TRS Standard pair #516967950

details

property	value
status	complete
benchmark	cade13t.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.96460294724 seconds
cpu usage	8.344340263
max memory	5.23698176E8

stage attributes

key	value
output-size	16964
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 13 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, 7 ms]
        (27) AND
            (28) QDP
                (29) DependencyGraphProof [EQUIVALENT, 0 ms]
                (30) TRUE
            (31) QDP
                (32) DependencyGraphProof [EQUIVALENT, 0 ms]
                (33) TRUE


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

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

   div(x, s(y)) -> d(x, s(y), 0)
   d(x, s(y), z) -> cond(ge(x, z), x, y, z)
   cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z)))
   cond(false, x, y, z) -> 0
   ge(u, 0) -> true
   ge(0, s(v)) -> false
   ge(s(u), s(v)) -> ge(u, v)
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))

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:

   div(x, s(y)) -> d(x, s(y), 0)
   d(x, s(y), z) -> cond(ge(x, z), x, y, z)
   cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z)))
   cond(false, x, y, z) -> 0
   ge(u, 0) -> true
   ge(0, s(v)) -> false
   ge(s(u), s(v)) -> ge(u, v)
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))

The set Q consists of the following terms:

   div(x0, s(x1))
   d(x0, s(x1), x2)
   cond(true, x0, x1, x2)
   cond(false, x0, x1, x2)
   ge(x0, 0)
   ge(0, s(x0))
   ge(s(x0), s(x1))
   plus(x0, 0)
   plus(x0, s(x1))

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