Derivational Complexity: TRS pair #487103312

details

property	value
status	complete
benchmark	26910.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.181 seconds
cpu usage	822.396
user time	814.581
system time	7.81499
max virtual memory	1.8915912E7
max residence set size	1.4920432E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 157 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), 6 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), 6 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1446 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 2 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 6 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2002 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 126 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 115 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 1 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 31 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 896 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 18 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), 7011 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2110 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2093 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2133 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2132 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2103 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(0(1(2(0(3(3(4(x1)))))))) -> 0(0(2(1(0(3(3(4(x1))))))))
   1(0(3(2(5(1(2(0(x1)))))))) -> 1(0(3(2(1(5(2(0(x1))))))))
   1(1(0(5(5(0(1(5(x1)))))))) -> 1(1(5(0(5(0(1(5(x1))))))))
   5(4(5(3(2(0(1(1(x1)))))))) -> 5(4(5(1(0(2(3(1(x1))))))))
   0(0(0(5(1(0(4(0(0(5(x1)))))))))) -> 0(4(5(3(1(5(0(1(4(5(x1))))))))))
   1(1(4(2(0(1(3(3(3(0(x1)))))))))) -> 3(5(0(4(1(3(3(5(2(0(x1))))))))))
   1(4(1(5(1(2(3(4(4(0(x1)))))))))) -> 1(4(1(5(1(3(2(4(4(0(x1))))))))))
   2(4(0(1(4(0(5(1(2(4(x1)))))))))) -> 2(4(0(1(4(0(1(5(2(4(x1))))))))))
   4(4(4(2(0(2(1(3(4(4(x1)))))))))) -> 4(4(2(4(2(0(1(3(4(4(x1))))))))))
   0(3(0(0(0(3(0(4(3(2(5(x1))))))))))) -> 3(3(0(5(0(4(5(3(5(2(x1))))))))))
   0(4(5(3(1(1(0(5(0(3(4(x1))))))))))) -> 4(2(5(3(2(4(5(3(1(4(x1))))))))))
   0(5(4(1(1(2(1(2(0(3(4(x1))))))))))) -> 2(4(3(0(4(2(1(1(4(2(x1))))))))))
   0(5(5(5(0(3(5(2(3(3(2(x1))))))))))) -> 0(4(4(3(2(2(1(5(0(0(x1))))))))))
   1(2(1(1(1(1(5(4(0(0(1(x1))))))))))) -> 1(0(1(4(2(5(0(1(4(3(x1))))))))))
   1(3(1(1(3(2(5(2(0(1(3(x1))))))))))) -> 4(2(4(1(2(0(2(5(0(2(x1))))))))))
   1(4(0(0(3(2(0(2(1(5(3(x1))))))))))) -> 5(4(1(0(1(1(2(0(4(2(x1))))))))))
   1(4(2(1(4(1(1(0(5(3(0(x1))))))))))) -> 5(5(0(2(1(4(5(0(1(0(x1))))))))))
   2(1(2(4(0(4(2(0(4(0(3(x1))))))))))) -> 1(4(1(2(2(4(0(1(5(5(x1))))))))))
   2(1(5(2(0(5(5(4(1(0(5(x1))))))))))) -> 2(2(1(2(0(4(0(1(4(0(x1))))))))))
   2(3(2(3(3(5(2(0(3(3(5(x1))))))))))) -> 5(3(2(4(2(4(3(5(0(4(x1))))))))))
   2(4(4(5(4(3(3(3(3(5(1(x1))))))))))) -> 5(5(2(4(1(4(5(0(0(1(x1))))))))))
   2(4(5(1(3(0(0(0(1(2(3(x1))))))))))) -> 0(3(1(3(2(4(3(3(4(4(x1))))))))))
   2(5(3(3(2(5(2(3(5(1(0(x1))))))))))) -> 5(5(0(3(1(2(4(2(3(3(x1))))))))))
   2(5(4(3(0(2(4(3(5(2(1(x1))))))))))) -> 2(5(4(5(3(2(1(3(2(5(x1))))))))))
   3(0(0(0(4(2(1(4(3(3(1(x1))))))))))) -> 4(2(4(2(2(5(1(0(0(0(x1))))))))))

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