Derivational Complexity: TRS pair #487103456

details
property	value
status	complete
benchmark	40033.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.071 seconds
cpu usage	920.226
user time	912.733
system time	7.49295
max virtual memory	1.8820448E7
max residence set size	1.5138096E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 34 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), 2492 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 37 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), 2863 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 135 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 106 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 40 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 1720 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 10 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 13.6 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4068 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4080 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4081 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(0(0(0(1(1(0(2(3(4(0(3(0(2(1(4(1(0(4(5(x1)))))))))))))))))))) -> 5(5(2(5(4(4(5(5(1(2(3(5(1(3(3(1(0(3(0(1(x1))))))))))))))))))))
   0(1(0(5(5(1(2(3(3(2(2(0(1(5(5(0(3(1(4(5(x1)))))))))))))))))))) -> 0(4(2(1(1(5(1(0(4(0(3(2(3(5(2(1(0(5(1(5(x1))))))))))))))))))))
   0(1(2(3(2(0(4(1(5(5(0(2(1(2(2(0(3(1(4(0(x1)))))))))))))))))))) -> 5(5(1(1(1(5(1(5(0(0(3(2(0(2(0(2(5(3(0(2(x1))))))))))))))))))))
   0(1(5(4(1(5(1(0(1(1(2(5(3(4(4(1(3(3(1(0(x1)))))))))))))))))))) -> 4(1(0(4(2(5(5(3(1(3(5(2(2(1(4(1(2(2(1(2(x1))))))))))))))))))))
   0(2(0(5(5(0(4(5(3(4(5(5(2(3(2(1(0(1(2(0(x1)))))))))))))))))))) -> 3(1(0(3(2(0(3(1(3(4(1(5(5(3(0(2(2(2(1(1(x1))))))))))))))))))))
   0(2(1(0(5(1(2(4(5(3(2(5(0(5(3(1(1(1(0(5(x1)))))))))))))))))))) -> 5(4(4(5(5(3(5(2(0(5(5(4(2(5(0(0(0(2(5(2(x1))))))))))))))))))))
   0(2(4(0(3(4(1(2(2(5(0(0(2(5(2(3(5(3(1(2(x1)))))))))))))))))))) -> 1(2(3(0(1(5(2(3(2(3(0(5(0(5(3(0(4(4(5(5(x1))))))))))))))))))))
   0(2(5(1(0(2(2(5(0(1(2(0(3(3(3(3(3(3(0(1(x1)))))))))))))))))))) -> 1(1(3(1(5(2(4(4(5(2(4(1(0(2(2(1(4(0(3(0(x1))))))))))))))))))))
   0(3(1(5(0(5(5(1(5(4(4(3(1(0(4(2(3(3(1(0(x1)))))))))))))))))))) -> 2(3(4(0(0(4(2(1(3(1(0(4(0(3(3(5(3(0(1(3(x1))))))))))))))))))))
   0(3(2(5(0(4(2(2(5(4(1(0(1(0(3(1(3(1(0(3(x1)))))))))))))))))))) -> 2(0(0(4(1(3(5(0(0(1(0(3(5(1(5(5(4(2(3(5(x1))))))))))))))))))))
   0(3(4(0(5(0(2(4(5(0(4(5(3(0(3(4(1(2(3(3(x1)))))))))))))))))))) -> 2(0(1(0(4(0(2(3(5(4(2(1(1(1(5(5(0(5(4(3(x1))))))))))))))))))))
   0(3(5(5(0(0(2(4(4(1(1(2(0(1(5(4(5(2(1(2(x1)))))))))))))))))))) -> 3(4(3(5(2(4(4(3(0(0(0(1(0(3(4(5(5(1(5(1(x1))))))))))))))))))))
   0(4(2(4(3(2(4(1(5(5(5(0(0(2(0(4(1(2(2(0(x1)))))))))))))))))))) -> 1(4(3(4(2(0(4(4(3(0(5(1(3(5(0(5(1(1(1(1(x1))))))))))))))))))))
   0(4(4(4(1(2(5(2(0(3(1(3(5(0(3(4(5(4(5(5(x1)))))))))))))))))))) -> 4(4(3(5(3(0(5(3(5(3(2(1(3(0(0(3(5(3(2(4(x1))))))))))))))))))))
   0(4(5(3(0(1(4(4(3(5(5(2(4(4(1(1(2(0(3(5(x1)))))))))))))))))))) -> 0(2(1(0(0(3(2(3(1(4(2(3(1(3(0(5(1(1(5(4(x1))))))))))))))))))))
   0(5(0(4(0(0(3(2(5(0(5(2(1(1(0(3(2(1(3(0(x1)))))))))))))))))))) -> 5(1(3(5(0(3(5(0(3(0(1(3(0(3(2(3(1(0(1(0(x1))))))))))))))))))))
   0(5(1(5(4(5(2(0(3(0(1(3(1(1(4(1(5(2(0(1(x1)))))))))))))))))))) -> 0(1(1(1(4(1(0(5(0(0(2(5(2(3(5(0(5(5(5(4(x1))))))))))))))))))))
   1(0(3(1(2(4(3(4(5(1(2(0(1(2(0(5(0(0(3(1(x1)))))))))))))))))))) -> 0(3(0(2(1(3(1(0(3(4(4(4(1(4(1(3(5(1(5(1(x1))))))))))))))))))))
   1(1(1(3(5(3(1(4(2(2(4(2(5(1(0(2(5(3(5(0(x1)))))))))))))))))))) -> 2(1(0(3(3(0(3(4(4(1(5(0(1(3(3(5(0(1(4(1(x1))))))))))))))))))))
   1(1(3(5(4(0(1(2(3(1(4(2(1(4(4(5(4(2(1(0(x1)))))))))))))))))))) -> 4(3(0(1(4(1(5(2(0(3(5(5(1(5(3(0(2(2(5(0(x1))))))))))))))))))))
   1(2(3(5(1(4(4(5(3(1(5(0(2(1(5(3(0(4(5(0(x1)))))))))))))))))))) -> 4(4(0(4(3(5(3(4(0(4(0(5(1(2(0(0(3(3(0(4(x1))))))))))))))))))))
   1(2(5(1(1(0(1(0(1(0(3(5(5(4(0(0(2(5(1(2(x1)))))))))))))))))))) -> 1(1(5(0(5(0(3(0(1(1(5(4(0(5(5(1(0(3(3(0(x1))))))))))))))))))))
   1(3(2(2(3(4(1(1(5(1(3(5(1(4(0(1(0(1(0(0(x1)))))))))))))))))))) -> 0(3(5(3(5(4(0(0(2(3(2(3(3(3(5(2(1(0(0(4(x1))))))))))))))))))))
   1(3(3(1(0(2(0(4(3(5(3(3(3(5(0(4(3(4(0(3(x1)))))))))))))))))))) -> 2(0(4(3(0(5(0(1(3(5(2(3(1(0(4(0(0(3(4(3(x1))))))))))))))))))))
   1(3(5(3(0(5(3(4(0(2(2(3(4(5(3(5(4(1(5(5(x1)))))))))))))))))))) -> 0(3(5(0(3(5(5(5(1(5(4(1(1(5(1(0(1(5(1(1(x1))))))))))))))))))))
   1(4(5(0(1(5(4(0(3(5(3(1(4(5(5(5(5(0(4(3(x1)))))))))))))))))))) -> 5(4(3(0(2(0(3(0(3(0(3(5(0(3(4(4(1(0(4(3(x1))))))))))))))))))))
   1(5(3(0(2(0(0(2(5(1(1(2(5(3(3(5(0(1(2(3(x1)))))))))))))))))))) -> 2(0(3(2(3(0(1(1(5(5(0(3(5(2(3(1(2(0(2(4(x1))))))))))))))))))))
   2(0(0(4(0(0(0(3(1(0(0(1(1(1(3(2(5(2(4(2(x1)))))))))))))))))))) -> 4(2(4(2(3(2(3(0(1(1(1(3(4(0(4(0(1(1(3(5(x1))))))))))))))))))))
   2(0(4(0(4(4(5(0(3(1(0(2(2(1(4(2(0(1(1(2(x1)))))))))))))))))))) -> 0(5(1(4(4(4(5(3(5(0(0(4(3(1(1(4(0(3(4(5(x1))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS