Derivational Complexity: TRS pair #487103152

details
property	value
status	complete
benchmark	150815.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)	297.245 seconds
cpu usage	1164.74
user time	1159.43
system time	5.31357
max virtual memory	1.9174316E7
max residence set size	6927952.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 39 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), 6 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), 4056 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 18 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), 1701 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 114 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 33 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 29 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 3470 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 19 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8652 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 28.4 s]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8646 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8613 ms]
        (52) 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(x1)) -> 2(2(1(x1)))
   1(1(0(x1))) -> 1(2(2(1(x1))))
   0(2(2(0(0(1(1(x1))))))) -> 1(0(2(2(2(2(2(1(2(1(1(x1)))))))))))
   1(0(0(2(1(0(1(x1))))))) -> 0(2(2(2(1(0(2(2(x1))))))))
   0(1(1(0(0(2(0(2(0(1(2(0(x1)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(x1)))))))))))))
   1(2(1(0(1(2(2(0(1(1(1(1(x1)))))))))))) -> 1(2(1(2(1(0(2(0(2(2(1(2(0(x1)))))))))))))
   0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(x1))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(x1)))))))))))))))))))
   1(0(0(2(0(1(1(1(1(1(2(2(0(0(2(1(1(x1))))))))))))))))) -> 2(1(2(2(2(2(1(1(2(0(2(2(1(1(1(2(0(1(x1))))))))))))))))))
   1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(x1)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(x1)))))))))))))))))))))))
   0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(x1))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(x1)))))))))))))))))))))))))
   0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(x1)))))))))))))))))))))))
   2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(x1))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(x1))))))))))))))))))))))))
   2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(x1))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(x1))))))))))))))))))))))
   1(1(0(2(0(1(0(1(1(0(1(2(2(1(0(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(2(2(0(2(0(0(0(2(1(2(0(1(1(1(0(0(1(2(2(0(0(2(1(2(0(2(1(x1)))))))))))))))))))))))))))))
   0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(x1))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(x1))))))))))))))))))))))))))
   1(2(1(2(2(0(1(1(0(1(0(2(1(0(1(0(0(1(1(1(2(0(1(0(1(x1))))))))))))))))))))))))) -> 0(2(0(2(1(0(1(0(1(2(1(2(1(2(0(2(0(2(1(0(1(0(0(0(2(1(0(2(x1))))))))))))))))))))))))))))
   1(2(0(1(1(0(0(2(1(0(2(2(1(2(0(0(2(2(0(2(2(0(0(0(1(1(x1)))))))))))))))))))))))))) -> 2(0(0(0(2(2(2(0(0(2(1(0(2(2(0(0(2(1(2(2(1(1(0(0(2(0(0(1(0(0(x1))))))))))))))))))))))))))))))
   1(2(2(0(1(0(2(1(1(0(0(0(0(0(0(0(1(0(0(0(1(2(2(1(2(2(2(x1))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(0(2(2(0(0(0(0(2(1(0(0(0(1(0(2(2(2(0(0(0(2(1(x1)))))))))))))))))))))))))))))
   1(2(2(0(1(1(2(1(0(1(0(2(1(1(2(2(2(1(1(1(2(0(2(0(0(1(1(x1))))))))))))))))))))))))))) -> 2(2(1(0(0(2(2(1(2(1(2(2(2(2(1(2(2(2(1(0(2(1(2(0(0(0(0(1(2(1(0(x1)))))))))))))))))))))))))))))))
   1(1(0(1(1(0(1(2(0(0(0(1(0(1(0(0(2(2(0(1(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) -> 1(2(1(1(2(2(1(1(0(2(0(0(1(2(0(0(0(1(2(1(1(0(2(0(0(2(1(0(1(1(x1))))))))))))))))))))))))))))))
   0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(x1))))))))))))))))))))))))))))))
   2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(x1))))))))))))))))))))))))))))))
   0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(x1)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(x1))))))))))))))))))))))))))))))
   0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(x1)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(x1))))))))))))))))))))))))))))))
   2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(x1))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(x1)))))))))))))))))))))))))))))))
   2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(x1))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(x1)))))))))))))))))))))))))))))))))))))))))
   2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(x1))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(x1))))))))))))))))))))))))))))))))
   0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(x1)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(x1))))))))))))))))))))))))))))))))))
   2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(x1)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(x1)))))))))))))))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS