Derivational Complexity: TRS pair #487102740

details

property	value
status	complete
benchmark	25409.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.386 seconds
cpu usage	830.598
user time	822.81
system time	7.78791
max virtual memory	1.8776828E7
max residence set size	1.4798144E7

stage attributes

key	value
starexec-result	KILLED

output

KILLED
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 44 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), 1368 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 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), 2036 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 144 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 155 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 26 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 1004 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 3 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6728 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2021 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2030 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2013 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1991 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2038 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(0(1(2(3(x1)))))) -> 0(0(1(0(2(3(x1))))))
   0(2(4(1(4(1(0(1(5(x1))))))))) -> 0(2(4(4(0(1(1(1(5(x1)))))))))
   5(4(4(0(0(1(1(2(0(x1))))))))) -> 5(4(1(4(0(2(0(1(0(x1)))))))))
   0(3(1(2(4(3(4(3(3(4(x1)))))))))) -> 0(3(1(2(4(4(3(3(3(4(x1))))))))))
   0(5(4(4(3(4(0(0(1(0(x1)))))))))) -> 0(5(4(4(0(4(3(0(1(0(x1))))))))))
   0(1(3(5(4(1(3(5(4(5(1(x1))))))))))) -> 4(4(4(5(4(3(1(4(1(0(x1))))))))))
   0(2(2(0(1(2(1(0(4(4(2(x1))))))))))) -> 4(5(4(4(5(5(4(5(5(5(x1))))))))))
   0(2(2(1(0(3(5(5(5(0(4(x1))))))))))) -> 0(0(1(0(5(3(0(3(2(0(x1))))))))))
   0(4(1(0(4(3(2(4(3(0(1(x1))))))))))) -> 3(2(0(5(0(2(5(3(1(4(x1))))))))))
   0(4(1(4(4(2(0(1(1(5(2(x1))))))))))) -> 5(3(1(2(4(3(4(3(4(5(x1))))))))))
   0(4(2(4(1(3(0(1(0(2(1(x1))))))))))) -> 3(0(1(5(3(5(3(5(2(4(x1))))))))))
   0(4(4(1(4(3(1(4(0(3(3(x1))))))))))) -> 1(2(2(1(1(4(3(1(3(4(x1))))))))))
   0(4(5(4(2(4(5(5(5(1(2(x1))))))))))) -> 5(2(5(4(2(2(3(5(1(5(x1))))))))))
   0(5(5(3(1(1(5(0(3(1(0(x1))))))))))) -> 4(0(4(1(0(1(4(0(5(1(x1))))))))))
   1(2(2(1(0(3(1(4(2(2(2(x1))))))))))) -> 4(2(5(0(0(2(5(2(4(3(x1))))))))))
   1(2(3(2(0(1(0(3(1(5(5(x1))))))))))) -> 2(4(1(3(0(0(1(0(1(2(x1))))))))))
   1(2(3(4(2(5(1(2(3(3(1(x1))))))))))) -> 0(2(5(1(1(2(3(2(0(0(x1))))))))))
   1(2(5(5(2(4(3(0(1(0(4(x1))))))))))) -> 2(4(4(4(3(2(2(0(0(3(x1))))))))))
   1(3(2(0(0(5(0(3(2(3(5(x1))))))))))) -> 3(0(2(4(4(2(2(1(3(4(x1))))))))))
   1(4(3(5(4(5(1(3(4(0(4(x1))))))))))) -> 4(3(4(2(0(1(5(3(1(3(x1))))))))))
   1(5(0(2(2(5(4(4(0(4(2(x1))))))))))) -> 1(3(3(2(2(0(1(2(4(2(x1))))))))))
   1(5(4(2(3(1(5(5(0(2(3(x1))))))))))) -> 0(3(1(3(4(2(2(0(0(0(x1))))))))))
   2(0(0(4(2(4(0(2(0(0(0(x1))))))))))) -> 4(5(1(5(1(2(4(1(2(2(x1))))))))))
   2(0(2(1(0(4(4(0(4(2(5(x1))))))))))) -> 4(0(1(1(2(1(1(4(3(5(x1))))))))))
   2(0(3(1(1(0(0(5(1(0(1(x1))))))))))) -> 4(3(2(3(5(2(5(1(3(1(x1))))))))))

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actions all output return to Derivational Complexity: TRS