TRS Standard pair #487072968

details

property	value
status	complete
benchmark	wiehe12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.89912 seconds
cpu usage	8.02373
user time	7.63391
system time	0.389822
max virtual memory	1.908698E7
max residence set size	537240.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 58 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 13 ms]
        (24) QDP
        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (26) YES
    (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 27 ms]
        (29) QDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (41) YES
    (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 66 ms]
        (44) QDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES


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

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

   g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0))), k(n(s(x), s(y)), s(s(0))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y))))
   n(0, y) -> 0
   n(x, 0) -> 0
   n(s(x), s(y)) -> s(n(x, y))
   m(0, y) -> y
   m(x, 0) -> x
   m(s(x), s(y)) -> s(m(x, y))
   k(0, s(y)) -> 0
   k(s(x), s(y)) -> s(k(minus(x, y), s(y)))
   t(x) -> p(x, x)
   p(s(x), s(y)) -> s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
   p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x))
   p(0, y) -> y
   p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y))))
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   id(x) -> x
   if(true, x, y) -> x
   if(false, x, y) -> y
   not(x) -> if(x, false, true)
   and(x, false) -> false
   and(true, true) -> true
   f(0) -> true
   f(s(x)) -> h(x)
   h(0) -> false
   h(s(x)) -> f(x)
   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)

Q is empty.

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