Derivational Complexity: TRS pair #487103192

details

property	value
status	complete
benchmark	135115.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.647 seconds
cpu usage	823.269
user time	815.698
system time	7.5707
max virtual memory	1.874378E7
max residence set size	1.5061308E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) 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), 83 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), 2 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) RcToIrcProof [BOTH BOUNDS(ID, ID), 919 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1859 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 122 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 125 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 924 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 8 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6869 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2088 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2098 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2053 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2023 ms]
        (54) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(0(0(0(0(3(1(4(5(2(5(x1)))))))))))) -> 0(2(5(4(5(5(5(0(4(3(4(4(2(3(x1))))))))))))))
   0(0(1(2(5(0(0(0(0(0(5(2(x1)))))))))))) -> 1(4(5(3(0(4(1(1(5(2(4(4(4(0(1(4(3(x1)))))))))))))))))
   0(0(2(1(2(2(5(2(5(1(3(3(x1)))))))))))) -> 4(2(1(4(4(3(0(2(2(4(4(3(1(4(x1))))))))))))))
   0(0(2(2(2(0(3(3(3(3(2(0(x1)))))))))))) -> 4(4(4(2(2(4(5(1(1(5(5(4(0(4(5(0(1(5(x1))))))))))))))))))
   0(0(2(3(3(3(4(0(2(2(0(0(x1)))))))))))) -> 0(1(4(3(1(4(5(3(1(4(5(5(1(0(5(4(4(1(x1))))))))))))))))))
   0(0(2(4(2(5(2(4(0(3(1(3(x1)))))))))))) -> 1(0(5(4(4(4(2(1(0(3(5(2(5(3(5(x1)))))))))))))))
   0(0(3(1(2(0(1(1(2(0(3(4(x1)))))))))))) -> 1(5(0(1(1(4(0(1(4(1(1(4(5(5(4(2(5(3(x1))))))))))))))))))
   0(0(5(2(0(2(3(0(3(1(2(0(x1)))))))))))) -> 5(5(1(1(4(4(3(5(3(4(4(5(5(5(4(4(3(4(x1))))))))))))))))))
   0(1(2(0(2(0(3(5(5(1(4(0(x1)))))))))))) -> 4(5(4(4(1(1(1(4(1(5(4(4(1(0(5(1(x1))))))))))))))))
   0(2(0(2(2(0(3(2(0(1(3(2(x1)))))))))))) -> 5(4(0(5(1(4(5(5(2(0(3(3(2(4(4(0(x1))))))))))))))))
   0(2(2(2(0(5(0(2(2(3(2(5(x1)))))))))))) -> 1(0(5(1(2(5(4(5(5(3(5(4(4(4(5(x1)))))))))))))))
   0(2(3(0(0(5(2(2(3(2(0(5(x1)))))))))))) -> 4(2(4(1(0(1(0(4(1(5(3(2(1(1(5(4(4(x1)))))))))))))))))
   0(2(5(3(0(3(2(3(1(5(0(4(x1)))))))))))) -> 5(5(5(1(0(2(3(2(4(4(5(4(5(2(4(x1)))))))))))))))
   0(3(0(0(2(0(1(2(0(2(1(3(x1)))))))))))) -> 2(3(4(5(3(4(4(4(4(4(5(3(1(4(0(1(3(4(x1))))))))))))))))))
   0(3(0(0(3(0(2(0(3(1(5(0(x1)))))))))))) -> 4(0(4(4(0(1(0(4(1(5(3(5(4(5(3(4(4(x1)))))))))))))))))
   0(3(1(0(2(0(3(5(2(1(2(1(x1)))))))))))) -> 2(5(4(4(5(1(3(3(4(5(5(5(4(4(1(1(1(x1)))))))))))))))))
   0(3(2(0(4(2(2(2(2(2(4(0(x1)))))))))))) -> 1(5(3(1(1(1(0(5(4(4(2(1(4(4(5(3(1(x1)))))))))))))))))
   0(3(3(0(0(3(0(3(1(3(0(5(x1)))))))))))) -> 0(5(5(4(4(1(5(5(0(2(4(2(0(2(4(3(x1))))))))))))))))
   0(3(5(0(2(0(5(1(5(4(0(1(x1)))))))))))) -> 1(0(2(4(3(2(1(4(2(5(4(4(4(4(2(x1)))))))))))))))
   0(5(0(0(1(0(3(1(0(2(1(3(x1)))))))))))) -> 4(5(3(4(3(3(5(2(4(4(4(2(4(4(4(4(0(x1)))))))))))))))))
   0(5(0(3(1(4(2(1(3(3(0(3(x1)))))))))))) -> 0(1(4(4(4(1(4(4(4(4(1(0(4(0(2(4(5(5(x1))))))))))))))))))
   0(5(1(3(0(3(0(2(0(4(3(0(x1)))))))))))) -> 5(5(4(5(3(5(0(5(2(1(1(1(0(1(4(1(x1))))))))))))))))
   0(5(2(2(2(0(0(0(2(2(2(1(x1)))))))))))) -> 4(1(4(2(4(5(5(3(4(0(2(0(1(2(4(4(x1))))))))))))))))
   0(5(4(3(0(0(0(2(1(1(2(2(x1)))))))))))) -> 1(4(1(4(5(3(0(4(4(4(0(4(2(3(x1))))))))))))))
   1(0(1(3(3(0(5(0(0(3(1(5(x1)))))))))))) -> 1(5(3(4(4(5(5(4(5(3(4(0(4(4(1(4(0(x1)))))))))))))))))
   1(0(2(1(2(0(0(0(1(0(0(3(x1)))))))))))) -> 4(5(4(1(4(0(5(3(5(5(2(5(1(4(5(4(x1))))))))))))))))
   1(0(5(1(3(0(0(2(3(2(0(3(x1)))))))))))) -> 5(5(4(3(3(1(5(4(3(3(5(3(3(5(5(3(x1))))))))))))))))

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actions all output return to Derivational Complexity: TRS