Derivational Complexity: TRS pair #487103458

details

property	value
status	complete
benchmark	25388.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.405 seconds
cpu usage	945.254
user time	937.947
system time	7.30735
max virtual memory	1.8845344E7
max residence set size	1.5077332E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 1492 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 30 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), 1763 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 115 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 107 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 35 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 929 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, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7035 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2004 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2010 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1988 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1906 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1959 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1876 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(2(2(3(x1)))))))) -> 0(0(1(3(2(2(2(3(x1))))))))
   0(3(4(3(0(5(4(3(x1)))))))) -> 0(3(4(5(0(3(4(3(x1))))))))
   2(1(0(4(4(0(3(3(5(x1))))))))) -> 2(1(0(4(0(4(3(3(5(x1)))))))))
   1(0(1(1(1(2(1(1(3(4(x1)))))))))) -> 1(2(5(1(5(0(2(4(3(1(x1))))))))))
   1(0(1(3(5(5(5(3(2(3(x1)))))))))) -> 1(2(4(2(1(0(3(5(5(4(x1))))))))))
   1(5(3(5(3(4(3(0(1(2(x1)))))))))) -> 3(0(4(5(5(1(3(3(1(2(x1))))))))))
   2(5(4(3(3(4(2(1(1(3(x1)))))))))) -> 2(1(0(0(5(4(3(4(2(5(x1))))))))))
   3(0(3(1(2(1(3(3(2(1(x1)))))))))) -> 4(2(4(5(2(5(0(4(0(1(x1))))))))))
   5(1(2(2(1(3(1(5(1(1(x1)))))))))) -> 3(1(0(5(0(4(1(4(3(1(x1))))))))))
   0(0(0(5(3(2(5(5(5(4(1(x1))))))))))) -> 0(4(4(1(3(2(5(4(2(3(x1))))))))))
   0(0(1(4(1(0(2(5(0(5(1(x1))))))))))) -> 0(0(4(1(1(0(2(5(0(5(1(x1)))))))))))
   0(0(5(5(5(4(5(1(1(3(3(x1))))))))))) -> 1(1(4(1(3(0(4(0(5(5(x1))))))))))
   0(1(2(3(2(1(2(4(0(5(4(x1))))))))))) -> 0(1(2(3(2(1(4(2(0(5(4(x1)))))))))))
   0(1(2(3(5(4(0(2(0(3(1(x1))))))))))) -> 4(5(2(3(2(1(3(3(4(2(x1))))))))))
   0(2(1(5(0(4(2(1(5(2(5(x1))))))))))) -> 0(5(4(5(1(4(3(1(2(3(x1))))))))))
   0(2(3(0(5(1(1(2(1(4(3(x1))))))))))) -> 1(3(5(4(1(4(1(5(5(5(x1))))))))))
   0(3(3(2(1(3(0(2(1(0(5(x1))))))))))) -> 4(1(3(4(4(1(2(2(3(2(x1))))))))))
   0(3(3(3(4(1(2(5(3(0(4(x1))))))))))) -> 0(2(2(3(2(4(0(2(1(3(x1))))))))))
   0(4(0(0(1(0(4(5(2(0(0(x1))))))))))) -> 0(4(0(0(0(1(4(5(2(0(0(x1)))))))))))
   0(5(1(4(0(1(3(2(1(0(3(x1))))))))))) -> 2(1(4(0(2(0(5(1(0(0(x1))))))))))
   1(2(2(0(4(0(5(3(1(4(4(x1))))))))))) -> 0(2(2(2(1(0(4(5(2(1(x1))))))))))
   1(5(3(0(4(1(5(0(2(3(4(x1))))))))))) -> 2(2(2(5(4(2(1(4(3(0(x1))))))))))
   1(5(5(0(3(4(3(3(4(0(5(x1))))))))))) -> 0(4(0(5(4(2(2(1(3(3(x1))))))))))

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actions all output return to Derivational Complexity: TRS