Derivational Complexity: TRS Innermost pair #487107250

details

property	value
status	complete
benchmark	133881.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)	293.73 seconds
cpu usage	880.813
user time	872.751
system time	8.06223
max virtual memory	1.8885888E7
max residence set size	1.5351592E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 61 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), 43 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1996 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 205 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 163 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 1747 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 86 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 5 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9894 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2849 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2860 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2867 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2860 ms]
    (52) 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(3(0(5(2(5(0(2(4(0(0(x1)))))))))))) -> 2(3(4(3(3(2(1(5(1(4(0(1(4(3(0(0(x1))))))))))))))))
   0(1(2(2(4(0(3(0(3(1(5(2(x1)))))))))))) -> 4(0(0(0(1(1(3(5(1(0(2(4(1(1(2(3(x1))))))))))))))))
   0(2(2(3(4(4(3(3(0(0(4(2(x1)))))))))))) -> 1(5(1(3(3(2(3(3(3(4(4(3(3(1(4(1(x1))))))))))))))))
   0(2(2(4(4(4(4(5(0(2(3(3(x1)))))))))))) -> 0(0(5(5(4(4(1(3(4(2(1(3(4(0(1(3(x1))))))))))))))))
   0(2(4(0(5(2(5(3(0(1(4(3(x1)))))))))))) -> 5(3(1(0(1(3(3(1(3(4(5(1(2(0(2(3(x1))))))))))))))))
   0(2(5(2(4(3(0(3(0(4(5(0(x1)))))))))))) -> 3(1(1(1(0(4(2(5(2(1(3(1(1(3(x1))))))))))))))
   0(2(5(4(3(1(5(4(4(4(1(2(x1)))))))))))) -> 0(0(0(1(4(0(5(1(2(3(3(1(5(3(2(4(x1))))))))))))))))
   0(2(5(4(3(5(5(4(3(0(0(4(x1)))))))))))) -> 0(1(0(3(5(1(2(3(4(1(0(1(0(0(3(3(x1))))))))))))))))
   0(3(0(0(5(4(3(0(0(0(0(3(x1)))))))))))) -> 0(4(1(5(2(0(1(2(1(5(2(5(0(3(x1))))))))))))))
   0(3(0(4(3(5(2(4(4(3(1(1(x1)))))))))))) -> 0(0(5(3(3(1(5(1(1(0(1(5(2(2(3(3(5(x1)))))))))))))))))
   0(3(0(5(0(2(0(2(2(4(4(3(x1)))))))))))) -> 0(1(5(4(0(1(5(5(0(5(0(0(0(3(x1))))))))))))))
   0(3(2(4(4(3(0(4(0(3(0(4(x1)))))))))))) -> 2(0(2(0(1(2(1(5(1(1(1(5(1(2(0(1(3(x1)))))))))))))))))
   0(3(4(0(4(2(4(3(2(1(3(4(x1)))))))))))) -> 4(2(1(5(1(3(3(3(3(1(4(3(5(4(5(1(1(x1)))))))))))))))))
   0(3(4(2(2(2(4(3(1(5(3(1(x1)))))))))))) -> 1(3(0(1(3(1(1(5(2(1(2(3(2(5(0(x1)))))))))))))))
   0(3(5(0(2(4(5(4(4(4(3(5(x1)))))))))))) -> 3(3(1(1(1(0(5(0(1(1(0(3(2(2(3(3(3(x1)))))))))))))))))
   0(4(1(0(2(4(4(4(5(3(0(4(x1)))))))))))) -> 5(1(2(1(1(2(1(1(4(2(1(5(3(3(0(4(x1))))))))))))))))
   0(4(3(0(4(3(2(3(3(4(5(2(x1)))))))))))) -> 2(0(2(4(5(5(1(1(3(3(3(3(1(5(0(4(x1))))))))))))))))
   0(4(4(3(3(0(0(2(5(1(4(1(x1)))))))))))) -> 0(2(5(1(5(1(4(5(4(1(1(1(1(1(1(x1)))))))))))))))
   1(1(2(5(2(5(4(3(0(3(5(0(x1)))))))))))) -> 3(2(1(4(1(4(1(3(2(3(4(3(3(3(2(1(x1))))))))))))))))
   1(1(4(5(5(4(4(3(0(3(1(2(x1)))))))))))) -> 3(5(3(5(5(2(1(3(3(4(4(2(3(1(x1))))))))))))))
   1(2(0(1(0(4(4(4(5(4(1(4(x1)))))))))))) -> 5(1(1(3(3(0(2(1(4(5(1(1(1(5(4(1(3(x1)))))))))))))))))
   1(2(3(2(4(0(2(0(3(0(2(4(x1)))))))))))) -> 1(5(1(5(3(3(2(1(2(3(2(3(2(0(x1))))))))))))))
   1(4(3(4(0(0(2(4(0(4(3(2(x1)))))))))))) -> 1(4(0(2(3(1(1(5(5(5(0(3(5(4(x1))))))))))))))
   1(4(4(0(0(5(3(0(2(4(3(4(x1)))))))))))) -> 2(3(5(0(3(2(3(1(1(5(5(1(4(5(1(x1)))))))))))))))
   1(4(4(3(0(0(4(3(0(5(4(1(x1)))))))))))) -> 1(3(1(2(4(1(1(4(4(0(1(1(0(5(3(x1)))))))))))))))
   1(4(4(4(4(4(4(3(0(4(3(2(x1)))))))))))) -> 5(0(1(5(4(5(0(1(3(3(4(4(4(3(4(x1)))))))))))))))
   1(5(5(1(0(5(5(4(3(1(5(2(x1)))))))))))) -> 5(1(3(2(0(1(2(2(3(0(2(0(1(3(3(2(x1))))))))))))))))
   2(1(3(0(3(2(0(4(0(0(4(5(x1)))))))))))) -> 2(2(5(1(2(2(2(3(3(5(2(3(1(3(x1))))))))))))))
   2(2(0(1(0(4(3(4(5(3(2(5(x1)))))))))))) -> 5(4(5(4(1(3(1(2(3(1(0(1(2(5(x1))))))))))))))

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actions all output return to Derivational Complexity: TRS Innermost