TRS Condi 20667 pair #381733009

details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Mixed_CTRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.89218902588 seconds
cpu usage	4.496984793
max memory	2.65494528E8

stage attributes

key	value
output-size	9812
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Quasi decreasingness of the given CTRS could be proven:

(0) CTRS
(1) CTRSToQTRSProof [SOUND, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 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) QDPOrderProof [EQUIVALENT, 31 ms]
        (19) QDP
        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
        (21) TRUE


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

   less(x, 0) -> false
   less(0, s(x)) -> true
   less(s(x), s(y)) -> less(x, y)
   minus(0, s(y)) -> 0
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   gcd(x, x) -> x
   gcd(s(x), 0) -> s(x)
   gcd(0, s(y)) -> s(y)

The conditional TRS C consists of the following conditional rules:

   gcd(s(x), s(y)) -> gcd(minus(x, y), s(y)) <= less(y, x) -> true
   gcd(s(x), s(y)) -> gcd(s(x), minus(y, x)) <= less(x, y) -> true


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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:

   gcd(s(x), s(y)) -> U1(less(y, x), x, y)
   U1(true, x, y) -> gcd(minus(x, y), s(y))
   gcd(s(x), s(y)) -> U2(less(x, y), x, y)
   U2(true, x, y) -> gcd(s(x), minus(y, x))
   less(x, 0) -> false
   less(0, s(x)) -> true
   less(s(x), s(y)) -> less(x, y)
   minus(0, s(y)) -> 0
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   gcd(x, x) -> x
   gcd(s(x), 0) -> s(x)
   gcd(0, s(y)) -> s(y)

Q is empty.

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(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   GCD(s(x), s(y)) -> U1^1(less(y, x), x, y)
   GCD(s(x), s(y)) -> LESS(y, x)

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