Derivational Complexity: TRS pair #487103700

details

property	value
status	complete
benchmark	138269.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)	294.254 seconds
cpu usage	851.498
user time	843.704
system time	7.79403
max virtual memory	1.8752788E7
max residence set size	1.4902144E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 47 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), 1122 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 62 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), 1981 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 136 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 42 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), 925 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 1 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7423 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2231 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2209 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2222 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2249 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(0(2(2(3(5(3(4(4(4(5(x1)))))))))))) -> 3(1(0(0(3(1(1(0(0(1(2(3(1(0(0(x1)))))))))))))))
   0(1(3(1(5(1(1(5(2(4(1(3(x1)))))))))))) -> 5(3(2(3(0(0(5(2(0(3(3(2(3(3(1(x1)))))))))))))))
   0(1(5(1(4(1(2(4(1(4(1(3(x1)))))))))))) -> 3(3(0(2(0(5(0(5(3(3(5(1(1(5(3(1(1(x1)))))))))))))))))
   0(1(5(2(2(1(2(5(2(3(1(4(x1)))))))))))) -> 1(1(0(0(4(5(4(2(0(5(2(1(2(2(0(0(4(x1)))))))))))))))))
   0(1(5(5(5(2(3(2(2(2(2(1(x1)))))))))))) -> 1(5(0(0(3(2(0(0(4(0(3(4(0(3(2(3(4(x1)))))))))))))))))
   0(2(0(5(5(5(3(5(5(3(5(5(x1)))))))))))) -> 0(3(3(3(1(0(5(1(0(3(3(2(1(5(5(x1)))))))))))))))
   0(2(4(3(2(5(5(5(2(5(0(2(x1)))))))))))) -> 0(1(1(3(4(0(3(5(2(2(2(3(0(5(1(0(x1))))))))))))))))
   0(2(4(3(5(1(5(4(1(4(1(5(x1)))))))))))) -> 2(1(0(0(3(1(0(0(1(5(0(4(3(5(5(0(0(x1)))))))))))))))))
   0(4(1(2(5(2(1(1(2(2(5(1(x1)))))))))))) -> 0(0(0(1(1(0(1(4(5(4(3(1(0(1(4(5(4(x1)))))))))))))))))
   0(4(1(5(2(5(3(3(3(5(2(5(x1)))))))))))) -> 0(0(3(2(0(0(5(1(0(0(4(2(1(0(3(0(2(2(x1))))))))))))))))))
   0(5(2(5(0(3(0(1(2(5(5(4(x1)))))))))))) -> 4(3(1(3(3(1(1(0(2(4(4(0(0(5(4(4(4(x1)))))))))))))))))
   1(0(2(4(1(5(5(4(1(2(1(0(x1)))))))))))) -> 0(5(1(0(1(3(1(0(0(5(0(0(4(2(2(4(2(x1)))))))))))))))))
   1(0(4(1(4(3(2(5(5(3(2(4(x1)))))))))))) -> 3(0(0(3(2(4(3(2(1(3(2(0(0(4(4(0(0(x1)))))))))))))))))
   1(1(2(5(4(1(2(3(5(1(3(2(x1)))))))))))) -> 0(3(1(1(1(0(5(3(0(5(0(0(0(2(x1))))))))))))))
   1(2(1(4(3(5(2(2(1(5(5(4(x1)))))))))))) -> 3(3(5(3(5(5(0(0(5(0(0(2(0(1(1(x1)))))))))))))))
   1(3(2(4(4(2(3(2(2(3(2(0(x1)))))))))))) -> 3(3(0(4(0(0(4(5(3(0(3(1(0(0(0(x1)))))))))))))))
   1(4(0(4(1(1(1(4(1(2(4(1(x1)))))))))))) -> 2(1(3(0(0(2(1(2(3(3(5(1(3(2(x1))))))))))))))
   1(5(1(4(3(3(5(5(2(4(1(5(x1)))))))))))) -> 1(4(2(0(3(0(2(5(0(5(1(5(1(5(x1))))))))))))))
   2(0(0(5(5(2(0(1(4(4(5(0(x1)))))))))))) -> 4(0(3(1(3(0(2(3(4(2(5(1(0(1(x1))))))))))))))
   2(0(3(5(3(4(4(3(2(4(0(3(x1)))))))))))) -> 4(0(5(0(0(3(1(3(0(1(0(0(0(1(x1))))))))))))))
   2(0(5(2(2(5(1(4(1(1(1(2(x1)))))))))))) -> 4(0(0(0(0(3(1(0(0(2(1(0(2(4(4(3(0(x1)))))))))))))))))
   2(1(2(5(2(4(2(5(2(2(4(4(x1)))))))))))) -> 3(1(2(0(4(5(0(0(2(5(3(0(2(1(5(1(x1))))))))))))))))
   2(1(4(1(5(5(1(0(2(4(2(5(x1)))))))))))) -> 2(3(0(2(3(1(0(5(0(3(5(4(0(1(x1))))))))))))))
   2(1(5(5(2(5(5(0(3(0(5(2(x1)))))))))))) -> 0(3(1(2(4(4(0(0(5(3(0(0(2(1(0(5(1(0(x1))))))))))))))))))
   2(2(2(4(1(2(2(4(2(2(4(0(x1)))))))))))) -> 3(5(0(5(0(4(0(3(0(4(2(0(5(1(3(0(0(2(x1))))))))))))))))))
   2(2(2(5(2(2(2(3(1(4(1(4(x1)))))))))))) -> 2(4(0(1(3(1(1(3(3(3(1(1(2(0(2(3(0(x1)))))))))))))))))
   2(2(4(1(2(1(1(5(4(1(4(4(x1)))))))))))) -> 3(3(3(3(0(4(5(1(1(0(1(0(0(0(2(5(0(0(x1))))))))))))))))))

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actions all output return to Derivational Complexity: TRS