Derivational Complexity: TRS pair #487103438

details

property	value
status	complete
benchmark	25736.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.459 seconds
cpu usage	865.815
user time	857.415
system time	8.39934
max virtual memory	1.878472E7
max residence set size	1.4935884E7

stage attributes

key	value
starexec-result	KILLED

output

KILLED
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 84 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 7 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1394 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1968 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 136 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 112 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 910 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6349 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1908 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1873 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1853 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1836 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1900 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1878 ms]
        (58) CdtProblem


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

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


The TRS R consists of the following rules:

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

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