TRS Stand 20472 pair #381714048

details

property	value
status	complete
benchmark	otto11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n009.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.31685209274 seconds
cpu usage	5.46723605
max memory	2.80772608E8

stage attributes

key	value
output-size	16327
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 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) NonInfProof [EQUIVALENT, 46 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

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

   times(x, y) -> help(x, y, 0)
   help(x, y, c) -> if(lt(c, y), x, y, c)
   if(true, x, y, c) -> plus(x, help(x, y, s(c)))
   if(false, x, y, c) -> 0
   lt(0, s(x)) -> true
   lt(s(x), 0) -> false
   lt(s(x), s(y)) -> lt(x, y)
   plus(x, 0) -> x
   plus(0, x) -> x
   plus(x, s(y)) -> s(plus(x, y))
   plus(s(x), y) -> s(plus(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:

   times(x, y) -> help(x, y, 0)
   help(x, y, c) -> if(lt(c, y), x, y, c)
   if(true, x, y, c) -> plus(x, help(x, y, s(c)))
   if(false, x, y, c) -> 0
   lt(0, s(x)) -> true
   lt(s(x), 0) -> false
   lt(s(x), s(y)) -> lt(x, y)
   plus(x, 0) -> x
   plus(0, x) -> x
   plus(x, s(y)) -> s(plus(x, y))
   plus(s(x), y) -> s(plus(x, y))

The set Q consists of the following terms:

   times(x0, x1)
   help(x0, x1, x2)
   if(true, x0, x1, x2)
   if(false, x0, x1, x2)
   lt(0, s(x0))
   lt(s(x0), 0)
   lt(s(x0), s(x1))
   plus(x0, 0)
   plus(0, x0)

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