Derivational Complexity: TRS Innermost pair #487106652

details
property	value
status	complete
benchmark	167240.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.743 seconds
cpu usage	699.143
user time	695.453
system time	3.68945
max virtual memory	1.93867E7
max residence set size	6164160.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 66 ms]
(4) CpxRelTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 8492 ms]
(6) CdtProblem
(7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
(8) CdtProblem
(9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CdtProblem
(11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CdtProblem
(13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
(14) CdtProblem
(15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9 ms]
(16) CdtProblem
(17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 113 ms]
(18) CdtProblem
(19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 33 ms]
(20) CdtProblem
(21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 32 ms]
(22) CdtProblem
(23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) BOUNDS(1, 1)


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

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


The TRS R consists of the following rules:

   0(0(x1)) -> 1(2(1(x1)))
   0(2(x1)) -> 1(1(1(x1)))
   2(0(x1)) -> 1(2(1(x1)))
   2(2(2(x1))) -> 1(1(2(2(1(2(1(x1)))))))
   2(1(0(0(x1)))) -> 0(1(2(1(1(2(1(x1)))))))
   0(0(1(0(0(x1))))) -> 1(2(0(1(1(1(x1))))))
   1(1(2(2(0(x1))))) -> 1(1(1(2(2(1(x1))))))
   0(0(0(0(0(1(x1)))))) -> 1(2(0(2(1(2(1(1(2(1(1(1(0(1(2(1(2(1(0(0(1(x1)))))))))))))))))))))
   0(0(2(2(0(0(x1)))))) -> 1(2(2(0(1(2(1(1(1(x1)))))))))
   1(0(2(2(2(1(x1)))))) -> 1(1(1(0(1(1(0(1(x1))))))))
   2(0(0(0(0(1(0(x1))))))) -> 1(0(1(0(1(2(0(1(1(2(1(1(0(x1)))))))))))))
   2(2(0(0(1(2(0(x1))))))) -> 0(2(1(0(0(1(2(1(1(2(0(x1)))))))))))
   2(2(2(2(0(1(2(x1))))))) -> 2(2(2(0(2(1(2(x1)))))))
   0(1(0(1(1(2(1(0(x1)))))))) -> 1(1(2(0(1(2(1(1(2(1(x1))))))))))
   1(2(2(2(2(2(1(0(x1)))))))) -> 1(2(1(2(2(2(0(2(x1))))))))
   0(0(0(2(2(2(1(0(0(x1))))))))) -> 1(1(2(0(1(1(0(2(0(2(1(2(1(2(1(2(1(2(1(x1)))))))))))))))))))
   0(1(0(0(2(0(2(0(2(x1))))))))) -> 1(0(0(1(1(1(1(2(2(0(0(2(x1))))))))))))
   1(1(2(0(1(1(0(0(2(x1))))))))) -> 0(1(1(2(0(1(2(1(1(2(1(2(0(1(x1))))))))))))))
   2(0(0(2(1(2(2(2(1(x1))))))))) -> 2(1(2(2(1(1(2(0(1(2(1(0(0(1(x1))))))))))))))
   2(1(0(1(2(0(1(2(0(x1))))))))) -> 1(2(1(2(1(2(0(2(1(1(0(x1)))))))))))
   0(0(0(2(2(0(0(2(0(0(x1)))))))))) -> 1(1(2(2(0(0(0(0(1(1(2(x1)))))))))))
   0(1(1(0(2(2(2(1(0(0(x1)))))))))) -> 0(2(1(1(2(2(0(1(1(2(1(2(x1))))))))))))
   1(0(0(1(2(1(0(2(2(2(x1)))))))))) -> 1(2(1(2(2(1(0(2(1(2(1(1(x1))))))))))))
   1(2(0(2(0(2(0(0(2(0(x1)))))))))) -> 0(0(1(1(0(0(2(0(1(1(1(x1)))))))))))
   2(1(2(0(0(0(1(2(2(0(x1)))))))))) -> 1(2(1(1(0(2(1(2(0(1(0(1(1(x1)))))))))))))
   0(1(2(1(0(0(1(0(2(1(1(x1))))))))))) -> 1(1(0(0(0(1(2(0(1(2(1(x1)))))))))))
   0(2(1(0(0(1(0(1(0(2(0(x1))))))))))) -> 1(0(1(1(0(1(2(0(1(2(1(1(0(1(1(2(0(x1)))))))))))))))))
   1(2(1(0(0(0(2(2(2(2(0(x1))))))))))) -> 1(1(2(0(0(2(2(1(2(1(0(0(2(1(x1))))))))))))))
   1(2(2(0(0(0(0(0(1(0(2(x1))))))))))) -> 1(0(1(2(0(0(1(1(2(1(1(2(x1))))))))))))
   2(0(2(2(2(2(1(2(0(1(1(x1))))))))))) -> 2(1(2(0(2(2(2(0(2(1(1(x1)))))))))))
   2(1(0(2(0(0(1(2(2(1(2(x1))))))))))) -> 0(0(1(1(1(1(0(1(0(1(1(0(x1))))))))))))
   2(2(2(2(1(1(1(2(2(0(0(x1))))))))))) -> 1(1(1(0(1(0(0(1(1(2(0(2(1(x1)))))))))))))
   0(0(2(2(2(1(0(1(0(2(0(2(x1)))))))))))) -> 1(1(1(2(0(0(0(1(0(2(0(2(2(1(x1))))))))))))))
   1(0(0(1(1(0(0(1(1(0(2(0(x1)))))))))))) -> 1(1(1(2(0(0(0(1(1(0(0(0(x1))))))))))))
   1(0(2(0(0(1(0(2(0(0(1(2(x1)))))))))))) -> 0(0(0(1(2(1(1(2(0(2(0(0(x1))))))))))))
   2(0(0(0(2(2(2(0(1(2(2(0(x1)))))))))))) -> 2(0(2(0(1(2(1(0(0(0(0(1(0(x1)))))))))))))
   2(2(0(0(0(1(1(2(2(0(2(1(2(x1))))))))))))) -> 1(0(1(0(1(1(2(1(1(1(1(1(0(0(2(0(2(0(x1))))))))))))))))))
   0(1(1(1(1(0(2(2(1(1(1(0(2(2(x1)))))))))))))) -> 1(2(1(0(1(1(1(2(2(1(2(0(0(1(x1))))))))))))))
   0(1(2(2(1(2(0(0(0(2(2(1(1(0(x1)))))))))))))) -> 1(2(0(0(0(2(0(1(2(0(1(2(1(2(x1))))))))))))))
   0(0(0(2(1(2(0(1(2(1(2(2(2(1(0(x1))))))))))))))) -> 1(2(0(1(0(2(1(1(0(0(1(1(1(0(0(1(x1))))))))))))))))
   0(0(1(0(0(1(2(0(1(2(1(2(2(0(0(x1))))))))))))))) -> 1(0(1(2(1(1(0(2(1(2(1(2(0(2(1(0(x1))))))))))))))))
   2(0(0(0(2(1(0(0(1(0(2(1(0(0(2(x1))))))))))))))) -> 1(1(0(2(1(0(2(1(1(2(1(1(0(1(1(1(1(1(1(0(1(1(x1))))))))))))))))))))))
   2(0(1(0(2(2(0(1(1(2(0(2(2(2(0(x1))))))))))))))) -> 1(1(1(1(1(1(0(1(2(1(2(2(1(1(1(2(2(x1)))))))))))))))))
   0(2(2(0(2(2(1(1(0(2(1(0(1(2(0(0(x1)))))))))))))))) -> 1(2(2(1(1(1(1(1(0(2(1(2(0(0(0(0(1(2(x1))))))))))))))))))
   1(0(2(2(1(0(0(1(1(1(0(1(1(2(2(0(x1)))))))))))))))) -> 1(2(1(2(0(1(1(0(2(0(0(0(1(2(1(2(0(2(1(2(0(x1)))))))))))))))))))))
   2(2(0(2(2(1(0(1(0(2(2(2(2(1(2(0(x1)))))))))))))))) -> 1(0(1(0(1(0(2(0(1(1(0(2(0(0(0(1(1(x1)))))))))))))))))
   2(2(0(2(2(2(0(0(0(0(1(2(2(0(2(0(x1)))))))))))))))) -> 0(2(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(2(x1)))))))))))))))))))
   0(2(2(0(1(0(2(0(1(0(0(2(2(2(1(2(0(x1))))))))))))))))) -> 0(1(1(0(1(2(0(1(2(1(1(2(1(1(2(0(0(0(0(x1)))))))))))))))))))
   1(1(0(0(0(0(0(0(0(2(2(2(2(1(0(0(1(x1))))))))))))))))) -> 1(2(1(0(2(0(0(2(0(0(1(1(1(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))
   1(1(0(0(1(2(0(2(0(0(1(2(0(2(2(2(2(x1))))))))))))))))) -> 1(2(1(2(0(2(0(2(0(1(0(1(2(1(0(1(0(2(x1))))))))))))))))))
   2(0(0(2(2(2(2(1(2(2(1(0(2(2(0(1(0(x1))))))))))))))))) -> 2(2(2(0(1(1(1(1(1(0(1(1(1(2(0(1(2(1(1(1(1(2(1(2(x1))))))))))))))))))))))))
   2(0(1(1(1(1(0(2(0(1(0(1(1(1(2(2(1(x1))))))))))))))))) -> 1(2(1(0(1(1(2(0(2(1(1(0(0(1(1(2(1(x1)))))))))))))))))
   0(0(2(2(1(2(1(1(0(0(1(2(0(0(2(2(2(1(x1)))))))))))))))))) -> 1(1(2(1(0(2(1(0(1(1(2(0(1(0(0(1(1(0(1(0(0(1(0(1(x1))))))))))))))))))))))))
   0(1(0(0(1(1(0(0(0(1(2(1(2(2(1(0(0(2(x1)))))))))))))))))) -> 0(1(2(1(1(1(1(2(2(1(0(0(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))
   2(0(0(0(2(0(0(0(1(0(0(2(2(0(1(2(1(0(x1)))))))))))))))))) -> 0(2(2(1(1(0(1(0(1(0(2(1(1(2(1(2(0(0(0(0(1(1(1(x1)))))))))))))))))))))))
   2(2(0(1(1(0(0(0(2(0(1(0(1(0(1(0(1(2(x1)))))))))))))))))) -> 2(2(0(2(0(1(1(2(0(1(0(0(0(1(1(2(1(2(1(1(x1))))))))))))))))))))
   2(2(2(2(2(1(0(1(2(2(2(2(1(0(1(0(0(0(x1)))))))))))))))))) -> 0(1(2(1(1(1(2(1(0(0(0(1(1(0(1(1(2(2(2(2(2(2(1(0(0(x1)))))))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS Innermost