Derivational Complexity: TRS Innermost pair #487106212

details

property	value
status	complete
benchmark	166465.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)	296.267 seconds
cpu usage	942.492
user time	935.417
system time	7.07519
max virtual memory	1.9170792E7
max residence set size	1.4920536E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 130 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 6271 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 10.2 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 128 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), 10.2 s]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1568 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1562 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1534 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3586 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 124 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3869 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 69 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3948 ms]
    (62) CdtProblem
    (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 413 ms]
    (64) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(2(2(2(1(1(x1))))))))
   0(1(2(2(x1)))) -> 2(0(0(0(0(x1)))))
   0(1(2(2(x1)))) -> 2(0(0(2(0(2(2(1(x1))))))))
   1(2(1(1(x1)))) -> 1(0(0(2(0(0(0(2(x1))))))))
   1(1(2(1(2(x1))))) -> 1(1(1(2(2(x1)))))
   0(0(0(1(2(2(x1)))))) -> 0(0(0(2(2(1(x1))))))
   0(1(2(1(2(1(x1)))))) -> 2(0(2(2(0(0(0(1(2(0(0(0(2(x1)))))))))))))
   2(1(2(1(2(0(x1)))))) -> 1(1(0(2(2(2(x1))))))
   2(2(1(0(1(0(x1)))))) -> 0(1(1(0(2(0(2(x1)))))))
   0(1(1(2(1(1(2(x1))))))) -> 1(1(0(2(0(1(0(0(0(0(2(2(2(0(0(0(2(x1)))))))))))))))))
   0(1(2(0(0(0(0(x1))))))) -> 1(0(0(2(0(2(0(2(0(0(2(0(x1))))))))))))
   0(1(2(1(0(1(2(x1))))))) -> 0(2(2(1(2(0(2(2(1(x1)))))))))
   0(2(1(0(2(2(0(x1))))))) -> 2(0(2(0(0(0(2(0(0(2(2(x1)))))))))))
   2(2(1(0(1(2(1(x1))))))) -> 0(2(0(2(0(0(0(1(x1))))))))
   0(1(1(0(1(1(2(2(x1)))))))) -> 0(2(2(1(1(1(0(1(x1))))))))
   1(2(2(2(2(0(0(1(x1)))))))) -> 1(1(0(2(2(0(0(0(1(2(0(0(1(1(x1))))))))))))))
   2(2(1(1(2(2(0(1(x1)))))))) -> 2(0(2(0(0(0(2(0(0(2(2(1(1(x1)))))))))))))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Derivational Complexity: TRS Innermost