TRS Condi 20667 pair #381733067

details

property	value
status	complete
benchmark	353.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n089.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.28474116325 seconds
cpu usage	5.762362619
max memory	2.9136896E8

stage attributes

key	value
output-size	15629
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Quasi decreasingness of the given CTRS could be proven:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 114 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 0 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 0 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 6 ms]
(10) QTRS
(11) DependencyPairsProof [EQUIVALENT, 15 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) AND
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) MRRProof [EQUIVALENT, 18 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) TRUE


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

   ssp'(xs, 0) -> nil
   sub(z, 0) -> z
   get(cons(y, ys)) -> tp2(y, ys)

The conditional TRS C consists of the following conditional rules:

   ssp'(cons(y', ws), v) -> cons(y', ys') <= sub(v, y') -> w, ssp'(ws, w) -> ys'
   ssp'(cons(x', xs'), v) -> cons(y', ys') <= get(xs') -> tp2(y', zs), sub(v, y') -> w, ssp'(cons(x', zs), w) -> ys'
   sub(s(v), s(w)) -> z <= sub(v, w) -> z
   get(cons(x', xs')) -> tp2(y, cons(x', zs)) <= get(xs') -> tp2(y, zs)


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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:

   ssp'(cons(y', ws), v) -> U1(sub(v, y'), y', ws)
   U1(w, y', ws) -> U2(ssp'(ws, w), y')
   U2(ys', y') -> cons(y', ys')
   ssp'(cons(x', xs'), v) -> U3(get(xs'), x', v)
   U3(tp2(y', zs), x', v) -> U4(sub(v, y'), x', y', zs)
   U4(w, x', y', zs) -> U5(ssp'(cons(x', zs), w), y')
   U5(ys', y') -> cons(y', ys')
   sub(s(v), s(w)) -> U6(sub(v, w))
   U6(z) -> z
   get(cons(x', xs')) -> U7(get(xs'), x')
   U7(tp2(y, zs), x') -> tp2(y, cons(x', zs))
   ssp'(xs, 0) -> nil
   sub(z, 0) -> z
   get(cons(y, ys)) -> tp2(y, ys)

Q is empty.

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

   POL(0) = 0
   POL(U1(x_1, x_2, x_3)) = x_1 + x_2 + 2*x_3
   POL(U2(x_1, x_2)) = x_1 + x_2
   POL(U3(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + x_3
   POL(U4(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + x_3 + 2*x_4

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