Derivational Complexity: TRS pair #487102650

details

property	value
status	complete
benchmark	25734.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.974 seconds
cpu usage	875.572
user time	867.228
system time	8.3439
max virtual memory	1.8848456E7
max residence set size	1.5258604E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 69 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), 1302 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 32 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1840 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 178 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 164 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 840 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5987 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1788 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1791 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1790 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1827 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1790 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1835 ms]
        (58) 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(1(0(2(3(4(x1)))))) -> 0(1(0(3(2(4(x1))))))
   1(0(3(5(4(1(x1)))))) -> 1(1(3(0(5(4(x1))))))
   3(0(0(1(5(1(5(x1))))))) -> 3(0(0(5(1(1(5(x1)))))))
   5(5(1(3(0(4(5(x1))))))) -> 5(5(3(1(0(4(5(x1)))))))
   2(4(3(2(0(1(5(2(x1)))))))) -> 2(4(2(3(1(0(5(2(x1))))))))
   3(0(2(3(3(5(4(5(1(4(x1)))))))))) -> 3(0(3(2(3(5(4(5(1(4(x1))))))))))
   4(3(5(5(1(4(4(0(0(3(x1)))))))))) -> 4(3(5(5(1(4(0(4(0(3(x1))))))))))
   5(5(4(1(2(3(5(3(5(3(x1)))))))))) -> 5(5(1(4(5(2(3(3(5(3(x1))))))))))
   0(1(4(0(4(2(3(4(4(1(3(x1))))))))))) -> 3(1(5(3(2(2(1(1(5(0(x1))))))))))
   0(2(1(3(2(0(5(4(2(0(5(x1))))))))))) -> 2(2(1(1(3(1(4(5(4(0(x1))))))))))
   0(2(1(3(4(3(5(4(3(5(5(x1))))))))))) -> 1(0(0(1(1(4(1(4(1(3(x1))))))))))
   0(2(3(4(1(4(0(2(3(1(0(x1))))))))))) -> 3(1(0(2(2(1(4(1(5(1(x1))))))))))
   0(3(3(0(0(2(0(5(2(4(2(x1))))))))))) -> 5(4(5(0(3(0(3(0(5(0(x1))))))))))
   0(3(3(2(2(2(0(2(4(0(1(x1))))))))))) -> 5(4(3(1(5(0(0(0(4(2(x1))))))))))
   0(5(0(0(2(4(4(1(5(0(3(x1))))))))))) -> 1(4(3(4(3(3(2(4(3(3(x1))))))))))
   0(5(0(4(1(3(4(4(3(3(3(x1))))))))))) -> 0(0(3(0(3(4(0(4(4(4(x1))))))))))
   0(5(0(4(3(2(3(2(4(3(3(x1))))))))))) -> 3(5(0(0(5(5(1(5(0(0(x1))))))))))
   1(0(0(5(4(2(5(2(0(2(0(x1))))))))))) -> 3(0(0(5(4(5(5(4(4(2(x1))))))))))
   1(2(0(3(0(0(4(4(4(1(5(x1))))))))))) -> 1(0(0(2(4(4(0(4(2(3(x1))))))))))
   1(3(1(3(1(2(1(0(1(0(1(x1))))))))))) -> 1(2(0(2(4(5(0(1(5(2(x1))))))))))
   1(4(1(4(0(1(0(1(5(4(1(x1))))))))))) -> 3(0(3(2(2(0(1(3(0(2(x1))))))))))
   1(4(4(2(1(2(2(3(2(5(5(x1))))))))))) -> 1(1(1(5(1(0(1(5(4(2(x1))))))))))
   1(5(3(5(1(1(4(4(3(0(2(x1))))))))))) -> 0(5(0(0(0(0(2(0(1(3(x1))))))))))

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actions all output return to Derivational Complexity: TRS