Derivational Complexity: TRS pair #487103550

details

property	value
status	complete
benchmark	26875.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.246 seconds
cpu usage	924.622
user time	916.432
system time	8.18972
max virtual memory	1.8919304E7
max residence set size	1.5020412E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 44 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 3 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 7 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), 1607 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 2 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 42 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 11 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2164 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 161 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 153 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 9 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 1074 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, 9 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7168 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2112 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2180 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2168 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2157 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2163 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2139 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(2(1(3(1(x1)))))) -> 0(1(2(3(1(1(x1))))))
   3(4(4(2(2(3(5(x1))))))) -> 3(4(4(2(3(2(5(x1)))))))
   4(2(2(1(3(0(1(1(x1)))))))) -> 4(0(1(2(3(1(2(1(x1))))))))
   1(1(4(1(0(5(5(1(1(x1))))))))) -> 1(1(1(4(5(5(0(1(1(x1)))))))))
   4(3(2(3(0(2(4(0(1(x1))))))))) -> 4(2(3(3(2(0(4(0(1(x1)))))))))
   2(1(0(2(0(2(0(4(4(4(x1)))))))))) -> 4(4(0(1(4(1(2(3(3(4(x1))))))))))
   3(0(2(5(3(2(1(4(4(5(x1)))))))))) -> 5(0(1(5(3(3(0(1(3(3(x1))))))))))
   3(4(5(2(2(0(3(1(0(0(x1)))))))))) -> 2(3(3(0(3(4(1(0(3(3(x1))))))))))
   5(5(4(2(2(1(5(0(1(1(x1)))))))))) -> 4(4(3(3(0(2(2(4(2(1(x1))))))))))
   0(0(0(1(3(0(2(3(5(4(3(x1))))))))))) -> 4(2(2(3(0(2(5(0(2(4(x1))))))))))
   0(0(4(0(1(4(4(0(1(3(2(x1))))))))))) -> 4(5(0(4(0(0(2(3(5(5(x1))))))))))
   0(1(4(4(2(0(4(5(3(1(2(x1))))))))))) -> 1(5(4(5(4(3(2(1(2(1(x1))))))))))
   0(2(2(0(2(1(1(5(0(0(3(x1))))))))))) -> 2(0(0(4(2(1(1(2(3(5(x1))))))))))
   0(2(2(2(2(0(0(3(4(2(4(x1))))))))))) -> 5(0(4(5(1(4(4(0(0(4(x1))))))))))
   0(2(4(2(3(5(2(2(5(5(5(x1))))))))))) -> 4(2(0(0(2(4(3(1(2(4(x1))))))))))
   0(4(0(1(5(2(4(1(4(1(3(x1))))))))))) -> 0(0(3(5(0(1(5(4(2(2(x1))))))))))
   0(5(1(0(5(5(0(5(2(1(3(x1))))))))))) -> 4(4(4(5(0(3(3(4(0(4(x1))))))))))
   1(1(1(1(5(4(1(3(2(1(1(x1))))))))))) -> 1(5(5(2(4(5(2(1(4(4(x1))))))))))
   1(1(1(5(4(1(1(2(0(5(0(x1))))))))))) -> 3(2(0(0(0(5(5(4(0(2(x1))))))))))
   1(2(1(5(4(5(3(5(2(4(0(x1))))))))))) -> 1(2(1(5(4(5(5(3(2(4(0(x1)))))))))))
   1(2(5(5(1(4(0(1(4(2(5(x1))))))))))) -> 0(0(0(5(4(5(3(2(0(0(x1))))))))))
   1(3(0(2(3(4(5(3(2(3(3(x1))))))))))) -> 1(3(0(2(4(5(3(3(2(3(3(x1)))))))))))
   1(3(1(4(1(5(1(2(4(4(1(x1))))))))))) -> 3(0(4(3(4(0(1(4(1(0(x1))))))))))

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