Derivational Complexity: TRS pair #487103270

details

property	value
status	complete
benchmark	26965.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.528 seconds
cpu usage	933.365
user time	925.226
system time	8.13972
max virtual memory	1.8778992E7
max residence set size	1.4932712E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 47 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), 11 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), 1491 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 29 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 3 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2105 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 139 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 126 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 872 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 14 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), 6198 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1889 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1892 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1879 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1879 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1894 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1867 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(0(1(2(1(0(3(2(x1)))))))) -> 0(2(0(1(1(0(3(2(x1))))))))
   1(0(4(1(2(5(2(4(x1)))))))) -> 1(0(4(1(5(2(2(4(x1))))))))
   1(4(4(0(4(1(5(2(5(x1))))))))) -> 1(4(4(1(4(5(0(2(5(x1)))))))))
   4(4(1(3(0(5(5(5(3(x1))))))))) -> 4(1(4(3(5(0(5(5(3(x1)))))))))
   1(1(3(1(2(1(1(1(0(0(x1)))))))))) -> 2(0(3(3(2(0(3(5(0(1(x1))))))))))
   1(3(0(5(5(1(1(1(2(2(x1)))))))))) -> 1(3(5(5(1(0(1(1(2(2(x1))))))))))
   3(0(1(4(4(2(0(2(2(4(x1)))))))))) -> 1(1(1(4(4(0(5(3(5(3(x1))))))))))
   0(0(5(4(0(4(2(3(5(2(2(x1))))))))))) -> 1(5(0(2(4(4(4(0(4(2(x1))))))))))
   0(1(0(1(0(3(2(3(5(5(1(x1))))))))))) -> 3(2(2(3(4(4(3(1(3(4(x1))))))))))
   0(1(0(2(4(2(1(2(5(1(5(x1))))))))))) -> 1(5(3(1(3(1(1(5(2(1(x1))))))))))
   0(2(0(4(4(2(4(1(0(3(3(x1))))))))))) -> 4(5(2(3(1(4(1(3(5(2(x1))))))))))
   0(2(2(4(1(5(3(0(0(0(1(x1))))))))))) -> 4(1(1(3(1(0(5(1(2(0(x1))))))))))
   0(3(1(0(3(2(4(2(2(1(2(x1))))))))))) -> 1(3(3(1(3(4(0(1(0(3(x1))))))))))
   0(5(2(5(2(5(1(4(4(4(2(x1))))))))))) -> 2(2(1(5(4(4(4(5(5(0(2(x1)))))))))))
   1(0(0(3(4(2(5(4(2(1(1(x1))))))))))) -> 2(4(5(4(4(3(3(4(2(2(x1))))))))))
   1(2(2(0(2(0(4(4(1(1(5(x1))))))))))) -> 5(2(5(2(1(2(1(0(0(0(x1))))))))))
   1(3(1(3(2(4(5(0(2(2(1(x1))))))))))) -> 2(5(1(1(2(2(3(1(4(2(x1))))))))))
   1(3(1(4(1(2(2(1(1(1(5(x1))))))))))) -> 3(1(3(0(1(1(5(2(5(0(x1))))))))))
   1(3(5(1(2(3(5(0(1(5(3(x1))))))))))) -> 2(0(5(1(1(3(2(3(5(3(x1))))))))))
   1(4(2(5(0(0(4(2(3(5(3(x1))))))))))) -> 1(2(5(5(2(0(2(1(1(2(x1))))))))))
   1(5(2(0(4(1(0(2(1(3(2(x1))))))))))) -> 5(0(2(1(2(1(5(2(0(1(x1))))))))))
   1(5(3(2(1(3(0(2(1(0(3(x1))))))))))) -> 5(0(5(3(4(0(4(4(1(2(x1))))))))))
   2(1(0(1(4(2(3(5(2(4(4(x1))))))))))) -> 1(0(1(5(4(4(2(1(1(3(x1))))))))))

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actions all output return to Derivational Complexity: TRS