TRS Stand 20472 pair #381711914

details

property	value
status	complete
benchmark	thiemann10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n085.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.07703208923 seconds
cpu usage	5.105540742
max memory	3.57371904E8

stage attributes

key	value
output-size	13983
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 3 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, 79 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))
   lastbit(0) -> 0
   lastbit(s(0)) -> s(0)
   lastbit(s(s(x))) -> lastbit(x)
   zero(0) -> true
   zero(s(x)) -> false
   conv(x) -> conviter(x, cons(0, nil))
   conviter(x, l) -> if(zero(x), x, l)
   if(true, x, l) -> l
   if(false, x, l) -> conviter(half(x), cons(lastbit(x), l))

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))
   lastbit(0) -> 0
   lastbit(s(0)) -> s(0)
   lastbit(s(s(x))) -> lastbit(x)
   zero(0) -> true
   zero(s(x)) -> false
   conv(x) -> conviter(x, cons(0, nil))
   conviter(x, l) -> if(zero(x), x, l)
   if(true, x, l) -> l
   if(false, x, l) -> conviter(half(x), cons(lastbit(x), l))

The set Q consists of the following terms:

   half(0)
   half(s(0))
   half(s(s(x0)))
   lastbit(0)
   lastbit(s(0))
   lastbit(s(s(x0)))
   zero(0)

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