Haskell pair #487599015

details

property	value
status	complete
benchmark	Prelude_quotRem_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.45809221268 seconds
cpu usage	11.435065123
max memory	6.44673536E8

stage attributes

key	value
output-size	54523
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) IFR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) DependencyGraphProof [EQUIVALENT, 0 ms]
        (11) AND
            (12) QDP
                (13) MRRProof [EQUIVALENT, 2 ms]
                (14) QDP
                (15) PisEmptyProof [EQUIVALENT, 0 ms]
                (16) YES
            (17) QDP
                (18) QDPSizeChangeProof [EQUIVALENT, 5 ms]
                (19) YES
    (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) AND
            (23) QDP
                (24) MRRProof [EQUIVALENT, 0 ms]
                (25) QDP
                (26) PisEmptyProof [EQUIVALENT, 0 ms]
                (27) YES
            (28) QDP
                (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (30) YES
    (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(1) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
is transformed to
"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
primModNatS0 x y False = Succ x;
"
The following If expression
"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
is transformed to
"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
primDivNatS0 x y False = Zero;
"

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(3) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(5) COR (EQUIVALENT)

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