TRS Stand 20472 pair #381711301

details

property	value
status	complete
benchmark	19.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.78011894226 seconds
cpu usage	16.434373099
max memory	1.009209344E9

stage attributes

key	value
output-size	31218
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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, 2 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, 36 ms]
        (20) QDP
        (21) QDPQMonotonicMRRProof [EQUIVALENT, 32 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 46 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 35 ms]
        (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QReductionProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) NonInfProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) DependencyGraphProof [EQUIVALENT, 0 ms]
        (34) TRUE


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

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

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

The TRS R 2 is 
   cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z)
   cond2(true, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
   cond2(false, x, y, z) -> cond3(gr(y, 0), x, y, z)
   cond3(true, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
   cond3(false, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, y, z)

The signature Sigma is {cond1_4, cond2_4, cond3_4}
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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