Derivational Complexity: TRS pair #487103220

details

property	value
status	complete
benchmark	26957.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.453 seconds
cpu usage	795.339
user time	787.523
system time	7.81641
max virtual memory	1.8974884E7
max residence set size	1.4988564E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 56 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 5 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 13 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
(13) RelTrsToTrsProof [UPPER BOUND(ID), 1 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1487 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 32 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), 2020 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 124 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 177 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 21 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 828 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), 6419 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1976 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1981 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1921 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1928 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1913 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(2(3(1(2(4(0(x1)))))))) -> 0(1(2(3(2(1(4(0(x1))))))))
   1(5(1(3(0(3(1(2(5(x1))))))))) -> 1(5(1(0(1(3(2(3(5(x1)))))))))
   3(5(0(2(4(4(4(5(0(x1))))))))) -> 3(2(4(4(0(5(4(5(0(x1)))))))))
   4(1(2(1(4(0(2(2(3(x1))))))))) -> 4(1(1(2(0(4(2(2(3(x1)))))))))
   0(3(1(0(0(4(5(3(0(3(x1)))))))))) -> 5(4(0(0(5(2(5(1(0(3(x1))))))))))
   1(1(3(1(0(1(2(1(2(1(x1)))))))))) -> 1(1(0(1(1(3(2(1(2(1(x1))))))))))
   1(3(4(4(2(0(3(1(3(2(x1)))))))))) -> 4(3(2(1(1(2(2(5(2(5(x1))))))))))
   4(3(4(3(0(2(4(3(1(3(x1)))))))))) -> 4(1(2(2(3(5(4(2(5(5(x1))))))))))
   4(4(0(5(0(1(0(0(5(2(x1)))))))))) -> 1(2(5(0(2(4(5(2(2(2(x1))))))))))
   5(4(0(5(3(3(0(0(0(0(x1)))))))))) -> 5(4(0(5(3(0(3(0(0(0(x1))))))))))
   0(0(1(0(0(3(0(5(0(4(2(x1))))))))))) -> 5(0(0(3(2(0(2(1(3(0(x1))))))))))
   0(0(1(1(5(1(1(5(3(2(0(x1))))))))))) -> 0(5(5(2(1(2(0(4(3(2(x1))))))))))
   0(0(5(5(5(4(0(0(3(5(2(x1))))))))))) -> 1(0(4(2(1(0(4(0(4(3(x1))))))))))
   1(0(3(3(2(2(2(2(2(4(3(x1))))))))))) -> 4(0(4(3(1(1(2(3(2(3(x1))))))))))
   1(0(5(1(2(4(3(4(4(5(2(x1))))))))))) -> 0(3(2(5(1(1(1(1(0(3(x1))))))))))
   2(0(3(0(1(3(2(1(1(2(0(x1))))))))))) -> 2(0(2(1(0(2(5(3(0(3(x1))))))))))
   2(1(5(0(0(3(1(3(5(0(3(x1))))))))))) -> 2(5(3(2(3(1(5(2(2(4(x1))))))))))
   2(3(2(4(1(5(3(4(4(1(5(x1))))))))))) -> 5(2(0(1(3(3(3(5(5(2(x1))))))))))
   3(0(2(1(0(1(4(0(1(4(2(x1))))))))))) -> 5(2(2(2(5(4(2(2(3(4(x1))))))))))
   3(1(1(5(5(5(0(0(2(0(3(x1))))))))))) -> 0(0(0(4(5(5(4(2(1(5(x1))))))))))
   3(2(2(5(3(3(3(0(2(4(2(x1))))))))))) -> 3(2(2(5(3(3(0(3(2(4(2(x1)))))))))))
   3(3(5(4(1(0(2(2(2(3(0(x1))))))))))) -> 0(0(2(3(2(1(0(2(2(0(x1))))))))))
   3(4(0(3(2(3(2(2(3(5(3(x1))))))))))) -> 4(2(4(4(1(2(4(3(3(4(x1))))))))))
   3(4(0(5(3(1(5(1(1(0(3(x1))))))))))) -> 1(1(5(2(3(2(2(0(4(5(x1))))))))))
   3(4(1(2(1(1(4(3(0(0(1(x1))))))))))) -> 3(1(2(5(4(4(4(5(5(5(x1))))))))))

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