Derivational Complexity: TRS Innermost pair #487106172

details

property	value
status	complete
benchmark	27003.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)	297.818 seconds
cpu usage	857.209
user time	848.475
system time	8.73393
max virtual memory	1.8784644E7
max residence set size	1.470106E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 55 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), 8 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), 49 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 11 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2240 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 142 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 91 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 4 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 16 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2480 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 301 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), 5228 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2462 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2492 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2498 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2466 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2455 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(0(1(2(2(x1))))) -> 0(2(1(0(2(x1)))))
   0(1(3(4(5(2(2(2(x1)))))))) -> 0(1(5(2(4(3(2(2(x1))))))))
   0(0(2(2(2(5(2(1(1(x1))))))))) -> 0(2(2(0(2(5(2(1(1(x1)))))))))
   0(4(3(0(2(4(5(0(4(x1))))))))) -> 0(4(5(4(0(3(2(0(4(x1)))))))))
   0(0(1(2(3(5(0(0(2(2(x1)))))))))) -> 0(5(0(1(5(1(5(1(2(1(x1))))))))))
   0(4(2(1(0(3(2(3(2(2(x1)))))))))) -> 0(4(4(5(2(3(2(0(1(0(x1))))))))))
   1(3(3(3(2(1(5(4(1(3(x1)))))))))) -> 5(1(4(0(0(0(1(3(1(5(x1))))))))))
   1(3(3(4(0(3(2(3(1(5(x1)))))))))) -> 1(3(3(4(0(3(3(2(1(5(x1))))))))))
   1(3(5(3(2(2(5(5(2(3(x1)))))))))) -> 5(4(5(1(3(1(3(0(4(0(x1))))))))))
   1(5(0(5(3(1(0(5(1(5(x1)))))))))) -> 1(5(0(5(1(5(3(0(1(5(x1))))))))))
   2(2(0(4(1(2(0(0(5(2(x1)))))))))) -> 5(0(5(4(0(1(4(5(3(5(x1))))))))))
   3(2(5(2(0(3(0(3(5(2(x1)))))))))) -> 5(3(4(4(4(5(1(5(4(3(x1))))))))))
   3(5(0(2(3(4(5(0(2(3(x1)))))))))) -> 4(2(0(1(1(4(3(4(0(1(x1))))))))))
   3(5(5(1(2(3(3(4(3(5(x1)))))))))) -> 3(5(5(0(3(3(4(1(0(1(x1))))))))))
   4(0(0(2(2(0(5(1(2(2(x1)))))))))) -> 4(5(0(4(5(1(1(1(3(4(x1))))))))))
   4(5(0(5(5(2(5(2(3(2(x1)))))))))) -> 4(5(1(1(5(4(2(0(1(5(x1))))))))))
   5(3(0(3(1(1(2(1(3(2(x1)))))))))) -> 2(2(0(5(5(0(3(0(4(2(x1))))))))))
   0(2(2(5(3(3(5(4(5(1(3(x1))))))))))) -> 2(1(5(1(4(2(2(4(2(2(x1))))))))))
   0(2(4(5(1(2(0(5(1(2(4(x1))))))))))) -> 4(4(0(4(3(3(4(2(4(3(x1))))))))))
   0(3(1(4(4(5(4(5(3(5(5(x1))))))))))) -> 4(4(2(1(4(1(3(1(3(3(x1))))))))))
   0(5(2(1(3(4(5(1(0(1(5(x1))))))))))) -> 5(3(2(1(1(5(3(3(2(1(x1))))))))))
   0(5(5(3(4(3(3(3(1(2(0(x1))))))))))) -> 3(1(2(0(5(0(4(2(4(3(x1))))))))))
   1(0(1(5(5(1(5(2(2(5(2(x1))))))))))) -> 3(1(0(1(1(0(3(5(1(3(x1))))))))))
   1(1(0(1(4(0(1(1(1(3(2(x1))))))))))) -> 5(1(3(4(1(4(0(1(5(3(x1))))))))))
   1(1(0(3(3(3(0(5(4(1(4(x1))))))))))) -> 0(1(5(1(1(5(0(1(0(0(x1))))))))))
   1(1(3(0(1(4(1(5(0(3(1(x1))))))))))) -> 0(1(3(2(0(2(0(4(1(5(x1))))))))))
   1(2(2(1(5(1(5(1(3(5(2(x1))))))))))) -> 4(1(0(0(3(1(1(0(1(0(x1))))))))))

popout

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

job log

popout

actions all output return to Derivational Complexity: TRS Innermost