Derivational Complexity: TRS Innermost pair #487106672

details

property	value
status	complete
benchmark	26931.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)	293.649 seconds
cpu usage	914.218
user time	905.616
system time	8.60189
max virtual memory	1.8916132E7
max residence set size	1.5070176E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 55 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2492 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 252 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 215 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3025 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 380 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 18 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6412 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3078 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3005 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3068 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3048 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3037 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3002 ms]
    (56) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(1(1(2(2(2(3(x1))))))) -> 0(1(2(1(2(2(3(x1)))))))
   3(3(4(5(1(2(4(2(x1)))))))) -> 3(2(1(5(3(4(4(2(x1))))))))
   0(1(5(2(4(5(3(0(1(x1))))))))) -> 0(1(5(4(2(5(3(0(1(x1)))))))))
   1(0(0(4(1(3(2(4(3(x1))))))))) -> 1(0(0(4(3(1(2(4(3(x1)))))))))
   3(3(0(3(0(3(4(4(4(x1))))))))) -> 3(3(3(0(0(3(4(4(4(x1)))))))))
   5(1(2(0(1(1(5(5(4(x1))))))))) -> 5(1(2(1(0(1(5(5(4(x1)))))))))
   1(0(2(5(5(0(5(0(0(1(x1)))))))))) -> 5(3(0(4(3(4(1(4(3(5(x1))))))))))
   1(3(5(0(5(2(3(0(5(1(x1)))))))))) -> 3(1(2(4(5(4(2(4(4(0(x1))))))))))
   2(0(3(0(1(2(0(2(3(5(x1)))))))))) -> 2(0(0(3(1(2(0(2(3(5(x1))))))))))
   2(5(3(2(3(2(2(1(0(5(x1)))))))))) -> 2(5(2(0(3(1(2(4(4(4(x1))))))))))
   0(0(2(5(0(2(4(3(5(2(4(x1))))))))))) -> 2(0(1(3(1(1(2(1(0(2(x1))))))))))
   0(0(3(1(3(3(4(2(2(2(5(x1))))))))))) -> 1(2(0(1(3(3(4(4(1(0(x1))))))))))
   0(1(0(0(2(0(4(1(4(1(5(x1))))))))))) -> 1(2(5(0(4(4(1(4(2(0(x1))))))))))
   0(1(2(5(3(1(1(3(5(4(0(x1))))))))))) -> 0(1(2(5(5(3(4(1(1(4(x1))))))))))
   0(1(3(3(5(0(0(1(3(2(0(x1))))))))))) -> 0(2(2(1(1(4(2(2(3(5(x1))))))))))
   0(2(0(3(2(0(2(1(1(0(0(x1))))))))))) -> 0(3(4(0(5(5(4(3(4(5(x1))))))))))
   0(2(2(3(1(5(2(1(2(2(4(x1))))))))))) -> 4(3(5(5(3(1(0(3(4(3(x1))))))))))
   0(2(5(0(1(4(2(4(2(1(1(x1))))))))))) -> 0(0(1(0(5(4(0(3(5(5(x1))))))))))
   0(2(5(5(5(2(5(4(0(0(4(x1))))))))))) -> 0(4(3(4(2(3(4(1(1(0(x1))))))))))
   0(3(0(1(4(1(3(0(5(3(1(x1))))))))))) -> 0(2(2(3(0(1(5(0(4(2(x1))))))))))
   0(3(1(2(3(2(5(0(2(4(0(x1))))))))))) -> 1(2(3(3(5(3(2(1(3(1(x1))))))))))
   0(4(0(3(3(5(5(1(5(4(1(x1))))))))))) -> 2(4(0(4(5(0(3(4(4(2(x1))))))))))
   0(4(1(3(2(2(1(1(0(2(2(x1))))))))))) -> 1(0(5(5(0(4(5(4(4(4(x1))))))))))
   0(4(4(3(0(1(2(2(4(5(1(x1))))))))))) -> 5(5(2(3(4(3(1(3(0(3(x1))))))))))
   1(0(3(4(2(1(2(4(0(4(2(x1))))))))))) -> 3(4(4(0(1(3(3(3(0(2(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost