Derivational Complexity: TRS pair #487103568

details

property	value
status	complete
benchmark	25726.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.477 seconds
cpu usage	819.0
user time	811.355
system time	7.64483
max virtual memory	1.8775808E7
max residence set size	1.5271284E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 43 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), 23 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), 1201 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 17 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1851 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 162 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 129 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 5 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 845 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5810 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1725 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1738 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1706 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1727 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1739 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(0(1(2(0(1(x1)))))) -> 0(0(2(1(0(1(x1))))))
   2(2(0(3(2(2(3(x1))))))) -> 2(0(2(3(2(2(3(x1)))))))
   4(3(0(1(0(1(2(5(5(x1))))))))) -> 4(3(0(1(2(0(1(5(5(x1)))))))))
   4(3(4(0(2(2(2(4(2(x1))))))))) -> 4(3(4(2(2(0(2(4(2(x1)))))))))
   0(1(2(0(3(1(3(0(4(3(x1)))))))))) -> 0(2(1(2(0(4(4(2(4(4(x1))))))))))
   0(5(4(4(1(1(5(1(1(2(x1)))))))))) -> 0(5(5(4(1(1(1(4(1(2(x1))))))))))
   1(3(1(1(1(1(1(5(2(5(x1)))))))))) -> 1(3(5(2(0(2(2(3(4(4(x1))))))))))
   1(3(4(1(1(3(5(0(2(1(x1)))))))))) -> 1(1(4(0(0(0(4(0(3(1(x1))))))))))
   4(4(2(4(4(3(3(4(5(1(x1)))))))))) -> 4(4(2(2(2(4(4(2(0(2(x1))))))))))
   4(5(4(5(2(5(4(1(2(2(x1)))))))))) -> 4(5(4(5(5(2(4(1(2(2(x1))))))))))
   5(2(3(5(5(5(5(4(2(2(x1)))))))))) -> 3(4(3(3(0(2(5(4(4(2(x1))))))))))
   0(2(3(3(0(3(5(0(0(4(2(x1))))))))))) -> 1(4(4(1(4(1(3(3(0(0(x1))))))))))
   0(4(0(2(3(2(3(0(3(4(3(x1))))))))))) -> 3(4(2(4(1(1(3(0(3(0(x1))))))))))
   0(4(0(3(4(3(1(1(4(1(3(x1))))))))))) -> 2(2(4(5(1(2(4(1(0(5(x1))))))))))
   1(1(0(0(4(1(5(0(3(3(0(x1))))))))))) -> 1(1(0(0(1(4(5(0(3(3(0(x1)))))))))))
   1(1(1(2(3(3(4(2(2(2(1(x1))))))))))) -> 4(0(0(1(3(0(0(4(3(3(x1))))))))))
   1(1(4(3(3(2(1(1(4(3(0(x1))))))))))) -> 0(0(3(0(0(5(2(1(0(4(x1))))))))))
   1(3(1(2(5(1(2(5(1(3(5(x1))))))))))) -> 0(2(3(2(1(5(5(2(4(0(x1))))))))))
   1(3(3(3(5(2(2(3(0(4(3(x1))))))))))) -> 0(2(1(4(2(4(1(4(5(1(x1))))))))))
   1(3(5(3(0(3(3(1(5(5(4(x1))))))))))) -> 4(5(3(5(3(5(2(2(1(2(x1))))))))))
   1(4(1(1(0(2(3(3(3(3(4(x1))))))))))) -> 5(1(0(0(4(5(0(5(2(2(x1))))))))))
   1(4(1(3(4(5(0(3(1(5(5(x1))))))))))) -> 3(2(4(5(2(2(1(3(0(5(x1))))))))))
   1(5(0(5(5(0(3(0(2(2(5(x1))))))))))) -> 2(0(3(3(4(5(2(2(2(5(x1))))))))))
   2(0(0(2(4(0(3(5(0(0(1(x1))))))))))) -> 2(0(0(0(0(4(2(5(3(0(1(x1)))))))))))
   2(5(0(1(3(2(4(3(3(4(3(x1))))))))))) -> 4(3(2(2(4(2(2(4(2(3(x1))))))))))

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