TRS Inner 89993 pair #381733591

details

property	value
status	complete
benchmark	#4.24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.74254918098 seconds
cpu usage	4.04894182
max memory	2.55021056E8

stage attributes

key	value
output-size	8859
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 59 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 15 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 2 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QReductionProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QReductionProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES


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

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

   intlist(nil) -> nil
   intlist(cons(x, y)) -> cons(s(x), intlist(y))
   int(0, 0) -> cons(0, nil)
   int(0, s(y)) -> cons(0, int(s(0), s(y)))
   int(s(x), 0) -> nil
   int(s(x), s(y)) -> intlist(int(x, y))

The set Q consists of the following terms:

   intlist(nil)
   intlist(cons(x0, x1))
   int(0, 0)
   int(0, s(x0))
   int(s(x0), 0)
   int(s(x0), s(x1))


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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(cons(x_1, x_2)) = 2*x_1 + x_2
   POL(int(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
   POL(intlist(x_1)) = x_1
   POL(nil) = 0
   POL(s(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   int(0, 0) -> cons(0, nil)
   int(s(x), 0) -> nil




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

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

   intlist(nil) -> nil
   intlist(cons(x, y)) -> cons(s(x), intlist(y))
   int(0, s(y)) -> cons(0, int(s(0), s(y)))
   int(s(x), s(y)) -> intlist(int(x, y))

The set Q consists of the following terms:

   intlist(nil)
   intlist(cons(x0, x1))
   int(0, 0)
   int(0, s(x0))

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