Derivational Complexity: TRS pair #487103544

details

property	value
status	complete
benchmark	167294.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.496 seconds
cpu usage	1166.47
user time	1160.31
system time	6.15696
max virtual memory	1.909954E7
max residence set size	1.2017076E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 32 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 8 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 10 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), 2694 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 48 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), 5785 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 18 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 2500 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 20 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 19.4 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6008 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6054 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6094 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13.7 s]
        (54) 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(x1))) -> 1(1(2(1(2(x1)))))
   0(1(0(2(x1)))) -> 0(0(2(1(x1))))
   1(0(0(0(x1)))) -> 1(2(1(1(1(1(0(0(x1))))))))
   1(2(2(0(x1)))) -> 2(1(1(1(0(x1)))))
   2(1(2(0(x1)))) -> 2(2(1(1(0(x1)))))
   0(0(1(2(0(x1))))) -> 1(2(1(2(1(1(1(0(x1))))))))
   1(0(2(0(0(x1))))) -> 1(1(1(1(1(1(0(1(1(x1)))))))))
   0(1(0(2(1(0(2(x1))))))) -> 1(2(1(1(0(1(0(2(x1))))))))
   2(1(0(0(0(2(0(x1))))))) -> 1(1(2(0(2(1(1(1(x1))))))))
   1(0(0(1(0(2(1(2(x1)))))))) -> 1(0(1(1(2(1(1(2(0(1(x1))))))))))
   2(0(0(1(1(2(2(0(x1)))))))) -> 2(0(1(1(1(1(2(1(1(2(0(2(x1))))))))))))
   2(2(2(2(0(2(0(1(x1)))))))) -> 2(1(1(2(1(2(2(2(1(1(1(1(x1))))))))))))
   0(1(2(2(2(2(0(0(1(x1))))))))) -> 2(1(1(0(2(2(0(0(2(x1)))))))))
   0(2(0(2(0(2(1(2(2(x1))))))))) -> 1(1(2(1(2(2(2(2(2(2(x1))))))))))
   0(0(2(2(1(0(2(0(1(1(x1)))))))))) -> 1(1(1(1(0(1(0(1(1(1(1(1(x1))))))))))))
   0(1(1(2(2(2(1(2(0(0(x1)))))))))) -> 2(2(0(1(2(1(1(1(2(1(1(1(1(x1)))))))))))))
   0(2(0(2(2(1(2(0(2(0(x1)))))))))) -> 0(0(0(1(2(1(1(0(1(2(2(x1)))))))))))
   1(0(2(0(2(1(0(2(2(2(x1)))))))))) -> 1(1(1(0(1(2(2(1(1(0(2(1(0(1(1(x1)))))))))))))))
   1(1(2(0(0(0(2(2(2(2(x1)))))))))) -> 1(2(1(1(1(1(1(2(1(0(0(2(2(x1)))))))))))))
   2(1(2(1(1(2(0(0(2(1(x1)))))))))) -> 1(2(1(1(0(2(2(2(1(1(1(x1)))))))))))
   2(2(0(1(0(0(0(0(2(0(x1)))))))))) -> 2(2(1(0(1(1(0(1(2(2(1(2(1(1(1(x1)))))))))))))))
   1(0(1(2(1(1(2(2(1(1(2(x1))))))))))) -> 1(1(1(1(1(1(1(1(0(2(0(1(1(1(2(1(x1))))))))))))))))
   2(0(2(2(2(2(2(0(1(2(0(x1))))))))))) -> 2(2(0(0(2(1(1(1(2(1(1(0(1(x1)))))))))))))
   0(1(2(2(2(2(0(0(1(1(1(2(x1)))))))))))) -> 1(1(0(1(0(1(0(0(1(1(1(1(1(1(x1))))))))))))))
   1(1(2(2(0(2(0(1(2(1(0(2(x1)))))))))))) -> 1(1(1(1(2(0(1(1(1(2(2(2(0(x1)))))))))))))
   2(1(2(1(0(0(2(0(1(0(0(0(x1)))))))))))) -> 1(1(2(2(1(0(1(2(1(1(0(2(1(1(0(1(x1))))))))))))))))
   2(2(0(2(0(1(2(0(2(0(0(0(x1)))))))))))) -> 2(1(1(2(2(2(1(2(2(2(0(2(1(1(0(x1)))))))))))))))

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