TRS Standard pair #615303666

details

property	value
status	complete
benchmark	otto07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n043.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.22772216797 seconds
cpu usage	5.737090326
max memory	3.03681536E8

stage attributes

key	value
output-size	12277
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 4 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) NonInfProof [EQUIVALENT, 39 ms]
        (20) AND
            (21) QDP
                (22) DependencyGraphProof [EQUIVALENT, 0 ms]
                (23) TRUE
            (24) QDP
                (25) DependencyGraphProof [EQUIVALENT, 0 ms]
                (26) TRUE


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

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

   lt(0, s(x)) -> true
   lt(x, 0) -> false
   lt(s(x), s(y)) -> lt(x, y)
   minus(x, y) -> help(lt(y, x), x, y)
   help(true, x, y) -> s(minus(x, s(y)))
   help(false, x, y) -> 0

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:

   lt(0, s(x)) -> true
   lt(x, 0) -> false
   lt(s(x), s(y)) -> lt(x, y)
   minus(x, y) -> help(lt(y, x), x, y)
   help(true, x, y) -> s(minus(x, s(y)))
   help(false, x, y) -> 0

The set Q consists of the following terms:

   lt(0, s(x0))
   lt(x0, 0)
   lt(s(x0), s(x1))
   minus(x0, x1)
   help(true, x0, x1)
   help(false, x0, x1)


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

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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   LT(s(x), s(y)) -> LT(x, y)
   MINUS(x, y) -> HELP(lt(y, x), x, y)
   MINUS(x, y) -> LT(y, x)

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