TRS Standard pair #487073098

details

property	value
status	complete
benchmark	kabasci05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.12261 seconds
cpu usage	10.5753
user time	10.0563
system time	0.518964
max virtual memory	1.8677444E7
max residence set size	379008.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) QDPOrderProof [EQUIVALENT, 58 ms]
        (7) QDP
        (8) DependencyGraphProof [EQUIVALENT, 0 ms]
        (9) AND
            (10) QDP
                (11) UsableRulesProof [EQUIVALENT, 0 ms]
                (12) QDP
                (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (14) YES
            (15) QDP
                (16) UsableRulesProof [EQUIVALENT, 0 ms]
                (17) QDP
                (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 66 ms]
        (37) QDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES


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

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

   min(x, 0) -> 0
   min(0, y) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(x, 0) -> x
   max(0, y) -> y
   max(s(x), s(y)) -> s(max(x, y))
   minus(x, 0) -> x
   minus(s(x), s(y)) -> s(minus(x, y))
   gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y)))
   transform(x) -> s(s(x))
   transform(cons(x, y)) -> cons(cons(x, x), x)
   transform(cons(x, y)) -> y
   transform(s(x)) -> s(s(transform(x)))
   cons(x, y) -> y
   cons(x, cons(y, s(z))) -> cons(y, x)
   cons(cons(x, z), s(y)) -> transform(x)

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   MIN(s(x), s(y)) -> MIN(x, y)
   MAX(s(x), s(y)) -> MAX(x, y)
   MINUS(s(x), s(y)) -> MINUS(x, y)
   GCD(s(x), s(y)) -> GCD(minus(max(x, y), min(x, transform(y))), s(min(x, y)))
   GCD(s(x), s(y)) -> MINUS(max(x, y), min(x, transform(y)))
   GCD(s(x), s(y)) -> MAX(x, y)
   GCD(s(x), s(y)) -> MIN(x, transform(y))
   GCD(s(x), s(y)) -> TRANSFORM(y)
   GCD(s(x), s(y)) -> MIN(x, y)
   TRANSFORM(cons(x, y)) -> CONS(cons(x, x), x)
   TRANSFORM(cons(x, y)) -> CONS(x, x)
   TRANSFORM(s(x)) -> TRANSFORM(x)
   CONS(x, cons(y, s(z))) -> CONS(y, x)
   CONS(cons(x, z), s(y)) -> TRANSFORM(x)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard