Derivational Complexity: TRS pair #487102764

details

property	value
status	complete
benchmark	26969.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)	297.162 seconds
cpu usage	895.032
user time	887.761
system time	7.27115
max virtual memory	3.6710348E7
max residence set size	1.5156388E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 47 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 4 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 ms]
(12) TRS for Loop Detection
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1428 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 17 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2282 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 187 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 159 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 12 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 920 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 9 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6692 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1974 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1953 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1941 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1999 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1952 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1987 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(2(0(3(2(4(x1)))))))) -> 0(1(2(2(3(2(0(4(x1))))))))
   5(2(4(0(0(3(2(0(x1)))))))) -> 5(2(4(3(0(0(2(0(x1))))))))
   1(3(3(4(1(5(3(4(4(x1))))))))) -> 1(3(3(4(1(3(5(4(4(x1)))))))))
   3(2(2(2(5(1(5(5(2(x1))))))))) -> 3(2(5(2(1(2(5(5(2(x1)))))))))
   0(0(4(1(5(4(3(4(5(5(x1)))))))))) -> 0(0(4(1(5(3(4(4(5(5(x1))))))))))
   0(4(1(2(3(5(4(0(1(3(x1)))))))))) -> 1(3(4(4(5(3(3(4(4(3(x1))))))))))
   2(3(2(5(5(1(2(0(3(2(x1)))))))))) -> 2(3(2(5(1(5(2(0(3(2(x1))))))))))
   3(1(0(0(0(3(5(1(1(5(x1)))))))))) -> 1(3(1(1(4(5(3(4(1(4(x1))))))))))
   4(1(3(0(5(0(5(1(3(5(x1)))))))))) -> 4(2(1(5(2(0(1(4(3(5(x1))))))))))
   4(2(0(3(1(5(3(4(5(5(x1)))))))))) -> 4(1(3(3(4(4(4(3(4(2(x1))))))))))
   0(2(1(1(1(2(3(3(2(3(5(x1))))))))))) -> 1(5(2(0(2(3(4(1(4(4(x1))))))))))
   0(3(0(3(5(1(5(1(0(2(2(x1))))))))))) -> 0(2(3(1(2(0(0(5(3(5(1(x1)))))))))))
   0(4(1(4(4(1(1(4(5(3(5(x1))))))))))) -> 0(4(1(4(4(1(5(1(4(3(5(x1)))))))))))
   0(4(5(3(3(2(2(4(5(5(1(x1))))))))))) -> 0(4(5(3(2(3(2(4(5(5(1(x1)))))))))))
   0(5(3(5(1(1(0(1(3(0(2(x1))))))))))) -> 4(5(1(1(1(1(1(0(5(3(x1))))))))))
   1(0(1(3(5(3(4(5(4(5(4(x1))))))))))) -> 2(4(3(4(0(0(1(5(2(1(x1))))))))))
   1(2(4(2(2(5(5(5(5(3(4(x1))))))))))) -> 2(0(4(2(4(0(3(1(4(1(x1))))))))))
   1(3(1(4(0(3(2(0(5(3(4(x1))))))))))) -> 1(3(2(4(1(0(1(4(5(1(x1))))))))))
   1(3(5(5(1(5(4(1(3(5(4(x1))))))))))) -> 2(4(3(5(3(3(0(5(2(2(x1))))))))))
   2(0(3(3(0(1(5(2(3(2(5(x1))))))))))) -> 5(3(0(3(4(1(5(0(1(3(x1))))))))))
   2(0(4(3(0(5(0(0(4(4(5(x1))))))))))) -> 4(1(1(5(5(2(0(4(2(4(x1))))))))))
   2(0(4(4(3(2(5(4(1(4(3(x1))))))))))) -> 3(3(1(5(4(3(0(1(4(2(x1))))))))))
   2(1(3(4(1(1(2(5(0(3(2(x1))))))))))) -> 4(1(3(1(2(0(3(2(3(0(x1))))))))))

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