Derivational Complexity: TRS pair #487102716

details

property	value
status	complete
benchmark	26978.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.801 seconds
cpu usage	885.123
user time	877.34
system time	7.78279
max virtual memory	1.8974508E7
max residence set size	1.5056836E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 43 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), 1244 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 24 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), 1840 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 154 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 106 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), 860 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 5 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5350 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1555 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1564 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1564 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1497 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1505 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1512 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(0(x1))))) -> 0(1(0(2(0(x1)))))
   2(0(0(3(1(1(4(x1))))))) -> 2(0(0(1(3(4(1(x1)))))))
   3(2(0(2(4(0(3(2(3(x1))))))))) -> 3(2(0(2(2(3(4(0(3(x1)))))))))
   0(3(0(0(1(0(4(4(0(2(x1)))))))))) -> 1(4(3(5(4(2(0(1(0(2(x1))))))))))
   1(2(0(3(4(0(0(2(5(4(x1)))))))))) -> 1(2(1(5(4(5(5(1(1(1(x1))))))))))
   2(0(1(4(0(0(4(3(5(4(x1)))))))))) -> 2(0(1(0(4(0(4(3(5(4(x1))))))))))
   2(5(4(0(4(5(0(0(0(2(x1)))))))))) -> 3(5(3(0(1(4(1(1(3(1(x1))))))))))
   3(4(0(0(5(3(1(3(4(3(x1)))))))))) -> 3(4(3(1(0(4(3(5(1(3(x1))))))))))
   0(0(3(2(0(5(5(3(1(3(3(x1))))))))))) -> 0(2(3(3(1(2(1(2(3(4(x1))))))))))
   0(1(1(2(4(0(2(2(2(3(5(x1))))))))))) -> 0(4(5(5(1(5(2(4(5(1(x1))))))))))
   0(1(3(1(0(4(0(1(2(0(4(x1))))))))))) -> 4(5(4(3(5(5(3(2(4(2(x1))))))))))
   0(1(4(1(4(1(4(4(1(0(0(x1))))))))))) -> 3(0(3(5(2(4(5(1(0(0(x1))))))))))
   0(1(5(2(4(4(1(3(2(1(1(x1))))))))))) -> 4(3(3(2(3(3(3(4(0(4(x1))))))))))
   0(3(1(2(4(5(3(5(2(4(2(x1))))))))))) -> 0(4(3(0(2(4(2(1(4(3(x1))))))))))
   0(3(3(2(3(4(5(3(1(1(4(x1))))))))))) -> 3(3(5(5(3(5(0(0(4(0(x1))))))))))
   0(4(1(4(5(0(3(5(1(3(4(x1))))))))))) -> 1(2(1(4(2(1(4(0(3(4(x1))))))))))
   0(4(4(1(1(0(2(4(1(3(5(x1))))))))))) -> 0(3(2(2(0(0(1(1(0(2(x1))))))))))
   0(4(5(3(0(4(3(1(2(1(4(x1))))))))))) -> 3(0(4(5(2(5(2(4(3(5(x1))))))))))
   0(4(5(3(3(5(4(4(2(2(4(x1))))))))))) -> 1(4(0(1(2(2(2(5(0(3(x1))))))))))
   1(1(2(2(0(4(3(0(1(4(2(x1))))))))))) -> 0(2(5(2(3(0(5(2(5(3(x1))))))))))
   1(2(2(4(5(2(3(0(2(2(2(x1))))))))))) -> 5(1(3(0(1(2(4(0(2(5(x1))))))))))
   1(5(0(1(4(3(0(3(4(3(1(x1))))))))))) -> 4(3(5(0(5(0(3(4(0(4(x1))))))))))
   2(1(1(5(5(5(3(4(3(3(0(x1))))))))))) -> 4(5(5(3(3(4(4(0(0(4(x1))))))))))

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