Derivational Complexity: TRS pair #487103484

details
property	value
status	complete
benchmark	247020.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)	298.474 seconds
cpu usage	1064.55
user time	1058.91
system time	5.64113
max virtual memory	1.8966516E7
max residence set size	8307676.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 52 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) RewriteLemmaProof [LOWER BOUND(ID), 507 ms]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 23 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 50.8 s]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) NarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
            (30) CpxTypedWeightedCompleteTrs
            (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 15 ms]
            (32) CpxRNTS
            (33) SimplificationProof [BOTH BOUNDS(ID, ID), 19 ms]
            (34) CpxRNTS
        (35) CompletionProof [UPPER BOUND(ID), 4 ms]
        (36) CpxTypedWeightedCompleteTrs
            (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 2509 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (42) CdtProblem
        (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (48) CdtProblem
        (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 12.5 s]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2624 ms]
        (52) CdtProblem
        (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2628 ms]
        (56) CdtProblem
        (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2623 ms]
        (60) CdtProblem
        (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58.4 s]
        (64) 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(x1) -> 1(x1)
   0(0(x1)) -> 0(x1)
   3(4(5(x1))) -> 4(3(5(x1)))
   2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(0(1(0(1(0(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(0(1(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(0(0(0(0(1(0(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(0(0(1(1(0(1(1(1(1(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(0(0(1(0(1(1(1(0(0(1(1(1(1(0(0(0(0(0(0(1(1(0(1(1(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(0(0(1(1(1(0(0(1(1(0(1(0(0(0(0(1(0(0(1(0(0(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(0(1(1(1(1(1(0(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(1(0(1(0(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(0(0(1(1(1(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(0(0(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(0(1(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1(0(0(0(1(1(0(1(1(1(0(0(1(1(1(0(0(0(0(0(1(1(0(1(1(1(0(1(1(0(1(1(1(0(1(1(0(0(1(0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(0(1(0(0(0(1(1(1(0(1(1(1(0(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(1(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(1(1(1(0(0(1(0(0(1(0(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(1(1(0(1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(1(0(1(0(1(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(1(1(1(1(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(1(0(0(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(0(0(1(1(0(0(0(0(1(1(0(1(0(0(0(1(0(0(1(1(0(0(1(1(0(1(0(1(0(0(1(1(0(1(0(1(0(0(1(1(1(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(1(0(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(1(1(0(1(0(1(1(0(1(1(1(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
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actions all output return to Derivational Complexity: TRS