Derivational Complexity: TRS pair #487103556

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	n137.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.027 seconds
cpu usage	805.198
user time	797.467
system time	7.73028
max virtual memory	1.8911204E7
max residence set size	1.506228E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 46 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), 17 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), 1234 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 48 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), 1655 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 160 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 174 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 720 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 19 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5662 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1704 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1708 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1702 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1709 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1670 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1690 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(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))))))))))

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