Derivational Complexity: TRS Innermost pair #487106364

details

property	value
status	complete
benchmark	26882.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)	296.696 seconds
cpu usage	840.784
user time	833.073
system time	7.7114
max virtual memory	1.887588E7
max residence set size	1.4780652E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 46 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 36 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 17 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2061 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 170 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 107 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 7 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3158 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 360 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5135 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2733 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2737 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2727 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2714 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2728 ms]
    (54) 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(0(1(2(3(4(5(x1)))))))) -> 1(1(0(0(2(3(4(5(x1))))))))
   4(1(2(0(1(4(5(4(3(x1))))))))) -> 4(5(1(1(0(2(3(4(4(x1)))))))))
   4(4(5(5(0(0(0(3(1(x1))))))))) -> 4(4(5(0(5(0(0(3(1(x1)))))))))
   0(3(0(5(1(3(2(4(5(5(x1)))))))))) -> 1(2(3(3(0(4(1(5(1(3(x1))))))))))
   3(3(1(4(3(1(0(5(5(4(x1)))))))))) -> 5(4(1(1(4(5(2(3(3(2(x1))))))))))
   5(0(1(5(2(5(2(0(5(4(x1)))))))))) -> 3(5(1(2(4(1(0(0(1(3(x1))))))))))
   5(0(5(4(5(0(0(2(1(3(x1)))))))))) -> 3(5(3(0(2(4(3(2(0(4(x1))))))))))
   0(2(5(4(4(2(0(3(5(1(5(x1))))))))))) -> 0(0(2(4(4(4(1(0(5(3(x1))))))))))
   0(3(1(5(4(1(5(5(5(3(2(x1))))))))))) -> 1(0(4(4(1(4(2(0(5(3(x1))))))))))
   1(0(4(5(4(0(3(0(3(2(5(x1))))))))))) -> 0(5(5(5(0(1(1(1(2(4(x1))))))))))
   1(2(4(1(0(3(2(5(5(3(1(x1))))))))))) -> 3(1(1(3(5(2(5(5(2(1(x1))))))))))
   1(4(0(1(2(1(4(5(4(4(0(x1))))))))))) -> 4(3(3(4(1(0(3(1(2(4(x1))))))))))
   1(4(2(1(4(1(2(5(2(3(3(x1))))))))))) -> 3(0(0(2(3(2(4(1(4(3(x1))))))))))
   1(5(2(4(1(5(0(1(0(2(0(x1))))))))))) -> 1(1(3(4(5(2(5(4(1(1(x1))))))))))
   2(0(0(1(2(1(1(4(5(5(1(x1))))))))))) -> 3(1(3(4(1(0(0(0(2(2(x1))))))))))
   2(1(0(2(3(0(5(3(5(0(3(x1))))))))))) -> 0(1(1(0(3(2(0(5(4(2(x1))))))))))
   2(1(0(4(3(3(1(3(0(5(0(x1))))))))))) -> 5(1(5(0(4(4(2(5(0(2(x1))))))))))
   2(1(2(3(4(0(4(2(2(3(5(x1))))))))))) -> 3(1(2(2(4(3(3(3(2(4(x1))))))))))
   2(1(3(1(3(2(3(4(5(5(0(x1))))))))))) -> 2(1(3(1(3(2(4(3(5(5(0(x1)))))))))))
   2(1(4(5(5(1(2(5(4(3(5(x1))))))))))) -> 4(5(5(4(2(2(2(3(2(0(x1))))))))))
   2(3(0(3(2(4(3(5(3(3(1(x1))))))))))) -> 1(1(1(3(1(0(3(1(5(5(x1))))))))))
   2(3(3(1(3(2(3(3(1(1(2(x1))))))))))) -> 2(1(4(1(4(5(4(2(2(1(x1))))))))))
   2(4(0(0(4(1(0(2(1(0(4(x1))))))))))) -> 1(3(5(4(4(4(0(3(4(2(x1))))))))))
   2(4(0(2(0(0(0(1(0(5(3(x1))))))))))) -> 5(1(4(4(4(0(1(4(5(1(x1))))))))))
   2(5(2(1(1(0(3(1(3(4(3(x1))))))))))) -> 4(4(4(5(3(3(0(3(1(3(x1))))))))))
   3(0(5(1(2(4(4(5(1(0(3(x1))))))))))) -> 3(0(2(4(4(1(5(1(0(5(3(x1)))))))))))
   3(2(0(0(5(2(3(2(1(0(2(x1))))))))))) -> 4(1(2(4(0(2(5(3(4(2(x1))))))))))

popout

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

job log

popout

actions all output return to Derivational Complexity: TRS Innermost