Derivational Complexity: TRS Innermost pair #487106784

details

property	value
status	complete
benchmark	26998.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.157 seconds
cpu usage	845.808
user time	837.699
system time	8.10838
max virtual memory	1.871332E7
max residence set size	1.4882796E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (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), 78 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), 1 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 31 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 13 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2495 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 153 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 121 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 9 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 31 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2998 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 302 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5861 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2708 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2704 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2656 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2727 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2710 ms]
    (54) 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(0(2(x1)))))) -> 0(1(1(0(2(2(x1))))))
   1(3(4(4(1(2(1(x1))))))) -> 1(4(1(4(3(2(1(x1)))))))
   1(4(1(4(1(4(3(2(x1)))))))) -> 1(4(1(4(4(1(3(2(x1))))))))
   2(5(3(0(2(5(2(2(x1)))))))) -> 2(5(3(2(0(5(2(2(x1))))))))
   3(5(2(4(1(1(5(3(x1)))))))) -> 3(5(4(2(1(1(5(3(x1))))))))
   0(2(3(4(3(1(3(1(1(3(x1)))))))))) -> 0(2(3(3(4(1(3(1(1(3(x1))))))))))
   1(3(4(0(3(1(3(5(3(2(x1)))))))))) -> 1(2(5(3(3(1(1(5(5(2(x1))))))))))
   0(0(5(0(4(4(1(1(2(0(4(x1))))))))))) -> 2(4(4(3(2(0(1(3(0(5(x1))))))))))
   0(1(1(5(4(3(4(5(1(2(4(x1))))))))))) -> 0(4(5(3(3(1(2(0(5(2(x1))))))))))
   0(1(5(1(1(1(3(1(2(2(4(x1))))))))))) -> 0(5(4(4(2(5(5(0(2(4(x1))))))))))
   0(2(0(1(3(4(5(4(4(1(2(x1))))))))))) -> 0(2(0(3(1(4(5(4(4(1(2(x1)))))))))))
   0(2(2(2(1(1(2(5(1(2(1(x1))))))))))) -> 0(2(2(2(1(1(5(2(1(2(1(x1)))))))))))
   0(4(4(4(5(3(0(2(1(1(5(x1))))))))))) -> 5(5(5(2(2(2(0(2(3(0(x1))))))))))
   0(5(1(1(2(2(4(0(3(1(2(x1))))))))))) -> 2(5(1(4(4(0(3(4(2(5(x1))))))))))
   0(5(5(3(3(5(0(0(4(2(3(x1))))))))))) -> 3(2(2(2(2(4(5(1(3(4(x1))))))))))
   1(0(3(4(5(3(3(5(1(0(2(x1))))))))))) -> 4(5(0(5(1(5(5(5(4(2(x1))))))))))
   1(2(0(3(5(3(0(4(4(1(1(x1))))))))))) -> 2(4(2(3(0(1(3(5(2(5(x1))))))))))
   1(2(3(4(2(4(1(1(0(4(1(x1))))))))))) -> 1(0(0(1(3(5(3(0(2(1(x1))))))))))
   1(2(5(3(2(3(2(0(0(2(5(x1))))))))))) -> 1(2(1(1(0(1(0(4(2(3(x1))))))))))
   1(2(5(3(4(5(3(3(0(4(0(x1))))))))))) -> 0(4(5(3(1(1(3(5(4(5(x1))))))))))
   1(3(2(4(3(2(4(4(2(3(1(x1))))))))))) -> 4(3(1(2(4(5(3(5(1(3(x1))))))))))
   1(4(1(0(0(3(4(1(1(5(5(x1))))))))))) -> 5(5(5(4(2(3(0(3(5(1(x1))))))))))
   1(4(2(2(5(1(2(2(3(0(0(x1))))))))))) -> 0(0(4(4(1(2(5(4(0(2(x1))))))))))
   2(0(2(5(1(1(2(4(1(0(3(x1))))))))))) -> 0(3(5(0(5(1(4(2(2(1(x1))))))))))
   2(0(4(0(3(2(0(1(0(3(5(x1))))))))))) -> 2(0(2(5(1(5(1(1(2(2(x1))))))))))
   2(0(4(2(2(5(5(5(5(5(1(x1))))))))))) -> 1(5(4(0(3(4(4(2(0(2(x1))))))))))
   2(1(0(1(0(2(2(4(5(3(5(x1))))))))))) -> 2(5(0(5(4(4(0(4(4(5(x1))))))))))

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