Derivational Complexity: TRS Innermost pair #487106848

details

property	value
status	complete
benchmark	26980.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.927 seconds
cpu usage	813.325
user time	805.441
system time	7.88414
max virtual memory	1.8977532E7
max residence set size	1.4702708E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 50 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), 38 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), 1812 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 209 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 79 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2182 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 290 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), 5059 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2229 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2232 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2228 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2174 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2193 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(3(3(x1)))))) -> 0(1(1(3(2(3(x1))))))
   4(4(2(0(3(1(2(3(x1)))))))) -> 4(2(4(0(3(1(2(3(x1))))))))
   4(5(0(1(4(2(5(3(x1)))))))) -> 4(5(0(2(3(4(1(5(x1))))))))
   0(1(0(2(5(0(5(3(0(x1))))))))) -> 0(3(5(5(0(0(2(1(0(x1)))))))))
   1(1(0(2(3(3(2(2(5(x1))))))))) -> 1(1(3(2(3(2(0(2(5(x1)))))))))
   2(3(4(1(2(2(2(1(4(x1))))))))) -> 2(3(2(4(1(2(2(1(4(x1)))))))))
   5(5(3(1(1(4(1(2(0(x1))))))))) -> 5(5(3(1(1(1(4(2(0(x1)))))))))
   1(0(3(4(5(1(1(3(4(0(x1)))))))))) -> 0(2(3(0(0(0(1(0(3(3(x1))))))))))
   1(1(2(5(4(1(4(3(5(1(x1)))))))))) -> 1(4(4(3(5(1(0(0(1(4(x1))))))))))
   2(2(2(4(4(1(1(5(3(5(x1)))))))))) -> 3(0(0(2(2(2(1(0(2(0(x1))))))))))
   4(1(5(3(1(2(2(4(3(4(x1)))))))))) -> 2(4(2(2(1(5(3(3(4(0(x1))))))))))
   4(2(1(0(3(5(2(4(4(4(x1)))))))))) -> 4(0(1(0(3(1(3(0(0(5(x1))))))))))
   0(0(3(5(4(5(0(3(5(0(2(x1))))))))))) -> 0(0(3(5(4(0(5(5(3(0(2(x1)))))))))))
   0(1(2(0(4(2(4(3(3(0(5(x1))))))))))) -> 0(1(0(5(2(2(1(5(0(4(x1))))))))))
   0(1(3(0(4(2(5(1(3(5(3(x1))))))))))) -> 3(4(3(1(4(0(5(2(4(2(x1))))))))))
   0(4(4(3(1(4(3(1(2(0(0(x1))))))))))) -> 2(1(2(3(1(1(3(3(3(2(x1))))))))))
   0(5(0(0(5(2(0(4(0(4(0(x1))))))))))) -> 0(5(0(0(5(2(4(0(0(4(0(x1)))))))))))
   0(5(3(5(1(4(0(5(3(2(4(x1))))))))))) -> 2(3(2(0(2(3(5(5(5(4(x1))))))))))
   1(0(4(1(0(2(4(1(1(1(4(x1))))))))))) -> 5(5(2(2(3(4(2(4(3(5(x1))))))))))
   1(0(5(3(2(4(2(0(2(4(0(x1))))))))))) -> 0(1(1(1(0(4(0(1(2(5(x1))))))))))
   1(1(5(4(1(0(4(0(0(1(3(x1))))))))))) -> 4(2(0(2(4(1(3(2(1(5(x1))))))))))
   1(2(3(5(1(4(3(2(5(0(2(x1))))))))))) -> 4(0(0(5(2(2(0(2(1(5(x1))))))))))
   1(3(5(0(0(1(1(1(4(0(1(x1))))))))))) -> 0(4(5(0(5(0(5(1(3(0(x1))))))))))
   1(4(0(5(5(5(1(0(3(2(1(x1))))))))))) -> 3(2(0(1(5(2(4(2(1(1(x1))))))))))
   1(4(2(5(0(4(2(1(2(3(5(x1))))))))))) -> 2(4(5(3(0(4(5(0(0(5(x1))))))))))
   1(4(4(0(5(0(4(2(1(3(2(x1))))))))))) -> 3(3(1(4(5(5(1(4(5(2(x1))))))))))
   1(5(5(5(5(3(4(2(5(1(2(x1))))))))))) -> 4(1(0(4(5(2(4(3(0(3(x1))))))))))

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