TRS Standard pair #516968120

details

property	value
status	complete
benchmark	t005.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.18020892143 seconds
cpu usage	9.334144809
max memory	6.1730816E8

stage attributes

key	value
output-size	28626
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) DependencyPairsProof [EQUIVALENT, 82 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) MRRProof [EQUIVALENT, 38 ms]
        (9) QDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES


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

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

   c(0, x) -> x
   c(x, c(y, z)) -> c(+(x, y), z)
   +(0, 0) -> 0
   +(0, 1) -> 1
   +(0, 2) -> 2
   +(0, 3) -> 3
   +(0, 4) -> 4
   +(0, 5) -> 5
   +(0, 6) -> 6
   +(0, 7) -> 7
   +(0, 8) -> 8
   +(0, 9) -> 9
   +(1, 0) -> 1
   +(1, 1) -> 2
   +(1, 2) -> 3
   +(1, 3) -> 4
   +(1, 4) -> 5
   +(1, 5) -> 6
   +(1, 6) -> 7
   +(1, 7) -> 8
   +(1, 8) -> 9
   +(1, 9) -> c(1, 0)
   +(2, 0) -> 2
   +(2, 1) -> 3
   +(2, 2) -> 4
   +(2, 3) -> 5
   +(2, 4) -> 6
   +(2, 5) -> 7
   +(2, 6) -> 8
   +(2, 7) -> 9
   +(2, 8) -> c(1, 0)
   +(2, 9) -> c(1, 1)
   +(3, 0) -> 3
   +(3, 1) -> 4
   +(3, 2) -> 5
   +(3, 3) -> 6
   +(3, 4) -> 7
   +(3, 5) -> 8
   +(3, 6) -> 9
   +(3, 7) -> c(1, 0)
   +(3, 8) -> c(1, 1)
   +(3, 9) -> c(1, 2)
   +(4, 0) -> 4
   +(4, 1) -> 5
   +(4, 2) -> 6
   +(4, 3) -> 7
   +(4, 4) -> 8
   +(4, 5) -> 9
   +(4, 6) -> c(1, 0)
   +(4, 7) -> c(1, 1)
   +(4, 8) -> c(1, 2)
   +(4, 9) -> c(1, 3)
   +(5, 0) -> 5
   +(5, 1) -> 6
   +(5, 2) -> 7
   +(5, 3) -> 8
   +(5, 4) -> 9
   +(5, 5) -> c(1, 0)
   +(5, 6) -> c(1, 1)
   +(5, 7) -> c(1, 2)
   +(5, 8) -> c(1, 3)

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