TRS Standard pair #487073943

details

property	value
status	complete
benchmark	aprove4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.71286 seconds
cpu usage	6.28404
user time	6.02278
system time	0.261263
max virtual memory	1.8477524E7
max residence set size	366640.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 6 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) MNOCProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QReductionProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) TransformationProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QReductionProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) TransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
        (37) AND
            (38) QDP
                (39) TransformationProof [EQUIVALENT, 0 ms]
                (40) QDP
                (41) TransformationProof [EQUIVALENT, 0 ms]
                (42) QDP
                (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (44) YES
            (45) QDP
                (46) UsableRulesProof [EQUIVALENT, 0 ms]
                (47) QDP
                (48) QReductionProof [EQUIVALENT, 0 ms]
                (49) QDP
                (50) TransformationProof [EQUIVALENT, 0 ms]
                (51) QDP
                (52) TransformationProof [EQUIVALENT, 0 ms]
                (53) QDP
                (54) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (55) YES


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

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

   p(0) -> s(s(0))
   p(s(x)) -> x
   p(p(s(x))) -> p(x)
   le(p(s(x)), x) -> le(x, x)
   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   minus(x, y) -> if(le(x, y), x, y)
   if(true, x, y) -> 0
   if(false, x, y) -> s(minus(p(x), y))

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:

   P(p(s(x))) -> P(x)
   LE(p(s(x)), x) -> LE(x, x)
   LE(s(x), s(y)) -> LE(x, y)
   MINUS(x, y) -> IF(le(x, y), x, y)

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