Derivational Complexity: TRS pair #487102226

details

property	value
status	complete
benchmark	e.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.799 seconds
cpu usage	1084.84
user time	1072.03
system time	12.81
max virtual memory	1.9076652E7
max residence set size	1.5150648E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) 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), 193 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
(8) BEST
    (9) proven lower bound
        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
        (11) BOUNDS(n^1, INF)
    (12) TRS for Loop Detection


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


The TRS R consists of the following rules:

   2(7(x1)) -> 1(8(x1))
   2(8(1(x1))) -> 8(x1)
   2(8(x1)) -> 4(x1)
   5(9(x1)) -> 0(x1)
   4(x1) -> 5(2(3(x1)))
   5(3(x1)) -> 6(0(x1))
   2(8(x1)) -> 7(x1)
   4(7(x1)) -> 1(3(x1))
   5(2(6(x1))) -> 6(2(4(x1)))
   9(7(x1)) -> 7(5(x1))
   7(2(x1)) -> 4(x1)
   7(0(x1)) -> 9(3(x1))
   6(9(x1)) -> 9(x1)
   9(5(9(x1))) -> 5(7(x1))
   4(x1) -> 9(6(6(x1)))
   9(x1) -> 6(7(x1))
   6(2(x1)) -> 7(7(x1))
   2(4(x1)) -> 0(7(x1))
   6(6(x1)) -> 3(x1)
   0(3(x1)) -> 5(3(x1))

S is empty.
Rewrite Strategy: FULL
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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(1(x_1)) -> 1(encArg(x_1))
   encArg(8(x_1)) -> 8(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_9(x_1)) -> 9(encArg(x_1))
   encArg(cons_7(x_1)) -> 7(encArg(x_1))
   encArg(cons_6(x_1)) -> 6(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_7(x_1) -> 7(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_8(x_1) -> 8(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))
   encode_9(x_1) -> 9(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_6(x_1) -> 6(encArg(x_1))


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


The TRS R consists of the following rules:

   2(7(x1)) -> 1(8(x1))
   2(8(1(x1))) -> 8(x1)
   2(8(x1)) -> 4(x1)
   5(9(x1)) -> 0(x1)
   4(x1) -> 5(2(3(x1)))
   5(3(x1)) -> 6(0(x1))
   2(8(x1)) -> 7(x1)
   4(7(x1)) -> 1(3(x1))
   5(2(6(x1))) -> 6(2(4(x1)))
   9(7(x1)) -> 7(5(x1))

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