Derivational Complexity: TRS pair #487103396

details

property	value
status	complete
benchmark	136051.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.047 seconds
cpu usage	855.464
user time	846.947
system time	8.51679
max virtual memory	3.6976596E7
max residence set size	1.5013636E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 37 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 5 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 1 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), 1157 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 46 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 4 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1861 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 187 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 150 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 10 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 992 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), 7573 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2200 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2184 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2203 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2185 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2202 ms]
        (56) 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(0(0(0(4(1(4(4(0(5(1(4(x1)))))))))))) -> 2(0(4(4(1(3(2(2(1(5(5(2(0(0(2(3(x1))))))))))))))))
   0(0(0(0(5(0(2(0(3(1(0(5(x1)))))))))))) -> 3(4(2(4(5(2(3(1(1(2(1(4(3(2(x1))))))))))))))
   0(0(0(4(0(3(1(0(4(1(1(5(x1)))))))))))) -> 3(0(2(3(3(2(1(5(5(4(1(4(5(2(x1))))))))))))))
   0(0(3(0(1(1(1(3(4(1(4(1(x1)))))))))))) -> 0(0(1(3(3(2(2(0(3(1(0(1(2(0(3(x1)))))))))))))))
   0(0(4(0(3(0(1(1(1(2(5(0(x1)))))))))))) -> 4(3(3(4(2(3(2(2(5(1(4(5(2(1(3(2(4(3(x1))))))))))))))))))
   0(0(4(0(5(1(0(5(0(0(2(2(x1)))))))))))) -> 3(5(3(0(3(1(2(4(4(3(3(5(5(3(x1))))))))))))))
   0(0(5(0(4(4(4(0(1(0(4(1(x1)))))))))))) -> 5(3(2(1(0(5(2(0(2(0(3(2(2(2(5(0(x1))))))))))))))))
   0(1(0(0(4(0(4(0(4(0(0(1(x1)))))))))))) -> 5(1(5(4(2(3(3(2(1(1(1(3(2(1(5(2(5(1(x1))))))))))))))))))
   0(2(3(0(5(5(0(0(4(5(3(1(x1)))))))))))) -> 5(3(1(2(5(1(3(0(2(1(0(2(2(1(0(x1)))))))))))))))
   0(3(4(0(4(0(4(0(3(3(5(5(x1)))))))))))) -> 2(1(4(4(1(3(0(2(2(1(2(5(2(2(2(1(0(x1)))))))))))))))))
   0(4(0(4(3(0(0(5(5(3(0(0(x1)))))))))))) -> 2(2(2(0(1(0(5(1(2(2(5(1(3(5(2(2(0(3(x1))))))))))))))))))
   0(4(4(2(0(0(0(2(4(0(4(0(x1)))))))))))) -> 5(5(1(3(1(5(1(2(4(3(0(2(4(5(4(5(5(x1)))))))))))))))))
   0(4(5(4(0(2(5(4(0(2(4(5(x1)))))))))))) -> 0(2(2(2(0(4(3(1(3(2(3(2(5(5(x1))))))))))))))
   0(5(3(0(0(5(3(5(1(1(3(0(x1)))))))))))) -> 5(1(0(0(2(5(1(2(2(2(5(1(3(4(3(x1)))))))))))))))
   1(0(5(5(3(2(1(3(4(4(0(5(x1)))))))))))) -> 1(5(4(5(4(2(3(1(5(5(1(2(5(3(x1))))))))))))))
   1(1(0(2(4(2(0(3(4(0(4(0(x1)))))))))))) -> 3(4(0(2(4(3(3(4(2(3(2(4(3(5(x1))))))))))))))
   1(1(5(5(5(0(5(5(5(5(0(5(x1)))))))))))) -> 1(2(1(5(1(2(5(3(2(3(2(4(5(5(5(1(x1))))))))))))))))
   1(1(5(5(5(3(0(1(1(0(1(4(x1)))))))))))) -> 2(2(0(3(2(1(4(3(1(2(1(5(4(3(1(2(2(3(x1))))))))))))))))))
   1(2(3(0(5(4(0(5(0(4(0(0(x1)))))))))))) -> 1(3(5(1(1(1(3(2(3(1(5(2(2(2(0(3(4(1(x1))))))))))))))))))
   1(2(5(5(0(5(0(2(3(3(2(5(x1)))))))))))) -> 1(2(2(2(4(3(3(2(0(1(0(4(3(2(5(x1)))))))))))))))
   1(4(0(2(5(0(0(0(5(0(4(1(x1)))))))))))) -> 3(3(1(2(5(3(3(0(3(1(4(1(5(3(x1))))))))))))))
   1(4(4(1(4(3(3(4(4(0(5(3(x1)))))))))))) -> 1(1(0(4(3(1(4(5(4(3(0(3(5(2(x1))))))))))))))
   1(5(3(3(0(1(3(0(1(1(5(0(x1)))))))))))) -> 0(2(4(3(4(3(1(1(2(2(5(2(3(3(3(4(3(x1)))))))))))))))))
   1(5(5(0(2(0(1(3(5(1(3(1(x1)))))))))))) -> 4(2(2(3(5(1(0(2(3(5(2(1(2(1(2(x1)))))))))))))))
   2(0(5(0(4(0(4(4(0(2(2(0(x1)))))))))))) -> 4(1(5(2(2(3(1(5(0(1(2(4(2(4(2(3(2(x1)))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS