Derivational Complexity: TRS pair #487103450

details

property	value
status	complete
benchmark	131633.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)	295.816 seconds
cpu usage	797.887
user time	790.459
system time	7.42855
max virtual memory	1.8678244E7
max residence set size	1.4990432E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 43 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), 0 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), 1019 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 44 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), 2074 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 198 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 122 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), 921 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, 4 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7602 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2334 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2269 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2303 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2293 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(4(0(1(0(3(0(5(5(4(x1)))))))))))) -> 0(1(4(4(1(2(3(1(4(3(3(2(4(3(1(4(1(x1)))))))))))))))))
   0(0(0(4(3(0(2(4(0(3(0(4(x1)))))))))))) -> 5(1(3(2(4(3(3(2(2(1(4(1(1(0(4(x1)))))))))))))))
   0(0(0(4(4(3(0(0(0(0(1(0(x1)))))))))))) -> 5(0(1(3(4(3(0(2(3(1(1(5(3(3(1(1(3(5(x1))))))))))))))))))
   0(0(2(2(4(1(2(2(0(4(2(4(x1)))))))))))) -> 1(0(5(2(1(0(1(5(2(3(1(4(3(0(x1))))))))))))))
   0(0(2(4(4(4(2(3(2(0(4(1(x1)))))))))))) -> 0(1(3(1(2(3(3(5(3(2(5(1(4(0(0(3(x1))))))))))))))))
   0(0(4(2(4(0(0(0(4(5(5(0(x1)))))))))))) -> 1(3(2(4(5(3(3(5(5(3(3(4(1(4(3(4(3(0(x1))))))))))))))))))
   0(0(5(5(0(1(2(2(5(0(0(5(x1)))))))))))) -> 1(2(1(3(4(1(2(5(5(3(3(4(0(0(1(x1)))))))))))))))
   0(1(4(5(2(2(3(3(1(4(0(0(x1)))))))))))) -> 3(1(3(1(3(1(3(3(3(3(3(4(0(4(5(x1)))))))))))))))
   0(2(5(5(0(5(5(1(2(0(4(2(x1)))))))))))) -> 5(1(2(1(4(5(1(0(1(2(1(5(5(4(5(1(x1))))))))))))))))
   0(3(0(5(5(0(2(2(2(4(0(2(x1)))))))))))) -> 3(5(4(3(3(2(4(3(3(3(3(1(4(0(3(0(3(4(x1))))))))))))))))))
   0(3(1(5(5(0(4(2(4(0(4(4(x1)))))))))))) -> 4(5(5(5(1(3(3(1(2(1(0(1(3(4(x1))))))))))))))
   0(3(2(0(4(1(0(2(4(0(4(1(x1)))))))))))) -> 4(5(3(4(2(1(3(1(1(3(4(3(4(0(2(x1)))))))))))))))
   0(4(2(0(5(2(1(4(5(0(5(0(x1)))))))))))) -> 5(5(3(3(1(1(0(3(4(1(1(4(1(3(4(2(x1))))))))))))))))
   0(4(3(2(2(0(4(2(0(5(0(4(x1)))))))))))) -> 5(3(3(5(4(3(5(4(2(3(2(5(2(3(3(4(x1))))))))))))))))
   0(4(5(4(1(2(0(4(0(4(2(0(x1)))))))))))) -> 1(3(3(1(5(4(3(0(3(0(5(4(1(0(1(3(3(x1)))))))))))))))))
   0(5(0(0(0(2(3(5(4(4(0(4(x1)))))))))))) -> 2(3(4(3(3(1(1(3(1(2(3(3(5(4(2(4(5(3(x1))))))))))))))))))
   0(5(0(2(4(4(4(2(4(3(3(1(x1)))))))))))) -> 0(3(1(4(1(1(1(5(4(2(3(4(5(3(5(0(1(3(x1))))))))))))))))))
   0(5(0(5(4(0(4(1(2(4(2(1(x1)))))))))))) -> 0(1(0(3(1(4(5(3(3(4(5(5(2(1(5(4(0(3(x1))))))))))))))))))
   0(5(3(4(2(5(4(4(0(5(3(1(x1)))))))))))) -> 0(3(1(5(4(1(3(3(1(5(3(4(5(3(3(2(3(2(x1))))))))))))))))))
   1(0(5(3(5(4(5(5(1(2(1(2(x1)))))))))))) -> 3(1(5(5(1(4(1(0(1(3(1(5(2(3(1(1(x1))))))))))))))))
   1(1(0(4(3(3(1(4(5(0(4(5(x1)))))))))))) -> 3(1(1(3(2(1(3(3(3(3(1(3(1(4(1(1(0(3(x1))))))))))))))))))
   1(1(4(2(2(3(1(0(5(2(2(5(x1)))))))))))) -> 1(3(3(3(3(3(1(1(1(1(0(3(3(1(2(5(3(0(x1))))))))))))))))))
   1(1(4(2(3(2(5(1(4(4(2(5(x1)))))))))))) -> 0(1(3(3(5(4(3(0(2(0(1(1(1(5(x1))))))))))))))
   1(2(2(2(0(5(5(0(2(0(1(4(x1)))))))))))) -> 2(2(4(5(0(3(3(1(5(0(0(3(3(3(1(1(4(x1)))))))))))))))))
   1(2(4(0(0(5(0(3(4(2(4(5(x1)))))))))))) -> 5(1(3(1(5(4(4(2(4(4(5(5(2(3(0(x1)))))))))))))))
   1(2(5(0(3(5(2(5(0(0(5(0(x1)))))))))))) -> 2(1(3(2(1(0(4(5(1(4(2(5(3(1(3(3(3(4(x1))))))))))))))))))
   1(4(2(4(2(4(1(0(0(4(0(0(x1)))))))))))) -> 2(1(3(3(3(5(3(5(3(2(3(4(1(1(4(0(0(x1)))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS