Derivational Complexity: TRS pair #487102638

details

property	value
status	complete
benchmark	26943.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)	297.717 seconds
cpu usage	965.213
user time	956.321
system time	8.89215
max virtual memory	1.8775744E7
max residence set size	1.5219052E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 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), 1365 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 37 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1565 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 185 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 119 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 862 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 7 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5783 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1665 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1619 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1655 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1661 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1644 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1626 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3782 ms]
        (60) 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(2(0(3(2(4(5(x1)))))))) -> 0(1(0(3(2(2(4(5(x1))))))))
   0(4(2(1(1(1(2(5(1(x1))))))))) -> 0(4(2(2(1(1(5(1(1(x1)))))))))
   0(2(3(1(0(1(5(3(5(2(x1)))))))))) -> 0(2(1(3(0(1(5(3(5(2(x1))))))))))
   1(2(2(0(5(3(2(5(0(4(x1)))))))))) -> 1(2(2(5(0(3(2(5(0(4(x1))))))))))
   4(4(4(5(0(4(2(1(1(0(x1)))))))))) -> 3(2(2(0(5(5(2(4(2(0(x1))))))))))
   0(2(0(3(5(1(0(5(4(0(3(x1))))))))))) -> 5(2(4(3(0(5(4(2(2(2(x1))))))))))
   0(2(5(4(0(5(0(4(0(4(5(x1))))))))))) -> 2(4(2(4(1(2(5(0(5(4(x1))))))))))
   0(4(1(3(4(2(4(3(0(2(4(x1))))))))))) -> 2(4(2(5(4(1(3(5(4(4(x1))))))))))
   0(4(2(3(1(4(5(0(2(2(0(x1))))))))))) -> 1(0(1(4(3(2(1(5(3(3(x1))))))))))
   0(4(3(4(3(3(4(5(5(2(0(x1))))))))))) -> 5(0(4(0(1(2(4(1(3(3(x1))))))))))
   0(4(5(4(1(2(4(4(3(2(3(x1))))))))))) -> 5(5(0(5(0(4(4(5(0(3(x1))))))))))
   0(5(2(5(5(1(5(5(0(2(2(x1))))))))))) -> 0(5(2(3(1(3(2(0(2(3(x1))))))))))
   0(5(3(1(5(3(2(3(0(5(1(x1))))))))))) -> 4(3(0(4(0(2(5(5(5(1(x1))))))))))
   1(0(1(1(4(2(3(4(1(1(3(x1))))))))))) -> 1(3(0(0(0(0(1(2(1(0(x1))))))))))
   1(1(4(3(2(5(1(0(4(3(0(x1))))))))))) -> 5(3(2(0(4(5(2(4(4(3(x1))))))))))
   1(3(0(5(4(1(2(2(5(4(1(x1))))))))))) -> 2(0(5(3(5(5(3(3(4(5(x1))))))))))
   1(3(1(0(1(2(5(0(1(5(4(x1))))))))))) -> 0(4(1(2(5(3(3(2(0(3(x1))))))))))
   1(3(1(5(0(1(4(0(3(3(4(x1))))))))))) -> 4(1(4(1(1(2(4(1(4(5(x1))))))))))
   1(4(2(0(2(3(5(4(5(3(2(x1))))))))))) -> 2(5(4(1(1(1(3(1(5(4(x1))))))))))
   1(4(3(3(2(4(5(4(4(1(2(x1))))))))))) -> 4(3(2(2(4(3(3(5(3(0(x1))))))))))
   1(5(3(0(5(5(1(4(4(5(5(x1))))))))))) -> 4(4(0(1(1(1(0(0(4(4(x1))))))))))

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