TRS Innermost pair #487524177

details

property	value
status	complete
benchmark	Ex1_Zan97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.23848795891 seconds
cpu usage	9.475366374
max memory	1.13739776E9

stage attributes

key	value
output-size	16058
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [SOUND, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 1 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) UsableRulesProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 16 ms]
        (26) QDP
        (27) DependencyGraphProof [EQUIVALENT, 0 ms]
        (28) AND
            (29) QDP
                (30) QDPOrderProof [EQUIVALENT, 0 ms]
                (31) QDP
                (32) PisEmptyProof [EQUIVALENT, 0 ms]
                (33) YES
            (34) QDP
                (35) QDPOrderProof [EQUIVALENT, 0 ms]
                (36) QDP
                (37) PisEmptyProof [EQUIVALENT, 0 ms]
                (38) YES


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

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

   active(g(X)) -> mark(h(X))
   active(c) -> mark(d)
   active(h(d)) -> mark(g(c))
   proper(g(X)) -> g(proper(X))
   proper(h(X)) -> h(proper(X))
   proper(c) -> ok(c)
   proper(d) -> ok(d)
   g(ok(X)) -> ok(g(X))
   h(ok(X)) -> ok(h(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(g(x0))
   active(c)
   active(h(d))
   proper(g(x0))
   proper(h(x0))
   proper(c)
   proper(d)
   g(ok(x0))
   h(ok(x0))
   top(mark(x0))
   top(ok(x0))


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(1) QTRS Reverse (SOUND)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   g(active(X)) -> h(mark(X))

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