Derivational Complexity: TRS Innermost pair #487108078

details

property	value
status	complete
benchmark	tpa03.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	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.518 seconds
cpu usage	773.029
user time	766.56
system time	6.46819
max virtual memory	1.9576656E7
max residence set size	8383180.0

stage attributes

key	value
starexec-result	KILLED

output

KILLED
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) 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), 150 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 2649 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(18) CdtProblem
    (19) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CdtProblem
    (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CdtProblem
    (23) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CdtProblem
    (25) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (26) CdtProblem
    (27) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CdtProblem
    (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
    (32) CdtProblem
    (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 27 ms]
    (58) CdtProblem
    (59) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 111 ms]
    (62) CdtProblem
(63) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(64) CpxRelTRS
    (65) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CpxWeightedTrs
    (67) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CpxTypedWeightedTrs
    (69) CompletionProof [UPPER BOUND(ID), 0 ms]
    (70) CpxTypedWeightedCompleteTrs
        (71) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms]
        (72) CpxRNTS
    (73) CompletionProof [UPPER BOUND(ID), 2 ms]
    (74) CpxTypedWeightedCompleteTrs
        (75) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CpxTypedWeightedCompleteTrs
        (77) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms]
        (78) CpxRNTS
        (79) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CpxRNTS


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   f(x, f(y, x)) -> f(f(x, x), f(a, y))

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actions all output return to Derivational Complexity: TRS Innermost