5(3(3(4(5(5(4(3(0(4(5(2(1(3(3(3(5(3(5(4(0(5(4(0(3(0(5(4(4(1(1(2(2(2(5(1(4(3(2(1(1(2(0(5(1(5(5(5(5(5(3(3(2(5(3(4(5(0(4(0(2(4(5(0(2(0(2(0(5(4(5(2(4(0(5(1(0(5(4(4(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(4(4(3(5(5(0(5(5(4(1(5(1(2(3(5(4(1(2(5(1(2(5(5(3(1(2(4(5(2(0(3(3(5(0(0(5(2(4(3(3(5(0(3(1(0(4(2(0(3(0(2(4(0(1(5(0(3(0(3(0(2(2(3(4(4(5(5(1(1(1(4(3(1(2(2(1(5(2(1(1(4(3(1(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(0(5(0(4(5(1(5(4(2(2(5(1(4(4(0(5(5(5(2(1(4(3(0(4(1(3(3(4(5(1(5(3(0(2(1(0(5(4(0(3(3(5(5(1(3(4(1(5(0(5(1(4(0(4(2(1(3(5(2(5(1(0(4(3(5(3(4(3(0(4(3(5(3(4(3(1(1(0(4(5(3(0(1(5(5(4(4(3(5(0(2(5(5(5(0(1(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(5(0(2(0(1(5(2(4(3(3(2(4(3(1(3(4(3(1(2(3(5(2(2(3(3(0(1(1(1(1(3(1(0(4(0(3(5(3(2(1(0(4(4(0(3(5(2(1(3(1(3(2(1(1(3(1(4(1(3(4(1(0(2(1(4(1(4(5(0(3(1(2(5(5(2(2(4(4(4(2(0(3(4(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(4(5(5(2(2(0(5(3(3(0(0(5(3(3(3(1(0(0(0(2(4(3(2(5(5(5(4(2(2(5(1(3(0(4(5(2(4(0(2(2(2(1(3(5(3(0(1(1(4(1(5(4(1(2(3(4(2(2(0(4(1(4(2(3(5(0(2(3(4(0(1(0(5(3(0(2(2(5(5(1(0(1(5(5(1(0(3(1(5(0(4(1(0(1(0(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(5(4(1(0(0(4(3(3(4(2(0(3(2(1(0(3(2(3(2(4(1(0(4(1(0(4(2(2(4(3(0(2(3(2(3(2(4(4(0(5(0(0(0(0(4(4(1(1(3(4(4(5(3(5(5(4(4(4(2(5(4(0(4(4(2(4(1(1(2(3(2(0(2(0(3(3(1(2(2(5(2(1(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(3(1(5(3(2(2(4(3(3(5(1(0(1(4(3(3(3(2(5(4(3(1(2(5(0(0(0(1(4(0(2(3(5(0(5(3(4(2(0(5(3(1(1(5(1(3(2(3(2(1(2(0(2(5(3(3(3(1(5(2(0(5(0(4(5(4(0(3(3(3(3(5(0(4(1(2(2(0(2(4(3(2(3(1(5(0(4(3(3(2(0(4(2(3(3(4(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(0(1(2(3(5(5(2(4(2(5(5(4(1(1(4(1(2(2(0(5(4(2(5(3(1(5(5(3(2(1(3(1(4(3(2(1(3(4(0(1(3(0(4(5(0(1(5(3(4(0(3(4(5(4(2(3(1(0(0(3(0(5(0(3(1(5(3(2(4(3(5(2(3(2(4(2(4(2(1(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(0(0(5(2(1(5(3(3(1(4(2(5(2(3(0(5(0(0(4(3(2(3(0(0(2(2(0(1(5(2(5(4(0(2(1(5(0(1(5(1(1(5(4(1(0(1(0(1(3(0(2(5(5(0(3(0(1(1(3(1(1(4(1(0(4(3(5(5(2(2(4(4(0(4(0(4(0(5(4(3(2(3(0(3(5(2(5(1(0(3(2(2(0(5(5(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(0(3(3(1(0(4(2(4(4(4(1(1(3(5(2(1(1(4(3(1(5(4(0(4(4(0(2(2(2(5(1(1(1(5(5(4(0(5(2(5(3(4(2(2(3(2(5(2(4(1(5(4(1(0(2(2(4(1(4(4(3(3(2(4(2(4(5(1(5(4(5(4(2(4(2(0(4(3(5(1(5(5(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(4(1(0(5(1(0(5(1(3(1(5(3(0(0(4(5(4(2(5(0(3(1(2(5(1(0(2(2(3(2(0(3(1(5(2(4(2(3(2(4(1(4(0(0(4(3(2(0(5(3(5(5(5(4(5(2(1(5(4(2(2(0(0(5(3(3(2(0(0(4(1(4(2(5(5(3(0(5(4(0(0(4(5(4(0(4(0(1(4(5(2(0(0(2(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(3(2(4(0(2(3(2(0(2(2(4(4(4(5(3(1(4(1(3(0(2(4(3(2(4(3(0(5(3(4(4(1(3(4(0(3(1(5(2(5(3(5(3(3(5(3(3(3(1(5(1(3(0(5(5(2(4(1(3(0(5(4(2(5(0(2(1(3(3(4(4(0(0(2(0(5(0(2(5(0(2(3(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(2(0(4(5(1(4(2(1(3(5(5(2(5(2(0(3(0(2(5(0(1(4(0(1(5(2(0(1(2(1(1(5(1(5(0(4(4(2(1(4(3(3(3(3(3(1(3(0(5(4(3(5(2(4(4(0(5(1(4(0(4(1(1(2(3(2(2(1(5(0(0(0(0(2(2(5(0(0(3(0(4(5(1(2(0(1(4(1(2(3(0(0(0(2(0(0(3(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(4(2(1(3(2(5(3(1(4(2(0(2(4(0(1(4(2(2(5(0(3(1(4(0(4(2(4(2(0(4(1(2(0(3(5(2(1(4(5(2(2(5(1(2(3(1(3(1(4(2(0(1(2(2(0(5(3(2(1(4(3(1(3(5(1(3(5(4(3(0(5(1(3(3(0(1(5(1(2(2(5(2(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(3(5(1(2(1(4(5(0(5(3(4(3(5(0(5(3(4(5(2(1(4(1(4(4(1(5(0(1(0(5(5(3(4(3(1(5(5(0(2(0(3(4(4(4(3(3(2(0(0(0(0(3(2(2(4(5(1(4(5(2(2(2(5(2(4(3(3(2(1(3(1(4(1(4(0(2(1(2(5(2(0(5(5(1(2(5(1(3(2(3(1(1(2(5(5(2(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(5(3(0(3(3(0(4(0(3(2(0(3(1(0(5(5(4(3(4(5(3(2(1(2(3(4(2(2(1(5(0(4(4(5(3(5(1(0(5(5(5(4(1(1(3(1(0(2(2(0(2(4(4(5(4(0(4(2(5(3(1(4(2(1(2(2(2(4(1(0(1(3(4(1(2(1(0(0(2(3(3(5(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(4(3(2(4(3(5(2(3(1(1(1(5(3(2(3(2(1(0(0(1(2(3(4(2(1(2(3(0(5(1(3(2(3(4(0(4(1(4(2(0(5(0(5(5(3(5(2(3(2(2(0(5(5(0(5(4(1(0(5(5(1(4(5(5(5(5(0(5(0(5(4(2(0(1(5(1(1(2(1(0(1(0(5(3(0(0(2(0(2(0(2(0(4(5(2(5(0(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   3(4(2(1(4(5(2(1(0(4(1(3(0(4(4(2(0(2(2(0(4(5(1(1(5(5(3(3(2(4(0(0(2(2(1(2(5(0(5(4(4(3(5(0(1(1(0(4(5(1(0(3(3(4(0(2(3(0(4(4(4(5(1(4(4(1(5(5(1(0(3(0(0(4(5(0(1(0(5(4(5(0(0(2(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(5(1(0(5(5(3(5(1(5(0(1(1(4(1(0(4(1(5(0(5(4(0(3(4(2(1(2(5(2(5(4(3(5(5(1(1(1(4(5(0(5(3(3(0(2(1(4(3(0(5(5(2(3(2(4(3(5(2(0(5(1(5(2(3(4(1(0(5(1(0(4(1(1(5(4(3(5(5(5(2(0(3(0(0(2(1(3(1(2(2(5(3(5(1(0(0(0(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   3(5(0(4(4(0(3(0(2(0(4(1(2(4(2(3(0(3(2(4(4(5(3(0(0(1(1(4(4(3(3(0(4(1(3(1(4(4(1(3(0(5(3(2(4(4(2(4(0(3(1(5(0(4(4(3(5(0(2(3(2(4(3(5(3(2(4(1(2(5(2(2(3(5(1(3(1(0(3(0(4(5(3(2(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(5(5(5(5(0(1(3(2(4(1(1(4(5(1(5(2(5(2(0(4(0(1(3(1(3(4(1(5(0(0(3(1(4(1(5(5(0(1(5(5(0(2(0(3(0(3(0(2(2(0(1(3(1(1(4(4(5(4(4(0(5(0(2(0(4(3(1(4(2(3(5(4(3(0(0(0(4(1(0(3(0(4(2(4(1(3(2(4(5(5(3(5(3(3(0(0(3(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   4(0(3(1(4(1(1(2(0(1(1(1(2(4(4(2(3(1(5(0(4(5(2(4(0(4(4(1(5(5(4(5(2(3(4(2(5(2(4(0(0(0(2(2(3(5(0(1(5(2(5(2(4(0(2(2(3(4(1(2(1(2(1(3(3(5(2(3(5(1(3(4(4(5(4(4(0(0(0(4(2(1(4(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(4(3(5(0(1(5(3(2(0(0(1(0(4(1(5(0(0(5(4(4(2(5(3(4(1(0(5(5(5(5(0(0(1(1(1(4(1(2(4(0(0(4(4(0(5(1(0(5(4(2(3(2(1(1(5(3(5(5(0(2(1(5(1(1(3(3(1(4(5(1(4(3(0(5(3(0(3(2(5(4(4(4(2(0(3(2(1(2(4(1(0(0(0(0(1(5(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   4(5(5(5(4(3(3(1(0(0(2(1(0(4(4(1(1(0(4(4(5(2(1(2(4(0(0(4(0(0(2(3(1(1(5(2(3(2(4(0(1(3(0(0(2(3(4(0(2(0(2(3(1(1(3(4(1(1(4(2(5(4(0(3(5(2(5(1(4(1(4(5(3(5(2(1(4(3(5(1(1(1(3(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(5(5(3(1(5(2(0(5(2(5(4(0(1(3(4(0(5(4(3(4(3(5(0(4(5(0(1(2(5(4(0(0(5(1(2(5(1(0(1(0(2(2(4(3(1(2(0(2(3(2(5(1(3(3(1(1(0(0(5(5(5(0(5(3(2(5(2(3(1(2(5(0(5(5(4(1(0(1(3(1(1(3(0(4(3(2(0(4(1(4(4(1(5(1(5(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(0(5(0(1(1(0(2(4(0(4(5(0(1(2(4(5(5(2(1(3(2(4(5(3(3(2(5(4(4(3(1(1(5(3(5(2(3(1(2(2(4(5(3(4(3(5(2(3(2(4(1(1(3(0(1(1(1(4(4(0(4(1(3(1(2(1(3(5(1(0(0(0(4(2(4(0(2(3(0(1(0(3(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(3(3(1(4(5(2(2(0(5(4(3(0(4(1(1(2(1(0(0(4(1(3(4(0(1(0(2(5(1(1(5(5(3(0(1(4(1(5(5(0(2(4(2(0(1(0(4(5(5(3(5(4(1(0(4(5(0(5(1(1(5(4(3(0(1(4(1(4(0(4(1(1(4(4(0(4(1(5(2(1(4(2(1(2(5(2(5(3(3(0(4(2(5(5(1(0(4(4(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(4(4(1(5(0(0(5(3(0(3(5(4(2(1(1(0(1(0(5(4(3(4(1(3(5(5(4(5(4(5(2(2(0(5(5(3(3(0(5(2(0(1(5(1(2(3(2(2(5(4(1(0(4(1(4(1(0(2(1(0(3(5(4(4(4(2(0(2(2(4(3(4(1(4(4(3(1(2(2(3(1(2(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(3(4(4(1(3(5(1(1(5(3(5(5(5(5(0(3(5(3(5(0(5(0(0(4(3(3(1(1(0(3(5(3(3(1(2(4(0(1(5(3(5(1(5(3(0(4(3(0(5(5(2(3(5(3(1(4(0(5(5(3(3(0(0(2(1(5(5(5(0(3(2(5(4(2(0(5(1(5(5(4(2(1(5(5(1(0(4(2(5(0(2(1(2(3(1(0(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(5(1(3(4(0(2(0(0(3(2(4(2(1(2(2(0(4(3(2(4(3(1(2(1(2(0(4(1(0(1(5(2(5(3(1(0(3(5(1(4(4(1(0(1(5(3(0(1(2(4(5(2(1(2(1(4(5(3(2(0(1(5(3(2(2(1(1(0(5(0(2(5(4(1(3(3(3(4(1(5(1(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(0(0(1(5(0(4(5(0(2(3(4(1(3(1(3(1(0(1(5(0(5(4(3(2(1(0(5(5(2(3(3(4(0(1(5(2(4(2(5(3(5(0(5(3(0(1(2(0(0(4(4(2(0(5(4(0(2(3(2(0(1(5(3(5(5(0(2(2(0(5(1(4(3(3(3(2(0(1(3(0(3(0(4(3(4(4(2(0(5(5(0(5(0(5(4(0(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

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

(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(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))


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

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


The TRS R consists of the following rules:

   0(0(1(2(0(3(3(1(2(2(4(0(4(2(2(4(1(4(2(0(1(0(2(4(3(0(0(1(3(5(2(2(5(4(1(0(2(4(3(2(2(1(3(2(1(0(4(3(4(5(4(3(1(0(3(1(3(4(4(3(2(2(0(3(2(5(4(0(5(0(2(0(3(0(4(0(3(3(5(5(1(0(5(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(4(3(0(0(1(5(2(5(5(0(4(2(0(3(5(2(5(1(4(4(0(4(5(3(1(4(0(1(3(3(1(4(4(1(1(0(5(3(3(3(5(0(2(0(2(1(5(5(5(5(1(4(4(0(0(5(2(2(5(5(0(5(0(4(4(1(0(3(4(0(0(5(5(5(1(2(4(1(4(1(0(4(3(2(0(5(5(4(1(4(0(1(2(1(3(4(0(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   0(2(4(2(2(5(4(2(0(3(0(1(2(4(1(4(1(3(1(2(4(2(0(4(0(3(2(2(1(3(5(4(0(3(0(1(0(3(1(2(3(4(1(2(1(4(4(2(3(2(4(3(4(0(4(5(2(0(2(0(4(1(3(3(1(2(5(0(5(4(4(5(5(3(1(0(1(1(3(5(4(0(2(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(4(5(3(2(4(4(5(4(0(2(3(1(5(4(3(4(2(1(0(1(2(1(4(1(3(0(1(3(2(2(0(1(0(2(5(3(2(3(5(0(5(1(3(0(4(0(2(0(4(4(0(1(2(5(1(0(3(0(1(1(0(5(0(5(1(1(5(0(5(4(4(1(4(3(4(4(2(3(4(5(5(1(0(3(4(1(2(3(5(4(5(4(4(5(2(0(3(0(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   0(3(5(0(4(5(3(4(0(2(0(3(4(2(2(2(1(4(2(2(3(4(3(2(4(5(5(1(0(2(0(3(1(2(2(5(4(4(4(3(4(5(2(3(0(3(0(1(3(0(4(2(2(4(3(0(3(4(5(1(2(0(4(2(2(5(4(2(2(3(1(0(3(5(0(0(4(4(3(1(2(5(3(1(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(0(2(1(4(2(5(5(3(1(4(3(2(5(1(5(3(2(2(5(3(3(5(4(0(5(0(1(0(0(4(0(0(0(2(0(0(5(0(0(5(0(1(1(1(0(5(0(2(5(5(0(0(4(4(3(5(1(1(5(4(4(0(4(0(0(1(5(4(5(1(0(4(4(3(0(2(5(3(2(4(4(4(2(5(2(2(0(5(4(2(2(0(3(2(2(1(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(2(4(3(0(2(4(2(1(0(1(4(0(4(3(0(4(0(4(4(5(4(0(0(5(1(5(2(4(5(4(4(5(2(3(3(1(3(3(5(2(3(3(0(1(4(1(5(0(1(2(0(2(2(0(2(5(4(5(3(3(1(3(2(5(2(3(0(3(4(1(3(1(5(4(2(2(0(4(3(4(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(0(1(5(2(2(3(4(1(4(4(2(0(0(2(4(4(5(0(0(4(5(3(1(0(0(1(3(4(0(0(2(3(2(5(5(0(0(3(0(4(2(1(0(0(0(5(5(0(0(5(3(0(3(1(5(5(1(4(1(0(1(1(1(0(3(1(0(4(0(2(2(4(4(1(5(0(5(0(1(2(3(2(1(4(5(1(3(5(3(5(1(0(4(3(5(0(0(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(4(3(1(4(5(4(2(2(4(5(3(5(2(2(0(1(1(3(5(2(1(1(1(3(0(2(1(1(4(4(1(1(4(3(2(3(0(4(5(2(3(1(4(3(5(4(2(0(1(2(0(5(2(2(3(1(3(4(0(3(5(0(4(3(5(4(2(5(1(0(1(5(5(2(4(5(1(1(5(1(4(2(2(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(4(3(4(2(0(5(0(5(3(5(0(3(0(0(2(4(5(3(3(4(5(5(4(3(0(4(5(2(1(3(3(3(5(3(5(4(0(5(4(0(3(0(5(4(4(1(1(2(2(2(5(1(4(3(2(1(1(2(0(5(1(5(5(5(5(5(3(3(2(5(3(4(5(0(4(0(2(4(5(0(2(0(2(0(5(4(5(2(4(0(5(1(0(5(4(4(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(4(4(3(5(5(0(5(5(4(1(5(1(2(3(5(4(1(2(5(1(2(5(5(3(1(2(4(5(2(0(3(3(5(0(0(5(2(4(3(3(5(0(3(1(0(4(2(0(3(0(2(4(0(1(5(0(3(0(3(0(2(2(3(4(4(5(5(1(1(1(4(3(1(2(2(1(5(2(1(1(4(3(1(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(0(5(0(4(5(1(5(4(2(2(5(1(4(4(0(5(5(5(2(1(4(3(0(4(1(3(3(4(5(1(5(3(0(2(1(0(5(4(0(3(3(5(5(1(3(4(1(5(0(5(1(4(0(4(2(1(3(5(2(5(1(0(4(3(5(3(4(3(0(4(3(5(3(4(3(1(1(0(4(5(3(0(1(5(5(4(4(3(5(0(2(5(5(5(0(1(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(5(0(2(0(1(5(2(4(3(3(2(4(3(1(3(4(3(1(2(3(5(2(2(3(3(0(1(1(1(1(3(1(0(4(0(3(5(3(2(1(0(4(4(0(3(5(2(1(3(1(3(2(1(1(3(1(4(1(3(4(1(0(2(1(4(1(4(5(0(3(1(2(5(5(2(2(4(4(4(2(0(3(4(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(4(5(5(2(2(0(5(3(3(0(0(5(3(3(3(1(0(0(0(2(4(3(2(5(5(5(4(2(2(5(1(3(0(4(5(2(4(0(2(2(2(1(3(5(3(0(1(1(4(1(5(4(1(2(3(4(2(2(0(4(1(4(2(3(5(0(2(3(4(0(1(0(5(3(0(2(2(5(5(1(0(1(5(5(1(0(3(1(5(0(4(1(0(1(0(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(5(4(1(0(0(4(3(3(4(2(0(3(2(1(0(3(2(3(2(4(1(0(4(1(0(4(2(2(4(3(0(2(3(2(3(2(4(4(0(5(0(0(0(0(4(4(1(1(3(4(4(5(3(5(5(4(4(4(2(5(4(0(4(4(2(4(1(1(2(3(2(0(2(0(3(3(1(2(2(5(2(1(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(3(1(5(3(2(2(4(3(3(5(1(0(1(4(3(3(3(2(5(4(3(1(2(5(0(0(0(1(4(0(2(3(5(0(5(3(4(2(0(5(3(1(1(5(1(3(2(3(2(1(2(0(2(5(3(3(3(1(5(2(0(5(0(4(5(4(0(3(3(3(3(5(0(4(1(2(2(0(2(4(3(2(3(1(5(0(4(3(3(2(0(4(2(3(3(4(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(0(1(2(3(5(5(2(4(2(5(5(4(1(1(4(1(2(2(0(5(4(2(5(3(1(5(5(3(2(1(3(1(4(3(2(1(3(4(0(1(3(0(4(5(0(1(5(3(4(0(3(4(5(4(2(3(1(0(0(3(0(5(0(3(1(5(3(2(4(3(5(2(3(2(4(2(4(2(1(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(0(0(5(2(1(5(3(3(1(4(2(5(2(3(0(5(0(0(4(3(2(3(0(0(2(2(0(1(5(2(5(4(0(2(1(5(0(1(5(1(1(5(4(1(0(1(0(1(3(0(2(5(5(0(3(0(1(1(3(1(1(4(1(0(4(3(5(5(2(2(4(4(0(4(0(4(0(5(4(3(2(3(0(3(5(2(5(1(0(3(2(2(0(5(5(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(0(3(3(1(0(4(2(4(4(4(1(1(3(5(2(1(1(4(3(1(5(4(0(4(4(0(2(2(2(5(1(1(1(5(5(4(0(5(2(5(3(4(2(2(3(2(5(2(4(1(5(4(1(0(2(2(4(1(4(4(3(3(2(4(2(4(5(1(5(4(5(4(2(4(2(0(4(3(5(1(5(5(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(4(1(0(5(1(0(5(1(3(1(5(3(0(0(4(5(4(2(5(0(3(1(2(5(1(0(2(2(3(2(0(3(1(5(2(4(2(3(2(4(1(4(0(0(4(3(2(0(5(3(5(5(5(4(5(2(1(5(4(2(2(0(0(5(3(3(2(0(0(4(1(4(2(5(5(3(0(5(4(0(0(4(5(4(0(4(0(1(4(5(2(0(0(2(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(3(2(4(0(2(3(2(0(2(2(4(4(4(5(3(1(4(1(3(0(2(4(3(2(4(3(0(5(3(4(4(1(3(4(0(3(1(5(2(5(3(5(3(3(5(3(3(3(1(5(1(3(0(5(5(2(4(1(3(0(5(4(2(5(0(2(1(3(3(4(4(0(0(2(0(5(0(2(5(0(2(3(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(2(0(4(5(1(4(2(1(3(5(5(2(5(2(0(3(0(2(5(0(1(4(0(1(5(2(0(1(2(1(1(5(1(5(0(4(4(2(1(4(3(3(3(3(3(1(3(0(5(4(3(5(2(4(4(0(5(1(4(0(4(1(1(2(3(2(2(1(5(0(0(0(0(2(2(5(0(0(3(0(4(5(1(2(0(1(4(1(2(3(0(0(0(2(0(0(3(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(4(2(1(3(2(5(3(1(4(2(0(2(4(0(1(4(2(2(5(0(3(1(4(0(4(2(4(2(0(4(1(2(0(3(5(2(1(4(5(2(2(5(1(2(3(1(3(1(4(2(0(1(2(2(0(5(3(2(1(4(3(1(3(5(1(3(5(4(3(0(5(1(3(3(0(1(5(1(2(2(5(2(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(3(5(1(2(1(4(5(0(5(3(4(3(5(0(5(3(4(5(2(1(4(1(4(4(1(5(0(1(0(5(5(3(4(3(1(5(5(0(2(0(3(4(4(4(3(3(2(0(0(0(0(3(2(2(4(5(1(4(5(2(2(2(5(2(4(3(3(2(1(3(1(4(1(4(0(2(1(2(5(2(0(5(5(1(2(5(1(3(2(3(1(1(2(5(5(2(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   2(5(3(0(3(3(0(4(0(3(2(0(3(1(0(5(5(4(3(4(5(3(2(1(2(3(4(2(2(1(5(0(4(4(5(3(5(1(0(5(5(5(4(1(1(3(1(0(2(2(0(2(4(4(5(4(0(4(2(5(3(1(4(2(1(2(2(2(4(1(0(1(3(4(1(2(1(0(0(2(3(3(5(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(4(3(2(4(3(5(2(3(1(1(1(5(3(2(3(2(1(0(0(1(2(3(4(2(1(2(3(0(5(1(3(2(3(4(0(4(1(4(2(0(5(0(5(5(3(5(2(3(2(2(0(5(5(0(5(4(1(0(5(5(1(4(5(5(5(5(0(5(0(5(4(2(0(1(5(1(1(2(1(0(1(0(5(3(0(0(2(0(2(0(2(0(4(5(2(5(0(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   3(4(2(1(4(5(2(1(0(4(1(3(0(4(4(2(0(2(2(0(4(5(1(1(5(5(3(3(2(4(0(0(2(2(1(2(5(0(5(4(4(3(5(0(1(1(0(4(5(1(0(3(3(4(0(2(3(0(4(4(4(5(1(4(4(1(5(5(1(0(3(0(0(4(5(0(1(0(5(4(5(0(0(2(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(5(1(0(5(5(3(5(1(5(0(1(1(4(1(0(4(1(5(0(5(4(0(3(4(2(1(2(5(2(5(4(3(5(5(1(1(1(4(5(0(5(3(3(0(2(1(4(3(0(5(5(2(3(2(4(3(5(2(0(5(1(5(2(3(4(1(0(5(1(0(4(1(1(5(4(3(5(5(5(2(0(3(0(0(2(1(3(1(2(2(5(3(5(1(0(0(0(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   3(5(0(4(4(0(3(0(2(0(4(1(2(4(2(3(0(3(2(4(4(5(3(0(0(1(1(4(4(3(3(0(4(1(3(1(4(4(1(3(0(5(3(2(4(4(2(4(0(3(1(5(0(4(4(3(5(0(2(3(2(4(3(5(3(2(4(1(2(5(2(2(3(5(1(3(1(0(3(0(4(5(3(2(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(5(5(5(5(0(1(3(2(4(1(1(4(5(1(5(2(5(2(0(4(0(1(3(1(3(4(1(5(0(0(3(1(4(1(5(5(0(1(5(5(0(2(0(3(0(3(0(2(2(0(1(3(1(1(4(4(5(4(4(0(5(0(2(0(4(3(1(4(2(3(5(4(3(0(0(0(4(1(0(3(0(4(2(4(1(3(2(4(5(5(3(5(3(3(0(0(3(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   4(0(3(1(4(1(1(2(0(1(1(1(2(4(4(2(3(1(5(0(4(5(2(4(0(4(4(1(5(5(4(5(2(3(4(2(5(2(4(0(0(0(2(2(3(5(0(1(5(2(5(2(4(0(2(2(3(4(1(2(1(2(1(3(3(5(2(3(5(1(3(4(4(5(4(4(0(0(0(4(2(1(4(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(4(3(5(0(1(5(3(2(0(0(1(0(4(1(5(0(0(5(4(4(2(5(3(4(1(0(5(5(5(5(0(0(1(1(1(4(1(2(4(0(0(4(4(0(5(1(0(5(4(2(3(2(1(1(5(3(5(5(0(2(1(5(1(1(3(3(1(4(5(1(4(3(0(5(3(0(3(2(5(4(4(4(2(0(3(2(1(2(4(1(0(0(0(0(1(5(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   4(5(5(5(4(3(3(1(0(0(2(1(0(4(4(1(1(0(4(4(5(2(1(2(4(0(0(4(0(0(2(3(1(1(5(2(3(2(4(0(1(3(0(0(2(3(4(0(2(0(2(3(1(1(3(4(1(1(4(2(5(4(0(3(5(2(5(1(4(1(4(5(3(5(2(1(4(3(5(1(1(1(3(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(5(5(3(1(5(2(0(5(2(5(4(0(1(3(4(0(5(4(3(4(3(5(0(4(5(0(1(2(5(4(0(0(5(1(2(5(1(0(1(0(2(2(4(3(1(2(0(2(3(2(5(1(3(3(1(1(0(0(5(5(5(0(5(3(2(5(2(3(1(2(5(0(5(5(4(1(0(1(3(1(1(3(0(4(3(2(0(4(1(4(4(1(5(1(5(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(0(5(0(1(1(0(2(4(0(4(5(0(1(2(4(5(5(2(1(3(2(4(5(3(3(2(5(4(4(3(1(1(5(3(5(2(3(1(2(2(4(5(3(4(3(5(2(3(2(4(1(1(3(0(1(1(1(4(4(0(4(1(3(1(2(1(3(5(1(0(0(0(4(2(4(0(2(3(0(1(0(3(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(3(3(1(4(5(2(2(0(5(4(3(0(4(1(1(2(1(0(0(4(1(3(4(0(1(0(2(5(1(1(5(5(3(0(1(4(1(5(5(0(2(4(2(0(1(0(4(5(5(3(5(4(1(0(4(5(0(5(1(1(5(4(3(0(1(4(1(4(0(4(1(1(4(4(0(4(1(5(2(1(4(2(1(2(5(2(5(3(3(0(4(2(5(5(1(0(4(4(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(4(4(1(5(0(0(5(3(0(3(5(4(2(1(1(0(1(0(5(4(3(4(1(3(5(5(4(5(4(5(2(2(0(5(5(3(3(0(5(2(0(1(5(1(2(3(2(2(5(4(1(0(4(1(4(1(0(2(1(0(3(5(4(4(4(2(0(2(2(4(3(4(1(4(4(3(1(2(2(3(1(2(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(0(3(4(4(1(3(5(1(1(5(3(5(5(5(5(0(3(5(3(5(0(5(0(0(4(3(3(1(1(0(3(5(3(3(1(2(4(0(1(5(3(5(1(5(3(0(4(3(0(5(5(2(3(5(3(1(4(0(5(5(3(3(0(0(2(1(5(5(5(0(3(2(5(4(2(0(5(1(5(5(4(2(1(5(5(1(0(4(2(5(0(2(1(2(3(1(0(2(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   5(5(1(3(4(0(2(0(0(3(2(4(2(1(2(2(0(4(3(2(4(3(1(2(1(2(0(4(1(0(1(5(2(5(3(1(0(3(5(1(4(4(1(0(1(5(3(0(1(2(4(5(2(1(2(1(4(5(3(2(0(1(5(3(2(2(1(1(0(5(0(2(5(4(1(3(3(3(4(1(5(1(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(1(0(0(1(5(0(4(5(0(2(3(4(1(3(1(3(1(0(1(5(0(5(4(3(2(1(0(5(5(2(3(3(4(0(1(5(2(4(2(5(3(5(0(5(3(0(1(2(0(0(4(4(2(0(5(4(0(2(3(2(0(1(5(3(5(5(0(2(2(0(5(1(4(3(3(3(2(0(1(3(0(3(0(4(3(4(4(2(0(5(5(0(5(0(5(4(0(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

The (relative) TRS S consists of the following rules:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions all output return to Derivational Complexity: TRS