TRS Innermost pair #487524419

details

property	value
status	complete
benchmark	Ex14_Luc06_iGM.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	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.5111758709 seconds
cpu usage	6.476045595
max memory	4.79154176E8

stage attributes

key	value
output-size	39991
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) MRRProof [EQUIVALENT, 13 ms]
        (28) QDP
        (29) TransformationProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) TransformationProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) TransformationProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) TransformationProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) TransformationProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) QDPQMonotonicMRRProof [EQUIVALENT, 66 ms]
        (46) QDP
        (47) DependencyGraphProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QDPOrderProof [EQUIVALENT, 6 ms]
        (50) QDP
        (51) PisEmptyProof [EQUIVALENT, 0 ms]
        (52) YES


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

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   active(h(X)) -> mark(g(X, X))
   active(g(a, X)) -> mark(f(b, X))
   active(f(X, X)) -> mark(h(a))
   active(a) -> mark(b)
   mark(h(X)) -> active(h(mark(X)))
   mark(g(X1, X2)) -> active(g(mark(X1), X2))
   mark(a) -> active(a)
   mark(f(X1, X2)) -> active(f(mark(X1), X2))
   mark(b) -> active(b)
   h(mark(X)) -> h(X)
   h(active(X)) -> h(X)
   g(mark(X1), X2) -> g(X1, X2)
   g(X1, mark(X2)) -> g(X1, X2)
   g(active(X1), X2) -> g(X1, X2)
   g(X1, active(X2)) -> g(X1, X2)
   f(mark(X1), X2) -> f(X1, X2)
   f(X1, mark(X2)) -> f(X1, X2)
   f(active(X1), X2) -> f(X1, X2)
   f(X1, active(X2)) -> f(X1, X2)

The set Q consists of the following terms:

   active(h(x0))
   active(g(a, x0))
   active(f(x0, x0))

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