Derivational Complexity: TRS pair #487102684

details

property	value
status	complete
benchmark	27028.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.998 seconds
cpu usage	889.418
user time	881.617
system time	7.80077
max virtual memory	1.8705756E7
max residence set size	1.5141664E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 50 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), 1454 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 17 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 12 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1735 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 181 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 145 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 7 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 27 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 747 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 10 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5744 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1636 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1660 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1627 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1576 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1644 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1636 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(0(3(3(0(0(x1)))))))) -> 0(1(2(3(0(3(0(0(x1))))))))
   2(3(4(0(3(5(4(5(x1)))))))) -> 2(3(4(3(0(5(4(5(x1))))))))
   3(2(4(1(3(2(4(4(x1)))))))) -> 3(2(4(2(3(1(4(4(x1))))))))
   4(1(0(2(5(1(4(4(x1)))))))) -> 2(4(1(1(4(5(0(4(x1))))))))
   5(2(4(3(2(1(4(4(4(x1))))))))) -> 5(4(2(2(3(1(4(4(4(x1)))))))))
   2(0(1(1(4(4(5(2(5(5(x1)))))))))) -> 3(1(3(1(1(3(2(5(5(5(x1))))))))))
   2(1(2(1(1(1(0(1(0(5(x1)))))))))) -> 2(1(2(1(1(0(1(1(0(5(x1))))))))))
   5(5(4(5(5(5(3(2(5(3(x1)))))))))) -> 3(1(4(3(1(0(3(2(2(3(x1))))))))))
   0(0(0(0(4(4(1(2(4(0(3(x1))))))))))) -> 5(3(2(4(3(3(5(3(4(4(x1))))))))))
   0(0(0(2(4(0(1(2(0(2(2(x1))))))))))) -> 3(1(3(5(2(5(5(4(3(1(x1))))))))))
   0(0(1(0(3(3(2(2(1(5(4(x1))))))))))) -> 2(0(3(1(2(4(0(3(4(1(x1))))))))))
   0(1(0(4(2(0(1(5(4(0(4(x1))))))))))) -> 3(1(0(2(0(3(1(5(1(4(x1))))))))))
   0(1(1(0(2(0(2(3(2(5(0(x1))))))))))) -> 1(4(0(0(4(3(0(5(1(2(x1))))))))))
   0(1(4(5(3(4(1(0(3(3(5(x1))))))))))) -> 0(5(0(4(4(5(0(2(4(3(x1))))))))))
   0(2(2(0(5(3(0(1(2(3(1(x1))))))))))) -> 2(2(3(5(4(4(0(5(2(1(x1))))))))))
   0(2(4(2(0(3(0(1(2(5(1(x1))))))))))) -> 1(4(0(2(1(4(4(0(5(1(x1))))))))))
   0(5(2(5(2(1(4(1(4(2(1(x1))))))))))) -> 3(4(2(3(0(2(5(1(2(1(x1))))))))))
   1(0(0(5(0(2(0(2(0(5(0(x1))))))))))) -> 3(2(1(3(3(3(0(5(5(5(x1))))))))))
   1(0(1(2(4(1(1(1(2(5(4(x1))))))))))) -> 1(4(1(4(3(5(3(1(1(1(x1))))))))))
   1(2(0(0(2(2(1(5(4(4(3(x1))))))))))) -> 4(4(0(2(3(2(2(1(1(2(x1))))))))))
   1(4(0(5(5(4(2(1(4(4(5(x1))))))))))) -> 0(3(4(5(5(0(1(2(2(1(x1))))))))))
   1(5(3(4(2(5(5(0(4(5(3(x1))))))))))) -> 4(4(3(1(5(4(4(2(0(5(x1))))))))))
   2(0(4(0(3(1(5(3(3(2(5(x1))))))))))) -> 2(2(3(1(2(1(4(1(3(0(x1))))))))))

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