Derivational Complexity: TRS pair #487103040

details

property	value
status	complete
benchmark	26132.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.696 seconds
cpu usage	988.351
user time	980.313
system time	8.03881
max virtual memory	1.87226E7
max residence set size	1.4989352E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 41 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), 4 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), 1546 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 38 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 2 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2618 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 242 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 164 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 997 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 13 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 10 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7782 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2208 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2204 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2237 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2189 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2154 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2262 ms]
        (58) 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(3(4(x1)))))) -> 0(2(1(3(3(4(x1))))))
   4(4(3(0(4(2(4(x1))))))) -> 4(4(3(4(0(2(4(x1)))))))
   3(1(2(0(0(4(3(2(x1)))))))) -> 3(1(0(2(0(4(3(2(x1))))))))
   0(1(2(4(3(0(2(0(3(x1))))))))) -> 0(2(1(4(3(0(2(0(3(x1)))))))))
   0(5(5(3(5(3(0(5(3(3(x1)))))))))) -> 0(5(5(3(3(5(0(5(3(3(x1))))))))))
   2(1(2(4(5(4(1(2(5(0(x1)))))))))) -> 3(1(1(1(0(1(4(1(5(0(x1))))))))))
   2(4(4(2(0(2(1(5(4(5(x1)))))))))) -> 1(1(2(1(5(5(5(2(4(5(x1))))))))))
   4(1(1(1(0(0(0(0(2(0(x1)))))))))) -> 4(1(1(0(1(0(0(0(2(0(x1))))))))))
   4(4(1(5(1(1(0(0(4(3(x1)))))))))) -> 4(2(1(3(2(1(0(0(4(3(x1))))))))))
   0(0(5(3(1(3(0(2(2(2(3(x1))))))))))) -> 4(1(2(0(2(3(1(4(3(0(x1))))))))))
   0(5(1(0(4(5(5(3(4(1(3(x1))))))))))) -> 1(3(2(2(1(3(0(0(0(3(x1))))))))))
   0(5(1(4(5(2(2(4(4(5(1(x1))))))))))) -> 1(0(1(2(5(0(1(0(0(4(x1))))))))))
   0(5(3(2(4(4(3(1(1(5(0(x1))))))))))) -> 3(5(0(3(0(5(1(0(4(1(x1))))))))))
   1(1(4(5(3(4(5(5(3(2(0(x1))))))))))) -> 5(3(0(2(1(5(1(0(3(3(x1))))))))))
   1(2(4(3(0(2(3(0(0(5(1(x1))))))))))) -> 1(1(3(1(5(2(5(0(4(3(x1))))))))))
   1(5(1(3(4(4(3(3(5(4(2(x1))))))))))) -> 3(4(0(0(2(1(3(3(2(0(x1))))))))))
   2(0(0(0(4(1(1(2(4(3(3(x1))))))))))) -> 5(5(2(2(2(4(5(0(1(5(x1))))))))))
   2(0(4(5(4(4(4(5(3(2(4(x1))))))))))) -> 3(4(0(0(3(4(2(3(0(1(x1))))))))))
   2(2(3(1(1(4(4(5(5(3(5(x1))))))))))) -> 1(2(1(0(3(4(4(3(1(5(x1))))))))))
   2(5(5(1(4(4(0(2(0(4(2(x1))))))))))) -> 5(4(0(1(3(3(4(5(5(4(x1))))))))))
   3(0(0(4(3(1(5(4(2(2(1(x1))))))))))) -> 3(4(2(3(4(0(1(4(2(5(x1))))))))))
   3(0(5(5(1(4(5(1(0(2(2(x1))))))))))) -> 5(4(1(4(5(2(0(4(0(3(x1))))))))))
   3(1(0(2(2(5(0(0(2(3(2(x1))))))))))) -> 4(0(5(2(4(0(5(3(1(2(x1))))))))))

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