TRS Standard pair #487073043

details

property	value
status	complete
benchmark	thiemann16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.14836 seconds
cpu usage	6.15042
user time	5.90412
system time	0.246306
max virtual memory	1.8478552E7
max residence set size	389480.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Overlay + Local Confluence [EQUIVALENT, 0 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 4 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 109 ms]
        (34) QDP
        (35) PisEmptyProof [EQUIVALENT, 0 ms]
        (36) YES


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

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

   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(x)))) -> check(s(x))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> timesIter(x, y, 0)
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
   p(s(x)) -> x
   p(0) -> 0
   if(zero, x, y, z, u) -> z
   if(odd, x, y, z, u) -> timesIter(p(x), y, u)
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z))))

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:

   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(x)))) -> check(s(x))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> timesIter(x, y, 0)
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
   p(s(x)) -> x
   p(0) -> 0
   if(zero, x, y, z, u) -> z
   if(odd, x, y, z, u) -> timesIter(p(x), y, u)
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z))))

popout

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

job log

popout

actions all output return to TRS Standard