Derivational Complexity: TRS Innermost pair #487106104

details

property	value
status	complete
benchmark	25808.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.477 seconds
cpu usage	941.129
user time	933.115
system time	8.01344
max virtual memory	1.874636E7
max residence set size	1.5114176E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 58 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), 42 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), 2339 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 107 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 57 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 33 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3305 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 378 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), 5996 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2916 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2908 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2894 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2925 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2910 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2837 ms]
    (56) 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(0(3(1(2(x1))))))) -> 0(1(0(2(3(1(2(x1)))))))
   3(0(4(4(3(0(5(3(x1)))))))) -> 3(0(4(3(4(0(5(3(x1))))))))
   5(3(3(5(4(1(4(4(4(x1))))))))) -> 5(3(4(3(1(4(5(4(4(x1)))))))))
   0(0(1(3(2(5(1(0(4(3(x1)))))))))) -> 2(1(2(1(4(0(3(1(4(4(x1))))))))))
   0(0(3(2(1(0(1(3(1(0(x1)))))))))) -> 4(0(2(0(5(0(3(2(2(2(x1))))))))))
   0(0(3(3(5(0(4(1(1(2(x1)))))))))) -> 0(3(3(2(4(3(5(4(3(2(x1))))))))))
   3(3(0(4(4(1(2(5(4(2(x1)))))))))) -> 3(1(3(0(4(2(4(5(4(2(x1))))))))))
   3(5(3(5(1(5(0(4(1(4(x1)))))))))) -> 3(5(0(2(1(3(5(2(4(4(x1))))))))))
   4(0(2(2(1(1(5(2(2(1(x1)))))))))) -> 1(5(4(5(2(4(2(3(2(3(x1))))))))))
   4(3(3(3(3(4(1(0(1(5(x1)))))))))) -> 2(1(4(3(4(2(5(0(1(5(x1))))))))))
   5(0(3(4(0(1(1(5(1(1(x1)))))))))) -> 0(3(4(4(4(1(3(4(2(1(x1))))))))))
   5(3(0(0(2(0(1(0(4(1(x1)))))))))) -> 2(3(2(5(1(0(3(2(5(2(x1))))))))))
   5(3(5(0(1(3(0(3(2(0(x1)))))))))) -> 1(2(2(5(4(3(1(2(1(5(x1))))))))))
   5(4(3(5(3(3(3(4(1(1(x1)))))))))) -> 5(4(0(1(4(5(1(4(2(1(x1))))))))))
   0(0(2(2(1(2(1(0(1(1(0(x1))))))))))) -> 1(4(1(3(0(2(1(2(4(0(x1))))))))))
   0(2(2(4(0(0(4(4(1(5(1(x1))))))))))) -> 4(4(3(2(2(3(1(0(2(2(x1))))))))))
   0(2(4(4(3(5(3(0(3(1(5(x1))))))))))) -> 5(1(3(0(1(2(5(2(4(5(x1))))))))))
   0(3(1(4(4(1(1(1(3(3(4(x1))))))))))) -> 2(3(2(3(2(4(4(3(5(5(x1))))))))))
   0(3(2(3(3(2(2(2(0(0(0(x1))))))))))) -> 2(0(1(0(2(2(1(5(3(4(x1))))))))))
   0(5(2(0(1(1(4(3(0(5(5(x1))))))))))) -> 3(0(3(0(4(3(4(0(3(3(x1))))))))))
   1(3(0(4(3(0(0(2(1(0(2(x1))))))))))) -> 4(4(1(2(3(5(4(1(0(3(x1))))))))))
   1(5(3(0(0(4(1(2(4(4(5(x1))))))))))) -> 1(1(5(4(4(4(0(2(1(3(x1))))))))))
   1(5(5(3(5(1(3(5(3(3(4(x1))))))))))) -> 1(4(4(0(2(1(5(2(0(2(x1))))))))))
   2(5(2(1(3(1(3(0(0(3(5(x1))))))))))) -> 2(5(2(1(3(3(1(0(0(3(5(x1)))))))))))
   2(5(3(3(2(0(4(4(3(2(1(x1))))))))))) -> 2(0(1(5(5(0(5(2(2(1(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost