Derivational Complexity: TRS pair #487103022

details
property	value
status	complete
benchmark	91210.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.036 seconds
cpu usage	910.049
user time	903.175
system time	6.87409
max virtual memory	1.8685984E7
max residence set size	1.3883112E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 34 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) RewriteLemmaProof [LOWER BOUND(ID), 24.8 s]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 722 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) NarrowingProof [BOTH BOUNDS(ID, ID), 257 ms]
            (30) CpxTypedWeightedCompleteTrs
            (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 172 ms]
            (32) CpxRNTS
            (33) SimplificationProof [BOTH BOUNDS(ID, ID), 116 ms]
            (34) CpxRNTS
        (35) CompletionProof [UPPER BOUND(ID), 0 ms]
        (36) CpxTypedWeightedCompleteTrs
            (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 676 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 3886 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1166 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1191 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1165 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4277 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5204 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6119 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6984 ms]
        (62) 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(0(0(1(1(2(0(0(0(2(1(2(1(1(1(0(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 0(2(1(1(0(0(2(1(2(1(0(0(0(1(0(0(2(0(2(2(0(0(0(1(0(0(2(x1)))))))))))))))))))))))))))
   0(0(0(2(0(1(0(1(1(1(0(0(2(2(1(0(2(1(1(0(1(1(2(x1))))))))))))))))))))))) -> 0(2(1(2(1(0(0(2(1(0(2(2(0(0(2(1(1(1(0(1(2(1(0(0(0(0(1(x1)))))))))))))))))))))))))))
   0(0(1(2(2(0(1(1(1(2(0(1(2(1(1(2(0(2(0(2(1(0(2(x1))))))))))))))))))))))) -> 0(2(1(0(1(2(0(0(0(1(1(2(0(1(1(2(0(1(0(0(0(0(0(2(0(0(0(x1)))))))))))))))))))))))))))
   0(0(2(2(0(1(2(2(0(2(2(0(2(2(0(2(1(0(0(2(0(0(2(x1))))))))))))))))))))))) -> 0(2(0(2(0(0(2(1(1(1(1(0(2(1(0(0(2(0(0(0(0(0(0(0(2(0(1(x1)))))))))))))))))))))))))))
   0(1(0(0(0(1(1(2(2(0(2(1(1(1(1(1(1(2(0(0(0(2(2(x1))))))))))))))))))))))) -> 0(0(2(1(2(2(0(0(1(2(2(1(2(1(0(1(0(1(1(1(1(2(1(0(0(0(0(x1)))))))))))))))))))))))))))
   0(1(1(0(2(0(2(1(0(2(1(2(0(1(2(1(0(1(1(0(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(0(0(1(0(2(0(0(1(2(0(0(1(0(1(0(1(0(0(1(0(0(2(0(x1)))))))))))))))))))))))))))
   0(1(1(1(1(2(0(2(1(0(0(2(2(2(1(0(2(1(0(1(0(2(2(x1))))))))))))))))))))))) -> 0(2(1(0(0(0(0(2(1(2(2(1(0(0(1(2(0(0(0(2(0(1(2(0(0(0(0(x1)))))))))))))))))))))))))))
   0(1(1(2(2(0(0(0(1(0(1(1(1(2(1(1(1(0(0(1(1(2(2(x1))))))))))))))))))))))) -> 0(0(0(0(0(1(2(2(0(1(1(1(0(2(2(2(2(2(2(0(0(1(0(0(2(1(0(x1)))))))))))))))))))))))))))
   0(1(2(2(0(1(2(0(0(2(0(2(2(1(1(1(0(0(0(0(1(2(2(x1))))))))))))))))))))))) -> 0(0(1(0(1(2(1(0(2(1(0(0(2(0(0(2(2(2(0(2(2(0(0(1(1(0(1(x1)))))))))))))))))))))))))))
   0(2(0(1(0(0(2(2(1(1(0(0(2(2(1(2(1(1(1(0(2(1(2(x1))))))))))))))))))))))) -> 0(2(0(2(0(1(0(0(0(1(0(0(2(2(2(1(0(1(2(0(0(1(2(0(0(0(0(x1)))))))))))))))))))))))))))
   0(2(0(1(0(2(0(1(1(1(2(2(0(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))) -> 0(0(0(2(1(0(0(2(0(1(0(2(0(1(0(2(1(0(2(0(0(1(2(2(2(0(1(x1)))))))))))))))))))))))))))
   0(2(1(1(1(1(0(0(0(2(0(1(2(1(0(1(2(1(2(0(2(0(2(x1))))))))))))))))))))))) -> 0(1(2(2(0(1(0(2(2(1(0(1(0(1(0(0(2(1(0(0(2(0(2(1(2(0(0(x1)))))))))))))))))))))))))))
   0(2(1(1(2(2(0(2(2(1(2(1(0(1(1(0(0(1(0(2(0(1(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(2(1(1(0(0(0(1(0(2(1(2(0(0(2(0(1(2(1(0(0(2(1(x1)))))))))))))))))))))))))))
   1(0(0(0(2(2(2(1(1(0(2(0(2(0(0(0(1(0(1(0(1(2(0(x1))))))))))))))))))))))) -> 1(0(0(0(1(2(1(0(0(2(0(0(0(0(2(2(2(2(1(0(1(0(0(2(0(0(1(x1)))))))))))))))))))))))))))
   1(0(0(1(2(2(2(1(2(0(0(2(1(0(2(1(1(2(1(1(2(0(2(x1))))))))))))))))))))))) -> 1(0(0(2(1(0(2(0(0(0(0(0(1(1(1(2(1(0(2(0(2(0(0(0(2(0(2(x1)))))))))))))))))))))))))))
   1(0(0(2(0(1(2(0(2(2(0(0(1(2(2(0(1(0(2(2(0(1(1(x1))))))))))))))))))))))) -> 1(0(0(1(0(1(0(0(2(0(0(1(0(2(1(2(1(0(2(0(0(0(2(2(2(0(0(x1)))))))))))))))))))))))))))
   1(0(0(2(1(2(0(1(0(1(2(0(1(1(1(0(2(2(1(0(1(2(2(x1))))))))))))))))))))))) -> 1(0(2(1(2(1(0(2(2(0(0(2(1(0(1(1(0(2(1(0(2(0(1(0(2(2(2(x1)))))))))))))))))))))))))))
   1(0(2(2(0(0(1(1(2(0(1(0(1(0(0(2(2(1(1(2(1(1(2(x1))))))))))))))))))))))) -> 1(0(1(0(2(2(1(1(0(2(0(2(1(0(1(0(1(0(1(1(2(1(2(1(0(0(2(x1)))))))))))))))))))))))))))
   1(1(0(2(2(2(1(1(2(0(0(2(2(0(0(0(0(1(0(0(1(2(1(x1))))))))))))))))))))))) -> 1(0(1(0(2(0(0(1(0(1(0(1(0(0(1(0(0(0(0(0(0(2(2(0(2(1(0(x1)))))))))))))))))))))))))))
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