Derivational Complexity: TRS pair #487102934

details

property	value
status	complete
benchmark	25422.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)	293.014 seconds
cpu usage	824.886
user time	817.469
system time	7.41683
max virtual memory	1.8772416E7
max residence set size	1.45347E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 42 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), 1404 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), 6 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1914 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 158 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 139 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 11 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 797 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 13 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 1 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5476 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1657 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1675 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1667 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1657 ms]
        (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(3(3(3(0(x1))))))) -> 0(1(3(2(3(3(0(x1)))))))
   0(3(1(4(4(4(0(0(x1)))))))) -> 0(3(4(4(1(4(0(0(x1))))))))
   2(4(2(4(5(3(3(2(x1)))))))) -> 2(3(4(4(5(2(3(2(x1))))))))
   5(3(5(3(4(2(0(2(x1)))))))) -> 5(3(5(3(2(4(0(2(x1))))))))
   1(4(4(1(5(4(4(1(4(x1))))))))) -> 1(4(4(1(4(5(4(1(4(x1)))))))))
   3(3(5(4(1(1(4(2(1(x1))))))))) -> 3(3(4(1(5(1(4(2(1(x1)))))))))
   0(4(4(3(3(1(1(4(3(3(x1)))))))))) -> 4(4(1(2(4(0(3(1(5(3(x1))))))))))
   4(0(3(1(4(5(4(4(5(1(x1)))))))))) -> 4(0(3(1(4(4(5(4(5(1(x1))))))))))
   0(0(0(3(3(3(3(4(3(2(2(x1))))))))))) -> 1(3(3(3(0(5(5(3(4(3(x1))))))))))
   0(1(3(4(3(2(0(3(2(1(3(x1))))))))))) -> 1(2(2(5(1(0(2(0(0(4(x1))))))))))
   0(1(5(5(0(2(0(0(2(4(2(x1))))))))))) -> 0(4(3(0(1(0(2(2(2(0(x1))))))))))
   0(3(3(4(2(5(4(5(1(2(5(x1))))))))))) -> 2(5(4(4(2(1(5(3(4(4(x1))))))))))
   0(3(4(4(0(5(5(3(0(4(5(x1))))))))))) -> 3(4(5(5(2(3(2(3(0(4(x1))))))))))
   0(4(5(0(1(2(0(0(0(4(3(x1))))))))))) -> 4(0(3(4(0(1(2(3(2(5(x1))))))))))
   0(4(5(0(4(5(0(5(2(2(5(x1))))))))))) -> 1(5(4(3(1(0(3(3(4(0(x1))))))))))
   0(5(4(5(4(0(4(2(1(1(5(x1))))))))))) -> 0(4(0(1(3(2(5(5(3(3(x1))))))))))
   1(1(1(4(2(3(5(1(4(5(2(x1))))))))))) -> 0(3(3(5(2(3(4(2(5(4(x1))))))))))
   2(0(2(4(1(4(2(5(2(3(2(x1))))))))))) -> 0(1(5(3(3(4(4(3(0(5(x1))))))))))
   2(0(5(2(5(5(5(3(2(2(4(x1))))))))))) -> 4(5(1(2(2(1(3(5(0(1(x1))))))))))
   2(1(2(5(2(0(0(3(0(5(0(x1))))))))))) -> 0(3(2(1(1(3(1(3(1(0(x1))))))))))
   2(1(5(0(1(3(5(0(3(5(1(x1))))))))))) -> 4(2(4(1(5(3(2(5(5(2(x1))))))))))
   2(3(2(3(0(1(0(3(0(5(2(x1))))))))))) -> 2(0(1(1(1(5(3(2(1(1(x1))))))))))
   2(3(4(1(5(1(2(0(1(0(2(x1))))))))))) -> 1(2(5(4(2(1(1(1(3(3(x1))))))))))
   2(3(4(3(0(0(4(0(4(3(3(x1))))))))))) -> 2(5(2(4(4(5(2(5(1(0(x1))))))))))
   2(3(5(3(1(5(0(1(2(0(1(x1))))))))))) -> 2(0(1(1(5(0(3(3(2(5(1(x1)))))))))))
   2(5(0(1(2(0(3(4(5(0(1(x1))))))))))) -> 2(5(0(1(0(2(3(5(0(4(1(x1)))))))))))
   3(0(2(2(2(0(0(1(4(1(1(x1))))))))))) -> 3(0(2(0(2(2(0(1(4(1(1(x1)))))))))))

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