Derivational Complexity: TRS pair #487102828

details
property	value
status	complete
benchmark	136463.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	299.407 seconds
cpu usage	965.268
user time	958.977
system time	6.29144
max virtual memory	1.8885704E7
max residence set size	1.4627268E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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), 2482 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 23 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 3245 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 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), 1855 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 9 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 13.8 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4377 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4397 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4326 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4383 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(1(1(1(1(1(2(2(3(0(2(0(1(0(3(3(3(1(x1)))))))))))))))))))) -> 0(0(2(2(3(0(3(0(1(2(1(2(2(0(1(3(0(1(1(0(x1))))))))))))))))))))
   0(0(0(1(2(2(0(0(1(0(2(3(2(0(3(3(2(1(2(2(x1)))))))))))))))))))) -> 1(0(1(3(0(2(0(3(2(2(2(2(0(3(2(1(2(2(2(2(x1))))))))))))))))))))
   0(0(0(2(1(0(1(0(2(0(1(3(1(2(1(0(0(3(0(2(x1)))))))))))))))))))) -> 2(3(0(3(2(0(3(1(2(3(0(2(0(1(1(2(2(0(2(2(x1))))))))))))))))))))
   0(0(1(2(0(2(2(1(3(3(3(3(3(1(2(3(0(3(1(0(x1)))))))))))))))))))) -> 0(0(0(1(3(1(2(1(0(2(3(2(1(0(2(1(1(1(2(1(x1))))))))))))))))))))
   0(0(1(2(1(1(2(3(3(3(1(1(0(1(2(2(3(2(3(3(x1)))))))))))))))))))) -> 2(0(0(2(3(2(2(1(1(1(2(0(3(0(1(1(2(1(2(1(x1))))))))))))))))))))
   0(0(3(1(1(3(2(2(1(3(1(1(3(2(3(1(0(0(3(3(x1)))))))))))))))))))) -> 2(0(0(3(2(0(2(2(3(2(2(2(3(1(3(0(2(2(1(1(x1))))))))))))))))))))
   0(1(0(3(3(0(0(2(0(1(1(0(3(2(1(1(3(2(3(1(x1)))))))))))))))))))) -> 2(3(3(0(0(2(1(2(1(2(1(3(1(1(1(0(0(2(0(2(x1))))))))))))))))))))
   0(1(0(3(3(3(0(2(0(3(1(2(2(2(0(3(2(0(0(2(x1)))))))))))))))))))) -> 0(1(1(2(0(1(1(3(1(2(0(1(3(3(1(0(0(1(3(2(x1))))))))))))))))))))
   0(1(1(2(1(0(1(3(0(1(3(0(3(1(0(3(1(1(1(2(x1)))))))))))))))))))) -> 1(0(2(0(1(2(3(1(2(0(2(1(0(3(0(1(2(0(3(2(x1))))))))))))))))))))
   0(1(2(0(2(0(0(3(1(2(3(3(3(3(1(2(2(3(2(2(x1)))))))))))))))))))) -> 0(1(0(3(2(2(2(0(1(2(1(2(1(2(1(0(2(2(2(3(x1))))))))))))))))))))
   0(1(2(1(3(1(2(1(1(2(2(2(1(1(0(0(3(3(0(3(x1)))))))))))))))))))) -> 2(3(1(1(3(1(3(3(3(2(2(0(2(0(1(2(3(1(2(3(x1))))))))))))))))))))
   0(1(3(0(0(3(3(0(2(1(1(2(1(2(0(3(1(0(3(1(x1)))))))))))))))))))) -> 0(0(2(2(2(3(3(2(1(3(0(0(0(0(2(0(3(0(2(1(x1))))))))))))))))))))
   0(1(3(3(0(2(1(2(1(1(0(3(2(3(0(2(3(1(3(1(x1)))))))))))))))))))) -> 3(0(1(2(0(3(1(3(1(3(3(1(2(0(0(2(1(1(3(2(x1))))))))))))))))))))
   0(2(0(3(0(2(3(3(0(3(3(3(3(1(3(1(1(3(2(1(x1)))))))))))))))))))) -> 3(2(2(1(2(1(2(1(2(3(2(1(2(0(0(2(0(2(3(3(x1))))))))))))))))))))
   0(2(0(3(0(3(0(2(2(0(2(2(2(0(3(2(3(1(3(1(x1)))))))))))))))))))) -> 3(2(1(2(0(3(2(3(3(2(0(2(2(0(1(2(0(2(0(1(x1))))))))))))))))))))
   0(2(1(1(3(2(1(1(1(1(2(2(3(0(2(2(0(1(3(3(x1)))))))))))))))))))) -> 0(2(0(2(2(1(2(3(2(1(2(0(0(1(1(0(1(2(3(3(x1))))))))))))))))))))
   0(2(1(3(1(0(2(0(1(2(3(3(3(3(0(1(1(3(2(1(x1)))))))))))))))))))) -> 2(2(2(2(0(3(1(1(1(0(1(0(1(2(2(3(1(0(2(1(x1))))))))))))))))))))
   0(2(2(2(2(3(2(3(0(0(2(3(1(1(1(2(3(2(1(2(x1)))))))))))))))))))) -> 2(0(3(2(0(1(0(0(1(3(3(1(2(2(3(0(1(2(1(2(x1))))))))))))))))))))
   0(3(0(2(3(3(1(3(2(0(1(1(0(3(3(2(0(1(2(0(x1)))))))))))))))))))) -> 2(2(1(0(1(2(0(0(2(3(1(2(1(2(2(0(2(1(1(3(x1))))))))))))))))))))
   0(3(1(0(3(2(0(1(3(2(3(1(2(3(3(3(1(2(2(1(x1)))))))))))))))))))) -> 2(2(1(0(3(3(2(1(1(3(1(2(0(1(2(2(2(1(2(0(x1))))))))))))))))))))
   0(3(1(1(1(0(0(1(1(0(0(3(1(2(2(1(1(2(0(1(x1)))))))))))))))))))) -> 2(0(3(0(1(3(1(0(2(1(2(0(0(1(1(2(0(2(3(1(x1))))))))))))))))))))
   0(3(1(3(1(2(2(2(2(2(3(2(1(0(3(1(0(1(1(0(x1)))))))))))))))))))) -> 3(2(0(0(1(1(2(0(3(2(1(3(0(2(2(3(2(2(0(3(x1))))))))))))))))))))
   0(3(2(0(3(3(3(1(1(2(3(3(2(3(3(3(3(2(1(2(x1)))))))))))))))))))) -> 1(0(3(1(3(1(3(1(3(2(2(0(1(1(2(1(2(3(2(2(x1))))))))))))))))))))
   0(3(3(1(3(1(0(3(1(1(2(2(2(3(2(3(1(0(1(3(x1)))))))))))))))))))) -> 2(3(3(1(1(2(2(0(0(0(3(2(2(1(3(2(2(0(2(3(x1))))))))))))))))))))
   0(3(3(3(0(3(3(3(0(0(0(0(1(2(0(2(1(3(1(1(x1)))))))))))))))))))) -> 2(2(1(1(2(1(2(1(3(2(2(2(0(0(1(1(0(1(1(3(x1))))))))))))))))))))
   1(0(0(3(1(3(1(3(3(3(0(2(2(0(1(0(3(1(3(3(x1)))))))))))))))))))) -> 2(3(1(1(0(1(0(2(0(0(2(3(2(0(1(0(1(2(3(0(x1))))))))))))))))))))
   1(0(2(1(1(1(2(3(2(0(0(2(1(2(1(1(2(1(3(1(x1)))))))))))))))))))) -> 1(1(3(3(2(3(0(2(0(1(2(0(1(1(2(1(2(2(2(0(x1))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS