Derivational Complexity: TRS pair #487102858

details
property	value
status	complete
benchmark	231378.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	292.607 seconds
cpu usage	947.821
user time	941.478
system time	6.34348
max virtual memory	1.8963004E7
max residence set size	1.5069588E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 71 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), 2 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 48 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 521 ms]
    (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), 5658 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (30) CpxRNTS
        (31) CompletionProof [UPPER BOUND(ID), 0 ms]
        (32) CpxTypedWeightedCompleteTrs
            (33) NarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
            (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
            (37) SimplificationProof [BOTH BOUNDS(ID, ID), 12 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 805 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (42) CdtProblem
        (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (48) CdtProblem
        (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4627 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1194 ms]
        (52) CdtProblem
        (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1174 ms]
        (56) CdtProblem
        (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 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(x1) -> 1(x1)
   0(0(x1)) -> 0(x1)
   3(4(5(x1))) -> 4(3(5(x1)))
   2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(1(1(0(0(1(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   0(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions all output return to Derivational Complexity: TRS