TRS Standard pair #516960685

details

property	value
status	complete
benchmark	thiemann15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n136.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.54415512085 seconds
cpu usage	6.972565655
max memory	5.06200064E8

stage attributes

key	value
output-size	13368
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 4 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) QDPOrderProof [EQUIVALENT, 63 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

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

   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   inc(0) -> 0
   inc(s(x)) -> s(inc(x))
   zero(0) -> true
   zero(s(x)) -> false
   p(0) -> 0
   p(s(x)) -> x
   bits(x) -> bitIter(x, 0)
   bitIter(x, y) -> if(zero(x), x, inc(y))
   if(true, x, y) -> p(y)
   if(false, x, y) -> bitIter(half(x), y)

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:

   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   inc(0) -> 0
   inc(s(x)) -> s(inc(x))
   zero(0) -> true
   zero(s(x)) -> false
   p(0) -> 0
   p(s(x)) -> x
   bits(x) -> bitIter(x, 0)
   bitIter(x, y) -> if(zero(x), x, inc(y))
   if(true, x, y) -> p(y)
   if(false, x, y) -> bitIter(half(x), y)

The set Q consists of the following terms:

   half(0)
   half(s(0))
   half(s(s(x0)))
   inc(0)
   inc(s(x0))

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