Derivational Complexity: TRS Innermost pair #487106568

details

property	value
status	complete
benchmark	25416.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.976 seconds
cpu usage	846.902
user time	839.282
system time	7.62084
max virtual memory	1.8789104E7
max residence set size	1.4746616E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 26 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), 9 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), 38 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), 2391 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 223 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 208 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 28 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3121 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 343 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6115 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2934 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2993 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2955 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2948 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2954 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(0(1(2(3(4(x1)))))) -> 3(0(2(1(0(4(x1))))))
   3(0(3(3(2(1(5(x1))))))) -> 3(3(3(1(0(2(5(x1)))))))
   1(2(3(0(3(5(4(0(x1)))))))) -> 1(2(3(3(5(0(4(0(x1))))))))
   3(0(3(0(1(2(2(0(x1)))))))) -> 3(1(3(0(0(2(2(0(x1))))))))
   3(1(4(5(2(3(5(3(4(0(x1)))))))))) -> 3(1(4(3(5(2(5(3(4(0(x1))))))))))
   5(3(1(2(0(2(4(4(2(3(x1)))))))))) -> 0(5(4(0(2(3(4(4(1(3(x1))))))))))
   0(0(2(3(1(3(4(0(1(4(1(x1))))))))))) -> 0(2(3(1(2(5(3(5(3(0(x1))))))))))
   0(1(2(2(4(2(2(2(2(2(4(x1))))))))))) -> 4(1(5(5(4(5(4(5(0(1(x1))))))))))
   0(1(2(3(3(2(0(4(0(1(4(x1))))))))))) -> 2(0(5(4(3(5(2(3(4(1(x1))))))))))
   0(1(5(1(3(2(0(2(3(4(4(x1))))))))))) -> 3(0(1(0(4(0(2(2(0(5(x1))))))))))
   0(3(3(0(5(5(0(1(4(1(3(x1))))))))))) -> 4(4(0(2(0(3(4(0(4(1(x1))))))))))
   0(5(0(0(1(2(3(4(5(0(3(x1))))))))))) -> 4(0(1(3(3(5(2(5(0(0(x1))))))))))
   1(2(2(1(0(1(5(2(0(2(4(x1))))))))))) -> 1(2(2(0(1(1(5(2(0(2(4(x1)))))))))))
   1(3(3(4(0(3(4(0(5(5(2(x1))))))))))) -> 1(4(0(5(3(1(2(3(0(3(x1))))))))))
   1(4(2(2(5(2(4(1(2(1(2(x1))))))))))) -> 5(0(3(5(3(5(5(5(4(5(x1))))))))))
   2(0(2(1(1(5(2(5(3(3(5(x1))))))))))) -> 4(1(0(3(3(0(5(5(4(0(x1))))))))))
   2(0(5(3(2(2(1(4(3(0(5(x1))))))))))) -> 5(4(5(0(5(1(1(5(4(1(x1))))))))))
   2(1(1(2(3(0(3(5(2(2(5(x1))))))))))) -> 0(3(1(0(2(1(0(0(4(4(x1))))))))))
   2(2(1(3(0(1(4(3(3(3(4(x1))))))))))) -> 5(0(1(4(5(4(4(5(4(3(x1))))))))))
   2(5(2(3(0(2(5(0(2(0(5(x1))))))))))) -> 0(0(4(2(5(1(1(5(5(3(x1))))))))))
   2(5(5(5(1(1(5(4(5(2(0(x1))))))))))) -> 2(0(1(1(5(3(4(3(1(5(x1))))))))))
   3(0(5(3(5(2(0(3(0(1(4(x1))))))))))) -> 0(0(4(0(0(3(1(1(3(0(x1))))))))))
   3(1(5(2(1(0(2(0(4(3(3(x1))))))))))) -> 3(5(2(2(3(1(0(4(5(5(x1))))))))))
   3(2(1(3(1(2(2(1(3(1(3(x1))))))))))) -> 1(2(0(4(5(2(4(4(3(0(x1))))))))))
   3(3(0(2(5(5(4(1(3(4(0(x1))))))))))) -> 3(3(0(2(2(0(5(4(3(3(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost