TRS Stand 20472 pair #381712679

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	n023.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.87385582924 seconds
cpu usage	4.246597812
max memory	2.56630784E8

stage attributes

key	value
output-size	13976
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 1 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) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

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

   minus(X, s(Y)) -> pred(minus(X, Y))
   minus(X, 0) -> X
   pred(s(X)) -> X
   le(s(X), s(Y)) -> le(X, Y)
   le(s(X), 0) -> false
   le(0, Y) -> true
   gcd(0, Y) -> 0
   gcd(s(X), 0) -> s(X)
   gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y))
   if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y))
   if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X))

Q is empty.

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

(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

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

   minus(X, s(Y)) -> pred(minus(X, Y))
   minus(X, 0) -> X
   pred(s(X)) -> X
   le(s(X), s(Y)) -> le(X, Y)
   le(s(X), 0) -> false
   le(0, Y) -> true
   gcd(0, Y) -> 0
   gcd(s(X), 0) -> s(X)
   gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y))
   if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y))
   if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(X))

The set Q consists of the following terms:

   minus(x0, s(x1))
   minus(x0, 0)
   pred(s(x0))
   le(s(x0), s(x1))
   le(s(x0), 0)
   le(0, x0)
   gcd(0, x0)
   gcd(s(x0), 0)
   gcd(s(x0), s(x1))

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