TRS Standard pair #516964270

details

property	value
status	complete
benchmark	24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n170.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	16.1537230015 seconds
cpu usage	46.635894115
max memory	1.236074496E9

stage attributes

key	value
output-size	57680
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) AAECC Innermost [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) QDPQMonotonicMRRProof [EQUIVALENT, 69 ms]
        (20) QDP
        (21) QDPQMonotonicMRRProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 100 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 51 ms]
        (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QReductionProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) NonInfProof [EQUIVALENT, 20 ms]
        (32) AND
            (33) QDP
                (34) DependencyGraphProof [EQUIVALENT, 0 ms]
                (35) QDP
                (36) NonInfProof [EQUIVALENT, 0 ms]
                (37) AND
                    (38) QDP
                        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (40) TRUE
                    (41) QDP
                        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (43) TRUE
            (44) QDP
                (45) DependencyGraphProof [EQUIVALENT, 0 ms]
                (46) QDP
                (47) NonInfProof [EQUIVALENT, 23 ms]
                (48) QDP
                (49) DependencyGraphProof [EQUIVALENT, 0 ms]
                (50) TRUE


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

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

   cond1(true, x, y) -> cond2(gr(x, y), x, y)
   cond2(true, x, y) -> cond3(gr(x, 0), x, y)
   cond2(false, x, y) -> cond4(gr(y, 0), x, y)
   cond3(true, x, y) -> cond3(gr(x, 0), p(x), y)
   cond3(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y)
   cond4(true, x, y) -> cond4(gr(y, 0), x, p(y))
   cond4(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false
   p(0) -> 0
   p(s(x)) -> x

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   and(true, true) -> true
   and(false, x) -> false

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