TRS Conditional pair #487562906

details

property	value
status	complete
benchmark	378.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.07755303383 seconds
cpu usage	5.169824012
max memory	3.46689536E8

stage attributes

key	value
output-size	9120
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Quasi decreasingness of the given CTRS could be proven:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 63 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) MRRProof [EQUIVALENT, 25 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 36 ms]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE


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(0)
Obligation:
Conditional term rewrite system:
The TRS R consists of the following rules:

   cons(x, cons(x, rest)) -> cons(x, rest)
   orient(s(x), 0) -> pair(0, s(x))

The conditional TRS C consists of the following conditional rules:

   cons(x, cons(y, rest)) -> cons(z1, cons(z2, rest)) <= orient(x, y) -> pair(z1, z2)
   orient(s(x), s(y)) -> pair(s(z1), s(z2)) <= orient(x, y) -> pair(z1, z2)


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(1) CTRSToQTRSProof (SOUND)
The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
----------------------------------------

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

   cons(x, cons(y, rest)) -> U1(orient(x, y), rest)
   U1(pair(z1, z2), rest) -> cons(z1, cons(z2, rest))
   orient(s(x), s(y)) -> U2(orient(x, y))
   U2(pair(z1, z2)) -> pair(s(z1), s(z2))
   cons(x, cons(x, rest)) -> cons(x, rest)
   orient(s(x), 0) -> pair(0, s(x))

Q is empty.

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

   POL(0) = 0
   POL(U1(x_1, x_2)) = 2 + x_1 + x_2
   POL(U2(x_1)) = x_1
   POL(cons(x_1, x_2)) = 1 + x_1 + x_2
   POL(orient(x_1, x_2)) = x_1 + x_2
   POL(pair(x_1, x_2)) = 2*x_1 + x_2
   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:

   cons(x, cons(x, rest)) -> cons(x, rest)




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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   cons(x, cons(y, rest)) -> U1(orient(x, y), rest)

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