Derivational Complexity: TRS pair #487102888

details

property	value
status	complete
benchmark	91233.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)	297.284 seconds
cpu usage	1165.63
user time	1158.55
system time	7.07991
max virtual memory	1.8817428E7
max residence set size	1.4299452E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 51 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) RewriteLemmaProof [LOWER BOUND(ID), 72.8 s]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 738 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 41 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) NarrowingProof [BOTH BOUNDS(ID, ID), 280 ms]
            (30) CpxTypedWeightedCompleteTrs
            (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 187 ms]
            (32) CpxRNTS
            (33) SimplificationProof [BOTH BOUNDS(ID, ID), 129 ms]
            (34) CpxRNTS
        (35) CompletionProof [UPPER BOUND(ID), 0 ms]
        (36) CpxTypedWeightedCompleteTrs
            (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 669 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 2 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4137 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1198 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1151 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1167 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4268 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5228 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6383 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5504 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8229 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9006 ms]
        (66) 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(2(1(0(1(0(1(2(2(2(0(1(2(2(0(1(1(1(x1))))))))))))))))))))))) -> 0(0(0(1(2(2(1(1(0(2(1(1(2(2(2(2(1(2(0(0(1(1(2(2(1(1(1(x1)))))))))))))))))))))))))))
   0(0(0(2(0(1(1(1(1(2(1(1(2(1(2(1(2(1(2(1(1(1(0(x1))))))))))))))))))))))) -> 0(1(1(1(1(1(2(1(2(1(2(1(1(1(0(0(2(2(1(1(0(1(0(0(2(1(1(x1)))))))))))))))))))))))))))
   0(0(0(2(1(2(1(2(1(2(1(1(1(0(2(0(1(1(2(2(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(0(1(1(1(1(1(1(0(2(0(1(0(1(1(0(1(0(1(2(2(0(2(1(x1)))))))))))))))))))))))))))
   0(0(1(1(1(0(2(1(2(2(1(1(1(2(0(2(0(1(2(0(1(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(0(1(0(1(0(2(2(2(0(1(2(2(2(1(0(0(1(1(x1)))))))))))))))))))))))))))
   0(0(1(1(1(1(2(2(0(0(1(1(0(2(2(1(0(1(1(2(0(1(0(x1))))))))))))))))))))))) -> 2(2(1(1(2(2(2(0(1(1(1(2(0(1(1(1(2(1(2(1(0(1(2(2(1(1(0(x1)))))))))))))))))))))))))))
   0(1(0(1(1(2(0(1(1(2(2(0(0(2(1(0(2(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(1(2(1(1(0(1(0(1(0(1(2(1(0(0(2(1(1(1(2(1(1(1(2(x1)))))))))))))))))))))))))))
   0(1(1(0(2(1(0(2(1(0(2(0(2(2(0(1(1(0(1(2(2(1(1(x1))))))))))))))))))))))) -> 2(1(0(1(0(0(1(1(1(2(0(0(2(2(2(1(1(2(1(1(0(1(1(0(1(1(1(x1)))))))))))))))))))))))))))
   0(1(1(2(1(1(2(2(2(1(1(2(0(0(1(2(0(0(1(0(0(2(0(x1))))))))))))))))))))))) -> 0(0(2(2(1(0(2(1(2(1(1(2(1(2(2(1(1(1(1(1(0(0(1(2(1(2(0(x1)))))))))))))))))))))))))))
   0(1(2(1(2(0(0(1(0(1(1(2(1(1(2(2(1(1(1(2(2(0(2(x1))))))))))))))))))))))) -> 0(1(2(0(1(1(0(1(2(1(1(1(2(0(1(0(1(1(0(1(2(2(1(2(1(2(1(x1)))))))))))))))))))))))))))
   0(2(0(2(1(2(0(0(2(0(0(1(0(0(2(2(0(1(1(0(1(0(1(x1))))))))))))))))))))))) -> 0(1(0(2(0(0(2(1(1(1(0(0(2(1(0(2(2(2(1(1(0(1(1(1(1(0(1(x1)))))))))))))))))))))))))))
   0(2(0(2(1(2(1(0(0(1(1(2(1(1(0(1(0(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 1(2(1(2(2(1(1(1(1(1(1(0(2(2(2(1(1(2(1(2(1(0(2(1(1(0(1(x1)))))))))))))))))))))))))))
   0(2(1(0(2(0(0(2(0(1(1(1(2(0(1(1(2(1(1(0(1(0(0(x1))))))))))))))))))))))) -> 1(2(2(2(0(1(1(2(0(0(1(1(0(1(0(1(1(1(0(1(1(1(1(2(2(1(1(x1)))))))))))))))))))))))))))
   0(2(1(2(1(1(0(0(1(1(0(2(2(0(1(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(2(2(0(1(1(1(1(2(2(2(2(1(0(0(2(0(2(1(2(1(1(2(2(x1)))))))))))))))))))))))))))
   0(2(1(2(2(0(1(0(1(0(1(0(2(1(0(0(1(1(1(2(1(0(0(x1))))))))))))))))))))))) -> 2(2(2(2(2(1(1(2(2(1(0(1(1(1(1(0(1(1(2(2(1(1(1(2(0(1(2(x1)))))))))))))))))))))))))))
   0(2(2(1(1(1(1(2(2(1(2(1(2(0(0(1(2(1(0(0(2(0(0(x1))))))))))))))))))))))) -> 2(2(2(1(1(2(2(2(0(2(0(1(0(1(1(2(2(2(0(1(2(1(1(0(0(2(2(x1)))))))))))))))))))))))))))

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actions all output return to Derivational Complexity: TRS