TRS Standard pair #487072853

details

property	value
status	complete
benchmark	divExp.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.9438 seconds
cpu usage	4.6119
user time	4.37663
system time	0.235271
max virtual memory	1.8617292E7
max residence set size	357936.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 19 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) QDPOrderProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QReductionProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPQMonotonicMRRProof [EQUIVALENT, 10 ms]
        (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) TRUE


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

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

   minus(x, x) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   minus(0, x) -> 0
   minus(x, 0) -> x
   div(s(x), s(y)) -> s(div(minus(x, y), s(y)))
   div(0, s(y)) -> 0
   f(x, 0, b) -> x
   f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b)

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, x) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   minus(0, x) -> 0
   minus(x, 0) -> x
   div(s(x), s(y)) -> s(div(minus(x, y), s(y)))
   div(0, s(y)) -> 0
   f(x, 0, b) -> x
   f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b)

The set Q consists of the following terms:

   minus(x0, x0)
   minus(s(x0), s(x1))
   minus(0, x0)
   minus(x0, 0)
   div(s(x0), s(x1))
   div(0, s(x0))
   f(x0, 0, x1)
   f(x0, s(x1), x2)


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

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

(4)
Obligation:
Q DP problem:

popout

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

job log

popout

actions all output return to TRS Standard