Derivational Complexity: TRS pair #487103608

details

property	value
status	complete
benchmark	26923.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.241 seconds
cpu usage	824.74
user time	816.684
system time	8.0564
max virtual memory	1.8918664E7
max residence set size	1.49112E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (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), 79 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) RcToIrcProof [BOTH BOUNDS(ID, ID), 1722 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 30 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), 2104 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 155 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 189 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 33 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 880 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 19 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6822 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2007 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1967 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1958 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1983 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2000 ms]
        (56) 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(1(2(0(3(4(x1)))))) -> 0(1(0(2(3(4(x1))))))
   1(2(3(1(4(4(1(x1))))))) -> 1(2(1(3(4(4(1(x1)))))))
   2(2(5(3(2(4(5(3(x1)))))))) -> 2(2(5(2(3(4(5(3(x1))))))))
   4(2(3(5(4(2(2(0(x1)))))))) -> 4(2(5(3(4(2(2(0(x1))))))))
   5(3(5(1(5(3(5(3(x1)))))))) -> 5(3(5(1(3(5(5(3(x1))))))))
   3(2(3(1(3(5(4(1(1(x1))))))))) -> 3(1(3(3(4(2(1(5(1(x1)))))))))
   3(4(2(5(3(2(1(2(1(x1))))))))) -> 3(4(2(5(3(1(2(2(1(x1)))))))))
   3(1(3(0(4(5(2(4(5(0(x1)))))))))) -> 3(1(3(4(0(5(2(4(5(0(x1))))))))))
   4(5(5(1(2(1(3(2(3(2(x1)))))))))) -> 5(5(0(0(5(0(3(3(2(1(x1))))))))))
   5(0(1(4(1(2(5(1(5(2(x1)))))))))) -> 4(5(5(0(2(0(5(4(5(4(x1))))))))))
   5(0(5(4(0(3(1(5(4(2(x1)))))))))) -> 5(0(5(4(0(1(3(5(4(2(x1))))))))))
   0(3(0(2(4(1(2(2(4(0(5(x1))))))))))) -> 2(4(4(3(0(2(5(1(4(4(x1))))))))))
   0(5(0(3(0(1(2(4(0(4(3(x1))))))))))) -> 5(0(4(5(1(0(1(4(2(3(x1))))))))))
   0(5(2(4(1(5(0(2(1(5(1(x1))))))))))) -> 5(0(1(1(1(4(2(0(3(0(x1))))))))))
   0(5(3(5(0(5(3(3(2(1(3(x1))))))))))) -> 0(3(4(0(5(1(4(4(5(2(x1))))))))))
   0(5(4(4(1(0(5(1(4(5(5(x1))))))))))) -> 0(1(3(4(4(1(4(3(5(0(x1))))))))))
   1(3(2(2(5(5(1(5(1(2(1(x1))))))))))) -> 4(4(0(0(1(2(4(1(5(4(x1))))))))))
   1(4(4(5(2(2(1(0(0(0(2(x1))))))))))) -> 3(5(1(1(4(2(4(0(2(0(x1))))))))))
   1(5(0(4(0(1(2(5(5(5(3(x1))))))))))) -> 4(3(2(3(2(4(1(0(3(3(x1))))))))))
   1(5(1(2(2(1(1(0(5(5(0(x1))))))))))) -> 0(3(0(1(1(2(2(0(1(4(x1))))))))))
   2(0(0(4(5(0(5(3(0(4(2(x1))))))))))) -> 2(0(0(4(5(5(0(3(4(0(2(x1)))))))))))
   2(1(5(3(3(1(4(1(0(4(0(x1))))))))))) -> 4(4(3(5(0(0(5(3(2(4(x1))))))))))
   2(2(4(1(3(2(4(0(2(5(4(x1))))))))))) -> 0(4(2(3(1(2(3(0(1(4(x1))))))))))
   2(3(2(4(0(0(3(4(3(2(0(x1))))))))))) -> 5(2(1(5(0(5(1(1(5(3(x1))))))))))
   2(3(4(1(2(3(2(2(0(5(0(x1))))))))))) -> 2(2(3(0(5(1(4(1(1(2(x1))))))))))

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actions all output return to Derivational Complexity: TRS