Derivational Complexity: TRS Innermost pair #487106664

details

property	value
status	complete
benchmark	27013.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.898 seconds
cpu usage	832.97
user time	825.273
system time	7.69746
max virtual memory	1.8776276E7
max residence set size	1.4669792E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 44 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 6 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
(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), 13 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (26) CpxRNTS
    (27) CompletionProof [UPPER BOUND(ID), 0 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 1942 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 142 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, ID), 75 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2361 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 331 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), 4923 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2385 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2355 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2336 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2303 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2278 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(1(2(1(3(4(5(x1)))))))) -> 0(1(1(1(2(3(4(5(x1))))))))
   1(5(2(2(5(3(3(1(x1)))))))) -> 1(5(2(2(3(5(3(1(x1))))))))
   1(3(2(1(0(5(2(1(0(2(x1)))))))))) -> 1(1(5(0(0(2(2(3(1(2(x1))))))))))
   2(5(3(0(1(1(3(2(0(2(x1)))))))))) -> 2(5(0(3(1(1(3(2(0(2(x1))))))))))
   3(0(0(2(3(1(3(2(1(5(x1)))))))))) -> 3(0(0(2(3(1(2(3(1(5(x1))))))))))
   4(0(4(4(0(3(4(0(2(3(x1)))))))))) -> 0(0(3(0(5(3(0(1(2(3(x1))))))))))
   0(0(4(4(0(0(1(2(0(1(4(x1))))))))))) -> 4(1(2(2(1(0(0(4(0(2(x1))))))))))
   0(4(4(3(2(4(0(5(5(3(4(x1))))))))))) -> 1(4(1(3(1(1(1(2(4(4(x1))))))))))
   1(0(0(3(2(4(3(0(5(5(3(x1))))))))))) -> 5(2(0(4(1(4(0(0(1(1(x1))))))))))
   1(0(2(5(0(3(2(4(1(0(2(x1))))))))))) -> 4(2(2(5(2(0(1(5(4(2(x1))))))))))
   1(2(0(1(0(3(3(3(0(5(3(x1))))))))))) -> 1(2(1(5(1(0(2(1(2(5(x1))))))))))
   1(3(1(0(4(5(2(3(4(2(5(x1))))))))))) -> 5(4(2(0(0(5(4(5(4(5(x1))))))))))
   1(3(1(2(2(0(2(2(5(1(3(x1))))))))))) -> 1(3(3(3(2(3(5(4(1(4(x1))))))))))
   1(3(4(0(2(4(1(2(4(3(5(x1))))))))))) -> 0(2(4(2(3(3(0(3(2(5(x1))))))))))
   1(4(2(0(1(5(3(4(4(0(0(x1))))))))))) -> 1(2(1(4(5(1(5(4(2(4(x1))))))))))
   1(4(5(1(4(2(5(3(2(3(2(x1))))))))))) -> 2(4(2(4(0(1(3(2(0(2(x1))))))))))
   1(4(5(2(3(1(5(5(3(4(3(x1))))))))))) -> 5(3(4(1(4(0(2(2(2(2(x1))))))))))
   1(5(5(3(4(1(3(1(5(5(0(x1))))))))))) -> 5(3(0(1(2(0(3(3(4(3(x1))))))))))
   2(0(2(5(5(1(2(4(5(3(3(x1))))))))))) -> 2(3(5(2(0(0(4(2(1(5(x1))))))))))
   2(0(4(3(0(0(0(1(4(4(5(x1))))))))))) -> 0(0(1(5(0(1(5(3(2(2(x1))))))))))
   2(1(3(0(1(1(5(2(0(5(3(x1))))))))))) -> 4(0(3(5(0(2(2(1(1(0(x1))))))))))
   2(2(3(1(3(1(1(3(4(2(0(x1))))))))))) -> 4(1(5(0(5(4(1(3(0(5(x1))))))))))
   2(3(2(1(4(0(2(1(1(4(3(x1))))))))))) -> 1(4(2(4(5(2(2(0(5(1(x1))))))))))
   2(3(3(3(4(4(1(0(0(4(5(x1))))))))))) -> 5(4(3(5(3(1(0(1(0(0(x1))))))))))
   2(3(5(1(0(5(3(4(4(4(4(x1))))))))))) -> 3(3(4(5(2(4(2(4(4(2(x1))))))))))
   2(4(3(2(2(4(5(0(0(2(2(x1))))))))))) -> 0(2(1(0(3(5(4(5(0(4(x1))))))))))
   2(5(0(2(2(1(3(2(5(0(2(x1))))))))))) -> 2(1(1(2(4(4(2(4(2(0(x1))))))))))

popout

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

job log

popout

actions all output return to Derivational Complexity: TRS Innermost