Derivational Complexity: TRS pair #487102878

details

property	value
status	complete
benchmark	26116.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	298.301 seconds
cpu usage	855.505
user time	848.094
system time	7.41046
max virtual memory	3.7375892E7
max residence set size	1.4998812E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 83 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), 0 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), 1381 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 18 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 23 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 9 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 2110 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 139 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 84 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 926 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 10 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6306 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1808 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1791 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1818 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1787 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1850 ms]
        (56) 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(2(0(x1))))))) -> 0(1(2(1(0(2(0(x1)))))))
   3(1(1(0(0(1(2(2(x1)))))))) -> 3(2(1(1(0(1(0(2(x1))))))))
   0(4(2(0(4(3(4(4(5(x1))))))))) -> 0(4(2(0(3(4(4(4(5(x1)))))))))
   0(4(2(0(5(2(2(4(5(x1))))))))) -> 0(4(2(5(0(2(2(4(5(x1)))))))))
   3(4(3(3(2(0(3(3(0(x1))))))))) -> 3(3(4(3(0(2(3(3(0(x1)))))))))
   5(1(5(2(0(0(0(0(4(x1))))))))) -> 5(1(5(0(0(2(0(0(4(x1)))))))))
   1(5(3(1(3(2(5(3(3(1(x1)))))))))) -> 4(5(0(0(5(1(4(1(5(0(x1))))))))))
   2(0(4(2(0(5(4(1(0(2(x1)))))))))) -> 2(0(4(0(2(5(4(1(0(2(x1))))))))))
   3(4(0(4(4(3(0(4(2(3(x1)))))))))) -> 3(2(2(5(0(1(2(1(4(2(x1))))))))))
   5(0(0(5(2(2(1(4(2(5(x1)))))))))) -> 5(0(0(2(5(2(1(4(2(5(x1))))))))))
   0(0(5(2(2(0(5(4(4(1(0(x1))))))))))) -> 5(5(1(5(4(2(3(0(2(4(x1))))))))))
   0(1(5(3(4(3(5(4(0(3(1(x1))))))))))) -> 0(4(0(4(3(4(3(3(2(5(x1))))))))))
   0(2(0(3(2(1(0(3(2(2(2(x1))))))))))) -> 5(4(4(0(3(3(5(1(5(3(x1))))))))))
   0(2(2(4(5(5(5(5(3(3(1(x1))))))))))) -> 4(5(3(4(0(3(4(0(0(3(x1))))))))))
   0(3(0(1(2(5(2(1(4(5(2(x1))))))))))) -> 1(2(4(1(5(1(4(5(4(2(x1))))))))))
   0(3(5(2(4(5(1(3(2(3(5(x1))))))))))) -> 3(4(4(1(3(0(5(0(1(5(x1))))))))))
   0(4(0(1(5(5(4(3(3(0(2(x1))))))))))) -> 0(4(0(0(5(4(1(5(4(2(x1))))))))))
   0(4(2(3(2(3(0(2(5(5(1(x1))))))))))) -> 4(0(4(0(1(2(2(4(1(4(x1))))))))))
   1(1(1(1(2(5(0(2(5(4(3(x1))))))))))) -> 5(5(5(5(1(4(2(4(1(3(x1))))))))))
   1(2(1(4(0(3(1(4(4(0(4(x1))))))))))) -> 3(5(1(4(0(4(3(3(3(2(x1))))))))))
   1(2(3(0(0(4(2(1(1(4(1(x1))))))))))) -> 1(2(3(0(4(0(2(1(1(4(1(x1)))))))))))
   1(3(0(2(2(1(0(2(2(0(4(x1))))))))))) -> 0(0(0(4(0(0(0(0(5(5(x1))))))))))
   1(3(2(0(4(0(5(4(1(4(2(x1))))))))))) -> 2(1(0(1(1(5(2(5(3(1(x1))))))))))
   1(3(5(0(4(0(0(3(5(3(1(x1))))))))))) -> 1(3(5(2(4(0(3(3(1(3(x1))))))))))
   1(4(0(2(1(1(4(0(1(5(3(x1))))))))))) -> 4(0(1(1(1(5(3(1(2(3(x1))))))))))

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