Derivational Complexity: TRS pair #487103584

details
property	value
status	complete
benchmark	97901.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.522 seconds
cpu usage	1166.51
user time	1160.45
system time	6.05851
max virtual memory	1.8817176E7
max residence set size	1.1624008E7
stage attributes
key	value
starexec-result	KILLED
output
KILLED
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 164 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), 14 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), 853 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 44 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), 456 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 91 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 98 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 31 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 865 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), 5287 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1569 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1564 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1558 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5420 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7287 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8145 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10.5 s]
        (60) 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(0(1(0(1(2(0(1(1(0(0(0(0(2(0(1(2(2(1(0(x1))))))))))))))))))))))) -> 2(1(2(0(0(2(2(1(0(1(0(0(1(0(0(0(1(0(2(1(1(2(1(2(2(1(0(x1)))))))))))))))))))))))))))
   0(0(0(2(1(0(2(1(0(1(1(2(1(2(2(0(0(2(2(1(1(1(0(x1))))))))))))))))))))))) -> 0(1(0(0(1(0(1(1(2(1(1(1(2(0(0(0(2(1(2(0(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))))
   0(0(0(2(1(1(0(1(0(1(1(2(2(0(0(2(1(0(2(1(1(1(0(x1))))))))))))))))))))))) -> 1(0(1(1(2(0(2(1(0(0(0(1(1(0(2(1(0(0(1(0(0(0(1(1(2(1(1(x1)))))))))))))))))))))))))))
   0(0(0(2(2(1(1(0(1(0(0(2(1(2(0(1(2(1(2(1(0(2(2(x1))))))))))))))))))))))) -> 1(0(0(0(0(1(0(1(1(1(1(1(0(2(1(0(2(1(2(1(1(0(1(1(0(2(1(x1)))))))))))))))))))))))))))
   0(0(1(1(0(1(0(0(1(0(0(2(0(1(2(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) -> 0(1(2(1(1(2(1(2(2(0(0(2(1(0(0(1(0(1(2(0(2(2(1(1(1(1(0(x1)))))))))))))))))))))))))))
   0(0(1(2(1(2(2(0(0(0(1(0(0(0(0(1(0(1(2(1(2(0(1(x1))))))))))))))))))))))) -> 1(0(0(2(0(0(2(1(1(1(0(0(0(0(0(1(0(2(1(1(2(2(1(1(0(1(0(x1)))))))))))))))))))))))))))
   0(0(2(0(2(1(0(0(2(1(0(1(2(2(2(1(0(1(0(2(1(2(1(x1))))))))))))))))))))))) -> 1(1(0(0(0(0(1(1(2(0(1(0(2(1(2(2(1(0(0(2(1(0(0(2(1(1(1(x1)))))))))))))))))))))))))))
   0(0(2(1(1(2(1(0(2(2(2(0(0(0(0(2(2(1(0(1(0(0(0(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(2(1(2(1(1(0(0(2(0(1(0(2(2(1(2(0(1(1(1(0(x1)))))))))))))))))))))))))))
   0(1(0(2(1(0(2(1(0(1(2(1(0(2(2(2(1(0(0(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(2(1(1(0(1(0(1(0(0(0(2(0(1(0(2(0(1(0(2(1(1(0(1(1(1(x1)))))))))))))))))))))))))))
   0(1(0(2(2(1(0(1(2(2(1(0(2(1(1(2(1(2(2(1(2(1(1(x1))))))))))))))))))))))) -> 0(2(1(0(0(1(2(0(2(2(1(0(2(1(1(1(1(0(1(1(0(0(1(0(0(2(0(x1)))))))))))))))))))))))))))
   0(1(2(0(2(0(2(2(1(1(0(0(2(1(1(2(0(0(0(0(2(1(1(x1))))))))))))))))))))))) -> 0(0(0(2(1(1(1(2(0(2(2(2(1(1(0(1(2(1(2(1(0(0(2(0(1(0(1(x1)))))))))))))))))))))))))))
   0(1(2(1(0(1(1(0(2(0(1(1(2(2(2(1(0(2(2(0(0(1(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(0(1(2(1(0(1(1(2(2(1(2(2(1(0(0(1(2(0(1(x1)))))))))))))))))))))))))))
   0(1(2(1(2(1(0(0(1(0(2(0(2(1(1(2(1(1(0(2(1(1(0(x1))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(0(1(1(1(2(1(1(0(2(1(2(1(2(1(1(0(0(1(1(x1)))))))))))))))))))))))))))
   0(1(2(2(2(1(1(2(2(2(2(2(1(0(1(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))) -> 2(1(2(0(0(1(2(2(1(1(2(0(1(1(0(0(2(2(0(2(1(1(1(0(0(1(1(x1)))))))))))))))))))))))))))
   0(2(1(0(0(2(0(0(1(1(1(0(1(1(2(1(1(0(1(1(2(1(1(x1))))))))))))))))))))))) -> 2(1(0(0(1(0(2(1(1(1(1(1(1(1(1(0(2(1(1(0(1(0(0(0(1(2(1(x1)))))))))))))))))))))))))))
   0(2(2(0(2(1(0(2(0(2(2(1(0(1(0(1(0(0(2(1(0(0(0(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(1(0(1(1(0(0(1(2(1(1(2(2(1(2(0(1(0(0(1(2(0(x1)))))))))))))))))))))))))))
   0(2(2(1(0(1(1(0(1(0(2(1(1(0(0(0(0(2(1(0(2(2(2(x1))))))))))))))))))))))) -> 0(0(0(1(2(1(2(1(1(2(2(2(1(1(0(1(0(2(1(1(0(0(1(2(1(1(0(x1)))))))))))))))))))))))))))
   1(0(0(0(0(0(0(1(2(1(1(0(2(0(1(2(2(2(2(1(1(0(0(x1))))))))))))))))))))))) -> 1(2(0(0(2(1(2(1(0(1(1(2(1(0(1(2(1(0(2(1(1(2(1(2(2(2(1(x1)))))))))))))))))))))))))))
   1(0(0(2(1(1(0(2(1(1(2(0(0(0(2(0(0(0(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(0(2(1(1(1(2(1(0(0(1(0(2(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))))))))))))))))
   1(0(1(2(0(0(0(2(1(0(0(1(0(0(1(2(2(1(0(2(0(0(0(x1))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(2(0(1(0(0(1(1(0(0(1(2(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))))
   1(0(2(0(0(0(1(0(0(2(1(2(1(2(0(0(1(2(1(2(2(2(0(x1))))))))))))))))))))))) -> 1(1(0(0(1(2(0(2(1(1(0(1(1(0(0(1(0(2(0(0(1(0(0(1(2(2(0(x1)))))))))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS