Derivational Complexity: TRS Innermost pair #487107048

details

property	value
status	complete
benchmark	25743.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.017 seconds
cpu usage	884.446
user time	876.311
system time	8.1348
max virtual memory	1.8784716E7
max residence set size	1.5252084E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (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), 60 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), 10 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), 59 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 4 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 12 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2127 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 153 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 88 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 14 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 28 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2882 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 324 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), 5680 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2772 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2720 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2698 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2736 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2716 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(0(1(2(2(3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
   4(4(5(5(3(0(1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
   0(1(2(4(4(0(1(0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
   4(0(4(2(4(0(3(1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
   4(4(5(3(2(4(2(5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
   3(1(5(3(4(5(1(3(3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
   5(1(5(3(5(4(0(0(3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
   0(0(0(2(2(3(4(4(3(3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
   0(4(5(0(0(4(2(4(5(0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
   1(1(5(3(4(3(4(4(2(5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
   1(2(0(1(2(4(5(2(4(4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
   1(5(2(2(3(3(4(2(4(5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
   4(0(5(4(0(2(4(0(4(3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
   0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
   0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
   0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
   0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
   0(4(4(5(4(0(1(3(1(3(4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
   0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
   1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
   1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
   2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
   2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
   2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
   3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
   3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
   3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))

popout

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

job log

popout

actions all output return to Derivational Complexity: TRS Innermost