Derivational Complexity: TRS pair #487103340

details
property	value
status	complete
benchmark	153444.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)	296.104 seconds
cpu usage	921.607
user time	914.979
system time	6.62771
max virtual memory	1.8685916E7
max residence set size	1.4779828E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 63 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), 2897 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 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), 24 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2728 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 95 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 38 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 10 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 22 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 1796 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 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), 13.6 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4155 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4243 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4206 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4203 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(0(1(0(2(2(3(2(1(1(0(3(2(1(1(1(2(4(x1)))))))))))))))))))) -> 0(3(2(3(3(2(1(4(2(2(2(1(0(0(2(0(1(2(2(4(x1))))))))))))))))))))
   0(0(2(2(2(1(2(3(0(2(0(4(4(0(3(3(3(0(0(3(x1)))))))))))))))))))) -> 0(0(0(3(3(1(1(1(4(4(1(4(3(3(0(3(3(2(4(3(x1))))))))))))))))))))
   0(0(4(0(2(1(4(1(4(0(1(2(0(0(4(1(0(3(2(1(x1)))))))))))))))))))) -> 2(3(3(3(1(3(2(4(2(1(1(3(0(2(1(2(3(4(2(1(x1))))))))))))))))))))
   0(1(3(0(2(4(3(0(3(1(0(2(4(2(2(0(3(4(1(1(x1)))))))))))))))))))) -> 4(0(2(4(3(1(3(1(0(2(3(3(2(1(0(4(4(1(2(1(x1))))))))))))))))))))
   0(1(4(0(3(1(3(3(0(3(1(4(4(1(1(1(4(0(4(0(x1)))))))))))))))))))) -> 3(2(0(3(2(4(3(4(4(2(1(0(1(4(1(3(1(4(4(4(x1))))))))))))))))))))
   0(1(4(1(3(1(0(2(4(1(3(0(4(3(1(3(1(1(1(0(x1)))))))))))))))))))) -> 3(2(1(1(4(1(2(1(4(0(2(1(1(4(4(0(1(2(2(1(x1))))))))))))))))))))
   0(1(4(2(3(1(1(2(3(2(3(1(0(1(0(2(0(2(3(2(x1)))))))))))))))))))) -> 3(1(3(2(0(4(1(3(2(1(0(4(0(4(4(3(2(1(4(3(x1))))))))))))))))))))
   0(1(4(3(4(0(1(0(2(3(4(0(3(4(2(0(1(4(0(3(x1)))))))))))))))))))) -> 0(3(3(4(2(1(0(1(3(3(0(3(2(4(1(3(2(3(1(4(x1))))))))))))))))))))
   0(2(0(1(2(0(3(1(2(1(3(3(1(3(2(0(0(4(2(1(x1)))))))))))))))))))) -> 1(2(2(0(4(4(0(3(1(4(1(3(4(3(3(4(4(4(2(1(x1))))))))))))))))))))
   0(2(1(2(1(0(2(3(0(0(4(2(3(1(4(0(3(1(3(1(x1)))))))))))))))))))) -> 3(1(2(3(4(3(0(2(2(2(1(2(2(3(4(2(1(4(3(1(x1))))))))))))))))))))
   0(2(1(4(2(4(3(4(0(0(3(0(2(4(1(4(4(0(1(1(x1)))))))))))))))))))) -> 4(4(3(3(1(4(0(3(2(3(3(1(4(0(1(2(1(4(1(0(x1))))))))))))))))))))
   0(2(1(4(4(4(3(4(2(1(1(0(0(1(4(4(2(0(3(4(x1)))))))))))))))))))) -> 1(0(1(4(2(1(0(2(4(4(4(0(1(1(3(1(3(4(3(1(x1))))))))))))))))))))
   0(2(3(4(2(2(4(4(1(0(3(2(2(4(2(2(3(1(1(4(x1)))))))))))))))))))) -> 1(3(1(4(0(3(1(1(4(3(3(2(2(1(2(0(2(0(3(4(x1))))))))))))))))))))
   0(2(4(3(1(4(0(3(3(4(4(2(2(4(4(0(4(1(0(0(x1)))))))))))))))))))) -> 4(2(1(0(1(3(3(4(0(0(2(3(3(4(3(1(4(1(0(4(x1))))))))))))))))))))
   0(3(0(0(1(1(4(3(4(3(0(4(2(1(4(3(4(2(1(2(x1)))))))))))))))))))) -> 1(4(0(1(2(2(2(3(4(4(2(4(2(2(1(3(1(4(2(4(x1))))))))))))))))))))
   0(3(2(0(1(4(3(0(2(4(0(2(0(0(1(4(4(2(4(4(x1)))))))))))))))))))) -> 4(0(0(0(4(4(2(1(3(1(0(1(2(2(2(4(4(4(2(3(x1))))))))))))))))))))
   0(4(1(1(1(2(1(4(3(2(4(4(2(2(4(2(0(4(1(1(x1)))))))))))))))))))) -> 2(1(1(4(2(2(3(1(3(1(2(2(2(4(1(3(3(4(3(0(x1))))))))))))))))))))
   0(4(4(1(1(0(1(4(1(1(1(4(0(1(0(0(4(1(4(3(x1)))))))))))))))))))) -> 2(2(1(0(2(2(3(4(2(1(2(0(3(0(3(3(1(1(4(2(x1))))))))))))))))))))
   0(4(4(3(2(0(4(1(0(4(3(1(1(0(2(1(1(3(2(1(x1)))))))))))))))))))) -> 2(1(2(2(1(2(3(2(1(2(4(2(4(2(3(2(3(4(4(1(x1))))))))))))))))))))
   0(4(4(4(0(2(2(1(3(2(1(0(4(1(3(0(1(3(4(4(x1)))))))))))))))))))) -> 3(2(3(0(1(2(2(3(1(4(0(4(1(1(1(4(2(2(1(1(x1))))))))))))))))))))
   1(0(0(0(3(2(4(3(1(2(3(0(2(4(1(0(1(2(4(2(x1)))))))))))))))))))) -> 2(0(0(4(4(1(4(3(2(1(3(1(3(0(4(1(1(4(0(2(x1))))))))))))))))))))
   1(0(0(4(0(0(1(2(3(0(1(4(1(3(0(2(1(4(0(0(x1)))))))))))))))))))) -> 4(1(2(4(1(3(3(4(3(3(3(1(2(2(4(1(0(3(3(1(x1))))))))))))))))))))
   1(0(1(1(3(3(0(2(0(2(2(1(0(4(1(0(4(3(1(4(x1)))))))))))))))))))) -> 1(2(4(1(0(0(0(1(4(2(0(0(4(4(4(1(4(3(1(4(x1))))))))))))))))))))
   1(1(0(2(4(4(4(1(2(4(4(1(0(4(2(2(1(3(0(3(x1)))))))))))))))))))) -> 2(1(1(1(1(3(3(4(3(1(1(4(4(2(1(3(1(0(0(3(x1))))))))))))))))))))
   1(2(0(3(1(0(2(0(4(1(4(4(2(4(0(4(3(4(4(3(x1)))))))))))))))))))) -> 2(1(4(4(4(1(4(1(1(2(4(1(1(2(2(1(1(0(0(0(x1))))))))))))))))))))
   1(2(4(4(0(0(4(3(0(2(2(3(0(0(4(4(3(3(3(2(x1)))))))))))))))))))) -> 4(2(3(2(1(0(4(3(3(1(3(3(1(4(2(0(0(1(4(3(x1))))))))))))))))))))
   1(3(4(3(0(3(1(4(3(2(4(0(1(0(0(1(3(3(1(1(x1)))))))))))))))))))) -> 1(2(2(4(3(1(4(4(3(1(1(0(3(3(0(3(0(1(0(4(x1))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS