TRS Standard pair #516960725

details

property	value
status	complete
benchmark	otto08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.13801908493 seconds
cpu usage	10.998036486
max memory	6.11524608E8

stage attributes

key	value
output-size	23000
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 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, 0 ms]
        (32) QDP
        (33) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) NonInfProof [EQUIVALENT, 49 ms]
        (36) AND
            (37) QDP
                (38) DependencyGraphProof [EQUIVALENT, 0 ms]
                (39) TRUE
            (40) QDP
                (41) DependencyGraphProof [EQUIVALENT, 0 ms]
                (42) TRUE


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

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

   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   minus(x, 0) -> x
   minus(0, s(y)) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))
   mod(s(x), 0) -> 0
   mod(x, s(y)) -> help(x, s(y), 0)
   help(x, s(y), c) -> if(le(c, x), x, s(y), c)
   if(true, x, s(y), c) -> help(x, s(y), plus(c, s(y)))
   if(false, x, s(y), c) -> minus(x, minus(c, s(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:

   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   minus(x, 0) -> x
   minus(0, s(y)) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))

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