13.96/9.28 YES 16.55/9.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 16.55/9.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.55/9.96 16.55/9.96 16.55/9.96 H-Termination with start terms of the given HASKELL could be proven: 16.55/9.96 16.55/9.96 (0) HASKELL 16.55/9.96 (1) IFR [EQUIVALENT, 0 ms] 16.55/9.96 (2) HASKELL 16.55/9.96 (3) BR [EQUIVALENT, 0 ms] 16.55/9.96 (4) HASKELL 16.55/9.96 (5) COR [EQUIVALENT, 24 ms] 16.55/9.96 (6) HASKELL 16.55/9.96 (7) LetRed [EQUIVALENT, 0 ms] 16.55/9.96 (8) HASKELL 16.55/9.96 (9) NumRed [SOUND, 0 ms] 16.55/9.96 (10) HASKELL 16.55/9.96 (11) Narrow [SOUND, 0 ms] 16.55/9.96 (12) AND 16.55/9.96 (13) QDP 16.55/9.96 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (15) QDP 16.55/9.96 (16) QDPOrderProof [EQUIVALENT, 44 ms] 16.55/9.96 (17) QDP 16.55/9.96 (18) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (19) QDP 16.55/9.96 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.55/9.96 (21) YES 16.55/9.96 (22) QDP 16.55/9.96 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.55/9.96 (24) YES 16.55/9.96 (25) QDP 16.55/9.96 (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.55/9.96 (27) YES 16.55/9.96 (28) QDP 16.55/9.96 (29) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (30) QDP 16.55/9.96 (31) QDPOrderProof [EQUIVALENT, 0 ms] 16.55/9.96 (32) QDP 16.55/9.96 (33) QDPOrderProof [EQUIVALENT, 0 ms] 16.55/9.96 (34) QDP 16.55/9.96 (35) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (36) QDP 16.55/9.96 (37) QDPOrderProof [EQUIVALENT, 0 ms] 16.55/9.96 (38) QDP 16.55/9.96 (39) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (40) QDP 16.55/9.96 (41) InductionCalculusProof [EQUIVALENT, 16 ms] 16.55/9.96 (42) QDP 16.55/9.96 (43) NonInfProof [EQUIVALENT, 0 ms] 16.55/9.96 (44) QDP 16.55/9.96 (45) DependencyGraphProof [EQUIVALENT, 0 ms] 16.55/9.96 (46) QDP 16.55/9.96 (47) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.55/9.96 (48) YES 16.55/9.96 (49) QDP 16.55/9.96 (50) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.55/9.96 (51) YES 16.55/9.96 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (0) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (1) IFR (EQUIVALENT) 16.55/9.96 If Reductions: 16.55/9.96 The following If expression 16.55/9.96 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 16.55/9.96 is transformed to 16.55/9.96 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 16.55/9.96 primDivNatS0 x y False = Zero; 16.55/9.96 " 16.55/9.96 The following If expression 16.55/9.96 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 16.55/9.96 is transformed to 16.55/9.96 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 16.55/9.96 primModNatS0 x y False = Succ x; 16.55/9.96 " 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (2) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (3) BR (EQUIVALENT) 16.55/9.96 Replaced joker patterns by fresh variables and removed binding patterns. 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (4) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (5) COR (EQUIVALENT) 16.55/9.96 Cond Reductions: 16.55/9.96 The following Function with conditions 16.55/9.96 "absReal x|x >= 0x|otherwise`negate` x; 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "absReal x = absReal2 x; 16.55/9.96 " 16.55/9.96 "absReal0 x True = `negate` x; 16.55/9.96 " 16.55/9.96 "absReal1 x True = x; 16.55/9.96 absReal1 x False = absReal0 x otherwise; 16.55/9.96 " 16.55/9.96 "absReal2 x = absReal1 x (x >= 0); 16.55/9.96 " 16.55/9.96 The following Function with conditions 16.55/9.96 "gcd' x 0 = x; 16.55/9.96 gcd' x y = gcd' y (x `rem` y); 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "gcd' x xz = gcd'2 x xz; 16.55/9.96 gcd' x y = gcd'0 x y; 16.55/9.96 " 16.55/9.96 "gcd'0 x y = gcd' y (x `rem` y); 16.55/9.96 " 16.55/9.96 "gcd'1 True x xz = x; 16.55/9.96 gcd'1 yu yv yw = gcd'0 yv yw; 16.55/9.96 " 16.55/9.96 "gcd'2 x xz = gcd'1 (xz == 0) x xz; 16.55/9.96 gcd'2 yx yy = gcd'0 yx yy; 16.55/9.96 " 16.55/9.96 The following Function with conditions 16.55/9.96 "gcd 0 0 = error []; 16.55/9.96 gcd x y = gcd' (abs x) (abs y) where { 16.55/9.96 gcd' x 0 = x; 16.55/9.96 gcd' x y = gcd' y (x `rem` y); 16.55/9.96 } 16.55/9.96 ; 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "gcd yz zu = gcd3 yz zu; 16.55/9.96 gcd x y = gcd0 x y; 16.55/9.96 " 16.55/9.96 "gcd0 x y = gcd' (abs x) (abs y) where { 16.55/9.96 gcd' x xz = gcd'2 x xz; 16.55/9.96 gcd' x y = gcd'0 x y; 16.55/9.96 ; 16.55/9.96 gcd'0 x y = gcd' y (x `rem` y); 16.55/9.96 ; 16.55/9.96 gcd'1 True x xz = x; 16.55/9.96 gcd'1 yu yv yw = gcd'0 yv yw; 16.55/9.96 ; 16.55/9.96 gcd'2 x xz = gcd'1 (xz == 0) x xz; 16.55/9.96 gcd'2 yx yy = gcd'0 yx yy; 16.55/9.96 } 16.55/9.96 ; 16.55/9.96 " 16.55/9.96 "gcd1 True yz zu = error []; 16.55/9.96 gcd1 zv zw zx = gcd0 zw zx; 16.55/9.96 " 16.55/9.96 "gcd2 True yz zu = gcd1 (zu == 0) yz zu; 16.55/9.96 gcd2 zy zz vuu = gcd0 zz vuu; 16.55/9.96 " 16.55/9.96 "gcd3 yz zu = gcd2 (yz == 0) yz zu; 16.55/9.96 gcd3 vuv vuw = gcd0 vuv vuw; 16.55/9.96 " 16.55/9.96 The following Function with conditions 16.55/9.96 "undefined |Falseundefined; 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "undefined = undefined1; 16.55/9.96 " 16.55/9.96 "undefined0 True = undefined; 16.55/9.96 " 16.55/9.96 "undefined1 = undefined0 False; 16.55/9.96 " 16.55/9.96 The following Function with conditions 16.55/9.96 "reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where { 16.55/9.96 d = gcd x y; 16.55/9.96 } 16.55/9.96 ; 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "reduce x y = reduce2 x y; 16.55/9.96 " 16.55/9.96 "reduce2 x y = reduce1 x y (y == 0) where { 16.55/9.96 d = gcd x y; 16.55/9.96 ; 16.55/9.96 reduce0 x y True = x `quot` d :% (y `quot` d); 16.55/9.96 ; 16.55/9.96 reduce1 x y True = error []; 16.55/9.96 reduce1 x y False = reduce0 x y otherwise; 16.55/9.96 } 16.55/9.96 ; 16.55/9.96 " 16.55/9.96 The following Function with conditions 16.55/9.96 "signumReal x|x == 00|x > 01|otherwise-1; 16.55/9.96 " 16.55/9.96 is transformed to 16.55/9.96 "signumReal x = signumReal3 x; 16.55/9.96 " 16.55/9.96 "signumReal1 x True = 1; 16.55/9.96 signumReal1 x False = signumReal0 x otherwise; 16.55/9.96 " 16.55/9.96 "signumReal2 x True = 0; 16.55/9.96 signumReal2 x False = signumReal1 x (x > 0); 16.55/9.96 " 16.55/9.96 "signumReal0 x True = -1; 16.55/9.96 " 16.55/9.96 "signumReal3 x = signumReal2 x (x == 0); 16.55/9.96 " 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (6) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (7) LetRed (EQUIVALENT) 16.55/9.96 Let/Where Reductions: 16.55/9.96 The bindings of the following Let/Where expression 16.55/9.96 "gcd' (abs x) (abs y) where { 16.55/9.96 gcd' x xz = gcd'2 x xz; 16.55/9.96 gcd' x y = gcd'0 x y; 16.55/9.96 ; 16.55/9.96 gcd'0 x y = gcd' y (x `rem` y); 16.55/9.96 ; 16.55/9.96 gcd'1 True x xz = x; 16.55/9.96 gcd'1 yu yv yw = gcd'0 yv yw; 16.55/9.96 ; 16.55/9.96 gcd'2 x xz = gcd'1 (xz == 0) x xz; 16.55/9.96 gcd'2 yx yy = gcd'0 yx yy; 16.55/9.96 } 16.55/9.96 " 16.55/9.96 are unpacked to the following functions on top level 16.55/9.96 "gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz; 16.55/9.96 gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy; 16.55/9.96 " 16.55/9.96 "gcd0Gcd' x xz = gcd0Gcd'2 x xz; 16.55/9.96 gcd0Gcd' x y = gcd0Gcd'0 x y; 16.55/9.96 " 16.55/9.96 "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); 16.55/9.96 " 16.55/9.96 "gcd0Gcd'1 True x xz = x; 16.55/9.96 gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw; 16.55/9.96 " 16.55/9.96 The bindings of the following Let/Where expression 16.55/9.96 "reduce1 x y (y == 0) where { 16.55/9.96 d = gcd x y; 16.55/9.96 ; 16.55/9.96 reduce0 x y True = x `quot` d :% (y `quot` d); 16.55/9.96 ; 16.55/9.96 reduce1 x y True = error []; 16.55/9.96 reduce1 x y False = reduce0 x y otherwise; 16.55/9.96 } 16.55/9.96 " 16.55/9.96 are unpacked to the following functions on top level 16.55/9.96 "reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy); 16.55/9.96 " 16.55/9.96 "reduce2Reduce1 vux vuy x y True = error []; 16.55/9.96 reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise; 16.55/9.96 " 16.55/9.96 "reduce2D vux vuy = gcd vux vuy; 16.55/9.96 " 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (8) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (9) NumRed (SOUND) 16.55/9.96 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (10) 16.55/9.96 Obligation: 16.55/9.96 mainModule Main 16.55/9.96 module Main where { 16.55/9.96 import qualified Prelude; 16.55/9.96 } 16.55/9.96 16.55/9.96 ---------------------------------------- 16.55/9.96 16.55/9.96 (11) Narrow (SOUND) 16.55/9.96 Haskell To QDPs 16.55/9.96 16.55/9.96 digraph dp_graph { 16.55/9.96 node [outthreshold=100, inthreshold=100];1[label="fromDouble",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 16.55/9.96 3[label="fromDouble vuz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 16.55/9.96 4[label="doubleToRatio vuz3",fontsize=16,color="burlywood",shape="box"];3440[label="vuz3/Double vuz30 vuz31",fontsize=10,color="white",style="solid",shape="box"];4 -> 3440[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3440 -> 5[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 5[label="doubleToRatio (Double vuz30 vuz31)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 16.55/9.96 6[label="fromInt vuz30 % fromInt vuz31",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 16.55/9.96 7[label="reduce (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 16.55/9.96 8[label="reduce2 (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 16.55/9.96 9[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31)) (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31)) (abs (fromInt vuz31) == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 16.55/9.96 10[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31)) (fromInt vuz30 * signum (fromInt vuz31)) (abs (fromInt vuz31)) (primEqInt (abs (fromInt vuz31)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 16.55/9.96 11[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal (fromInt vuz31)) (fromInt vuz30 * signum (fromInt vuz31)) (absReal (fromInt vuz31)) (primEqInt (absReal (fromInt vuz31)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 16.55/9.96 12[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal2 (fromInt vuz31)) (fromInt vuz30 * signum (fromInt vuz31)) (absReal2 (fromInt vuz31)) (primEqInt (absReal2 (fromInt vuz31)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 16.55/9.96 13[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (fromInt vuz31 >= fromInt (Pos Zero))) (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (fromInt vuz31 >= fromInt (Pos Zero))) (primEqInt (absReal1 (fromInt vuz31) (fromInt vuz31 >= fromInt (Pos Zero))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 16.55/9.96 14[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (compare (fromInt vuz31) (fromInt (Pos Zero)) /= LT)) (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (compare (fromInt vuz31) (fromInt (Pos Zero)) /= LT)) (primEqInt (absReal1 (fromInt vuz31) (compare (fromInt vuz31) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 16.55/9.96 15[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (not (compare (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (not (compare (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 (fromInt vuz31) (not (compare (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 16.55/9.96 16[label="reduce2Reduce1 (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (not (primCmpInt (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (fromInt vuz31)) (absReal1 (fromInt vuz31) (not (primCmpInt (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 (fromInt vuz31) (not (primCmpInt (fromInt vuz31) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 16.55/9.96 17[label="reduce2Reduce1 (fromInt vuz30 * signum vuz31) (absReal1 vuz31 (not (primCmpInt vuz31 (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum vuz31) (absReal1 vuz31 (not (primCmpInt vuz31 (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 vuz31 (not (primCmpInt vuz31 (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3441[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];17 -> 3441[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3441 -> 18[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3442[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];17 -> 3442[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3442 -> 19[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 18[label="reduce2Reduce1 (fromInt vuz30 * signum (Pos vuz310)) (absReal1 (Pos vuz310) (not (primCmpInt (Pos vuz310) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (Pos vuz310)) (absReal1 (Pos vuz310) (not (primCmpInt (Pos vuz310) (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 (Pos vuz310) (not (primCmpInt (Pos vuz310) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3443[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];18 -> 3443[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3443 -> 20[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3444[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 3444[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3444 -> 21[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 19[label="reduce2Reduce1 (fromInt vuz30 * signum (Neg vuz310)) (absReal1 (Neg vuz310) (not (primCmpInt (Neg vuz310) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (Neg vuz310)) (absReal1 (Neg vuz310) (not (primCmpInt (Neg vuz310) (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 (Neg vuz310) (not (primCmpInt (Neg vuz310) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3445[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];19 -> 3445[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3445 -> 22[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3446[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 3446[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3446 -> 23[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 20[label="reduce2Reduce1 (fromInt vuz30 * signum (Pos (Succ vuz3100))) (absReal1 (Pos (Succ vuz3100)) (not (primCmpInt (Pos (Succ vuz3100)) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (Pos (Succ vuz3100))) (absReal1 (Pos (Succ vuz3100)) (not (primCmpInt (Pos (Succ vuz3100)) (fromInt (Pos Zero)) == LT))) (primEqInt (absReal1 (Pos (Succ vuz3100)) (not (primCmpInt (Pos (Succ vuz3100)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 16.55/9.96 21[label="reduce2Reduce1 (fromInt vuz30 * signum (Pos Zero)) (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))) (fromInt vuz30 * signum (Pos Zero)) (absReal1 (Pos Zero) (not 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134[label="",style="solid", color="black", weight=3]; 16.55/9.96 127[label="primQuotInt (primMulInt (Neg vuz300) (signumReal1 (Pos (Succ vuz3100)) (compare (Pos (Succ vuz3100)) (fromInt (Pos Zero)) == GT))) (reduce2D (primMulInt (Neg vuz300) (signumReal1 (Pos (Succ vuz3100)) (compare (Pos (Succ vuz3100)) (fromInt (Pos Zero)) == GT))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];127 -> 135[label="",style="solid", color="black", weight=3]; 16.55/9.96 128[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Pos vuz300) (signumReal2 (Pos (Succ vuz3100)) (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))))) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (signumReal2 (Pos (Succ vuz3100)) (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];128 -> 136[label="",style="solid", color="black", weight=3]; 16.55/9.96 129[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg 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160[label="",style="solid", color="black", weight=3]; 16.55/9.96 153[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg vuz300) (signumReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) > fromInt (Pos Zero)))) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (signumReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) > fromInt (Pos Zero)))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];153 -> 161[label="",style="solid", color="black", weight=3]; 16.55/9.96 154[label="primQuotInt (primMulInt (Pos vuz300) (signumReal1 (Neg (Succ vuz3100)) (compare (Neg (Succ vuz3100)) (fromInt (Pos Zero)) == GT))) (reduce2D (primMulInt (Pos vuz300) (signumReal1 (Neg (Succ vuz3100)) (compare (Neg (Succ vuz3100)) (fromInt (Pos Zero)) == GT))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];154 -> 162[label="",style="solid", color="black", weight=3]; 16.55/9.96 155[label="primQuotInt (primMulInt (Neg vuz300) (signumReal1 (Neg (Succ vuz3100)) (compare (Neg (Succ 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554[label="",style="dashed", color="red", weight=0]; 16.55/9.96 224[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos (primMulNat vuz300 (Succ Zero))) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];224 -> 555[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 224 -> 556[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 225 -> 612[label="",style="dashed", color="red", weight=0]; 16.55/9.96 225[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg (primMulNat vuz300 (Succ Zero))) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];225 -> 613[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 225 -> 614[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 226 -> 191[label="",style="dashed", color="red", weight=0]; 16.55/9.96 226[label="primQuotInt (Neg (primMulNat vuz300 (Succ Zero))) (reduce2D 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229[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg vuz300) (signumReal0 (Neg (Succ vuz3100)) otherwise)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (signumReal0 (Neg (Succ vuz3100)) otherwise)) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];229 -> 243[label="",style="solid", color="black", weight=3]; 16.55/9.96 230[label="primQuotInt (Pos (primMulNat (Succ vuz3000) (Succ Zero))) (gcd2 (primEqInt (Pos (primMulNat (Succ vuz3000) (Succ Zero))) (fromInt (Pos Zero))) (Pos (primMulNat (Succ vuz3000) (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];230 -> 244[label="",style="solid", color="black", weight=3]; 16.55/9.96 231[label="primQuotInt (Pos (primMulNat Zero (Succ Zero))) (gcd2 (primEqInt (Pos (primMulNat Zero (Succ Zero))) (fromInt (Pos Zero))) (Pos (primMulNat Zero (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];231 -> 245[label="",style="solid", color="black", weight=3]; 16.55/9.96 232[label="primQuotInt (Neg (primMulNat (Succ vuz3000) (Succ Zero))) (gcd2 (primEqInt (Neg (primMulNat (Succ vuz3000) (Succ Zero))) (fromInt (Pos Zero))) (Neg (primMulNat (Succ vuz3000) (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];232 -> 246[label="",style="solid", color="black", weight=3]; 16.55/9.96 233[label="primQuotInt (Neg (primMulNat Zero (Succ Zero))) (gcd2 (primEqInt (Neg (primMulNat Zero (Succ Zero))) (fromInt (Pos Zero))) (Neg (primMulNat Zero (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];233 -> 247[label="",style="solid", color="black", weight=3]; 16.55/9.96 555 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 555[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];555 -> 600[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 556 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 556[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];556 -> 601[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 554[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos vuz16) (fromInt (Pos Zero))) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="burlywood",shape="triangle"];3459[label="vuz16/Succ vuz160",fontsize=10,color="white",style="solid",shape="box"];554 -> 3459[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3459 -> 602[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3460[label="vuz16/Zero",fontsize=10,color="white",style="solid",shape="box"];554 -> 3460[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3460 -> 603[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 613 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 613[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];613 -> 658[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 614 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 614[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];614 -> 659[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 612[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg vuz30) (fromInt (Pos Zero))) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="burlywood",shape="triangle"];3461[label="vuz30/Succ vuz300",fontsize=10,color="white",style="solid",shape="box"];612 -> 3461[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3461 -> 660[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3462[label="vuz30/Zero",fontsize=10,color="white",style="solid",shape="box"];612 -> 3462[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3462 -> 661[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 238[label="vuz300",fontsize=16,color="green",shape="box"];239[label="vuz3100",fontsize=16,color="green",shape="box"];240[label="vuz300",fontsize=16,color="green",shape="box"];241[label="vuz3100",fontsize=16,color="green",shape="box"];242[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Pos vuz300) (signumReal0 (Neg (Succ vuz3100)) True)) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (signumReal0 (Neg (Succ vuz3100)) True)) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];242 -> 252[label="",style="solid", color="black", weight=3]; 16.55/9.96 243[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg vuz300) (signumReal0 (Neg (Succ vuz3100)) True)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (signumReal0 (Neg (Succ vuz3100)) True)) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];243 -> 253[label="",style="solid", color="black", weight=3]; 16.55/9.96 244 -> 462[label="",style="dashed", color="red", weight=0]; 16.55/9.96 244[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (gcd2 (primEqInt (Pos (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (fromInt (Pos Zero))) (Pos (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];244 -> 463[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 244 -> 464[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 245 -> 952[label="",style="dashed", color="red", weight=0]; 16.55/9.96 245[label="primQuotInt (Pos Zero) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];245 -> 953[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 246 -> 508[label="",style="dashed", color="red", weight=0]; 16.55/9.96 246[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (gcd2 (primEqInt (Neg (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (fromInt (Pos Zero))) (Neg (primPlusNat (primMulNat vuz3000 (Succ Zero)) (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];246 -> 509[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 246 -> 510[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 247[label="primQuotInt (Neg Zero) (gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];247 -> 259[label="",style="solid", color="black", weight=3]; 16.55/9.96 600[label="vuz300",fontsize=16,color="green",shape="box"];463[label="primMulNat vuz3000 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];3463[label="vuz3000/Succ vuz30000",fontsize=10,color="white",style="solid",shape="box"];463 -> 3463[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3463 -> 495[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3464[label="vuz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];463 -> 3464[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3464 -> 496[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 601[label="vuz300",fontsize=16,color="green",shape="box"];602[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos (Succ vuz160)) (fromInt (Pos Zero))) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];602 -> 662[label="",style="solid", color="black", weight=3]; 16.55/9.96 603[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];603 -> 663[label="",style="solid", color="black", weight=3]; 16.55/9.96 658[label="vuz300",fontsize=16,color="green",shape="box"];659[label="vuz300",fontsize=16,color="green",shape="box"];660[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg (Succ vuz300)) (fromInt (Pos Zero))) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];660 -> 673[label="",style="solid", color="black", weight=3]; 16.55/9.96 661[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];661 -> 674[label="",style="solid", color="black", weight=3]; 16.55/9.96 252[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Pos vuz300) (fromInt (Neg (Succ Zero)))) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (fromInt (Neg (Succ Zero)))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];252 -> 266[label="",style="solid", color="black", weight=3]; 16.55/9.96 253[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg vuz300) (fromInt (Neg (Succ Zero)))) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (fromInt (Neg (Succ Zero)))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];253 -> 267[label="",style="solid", color="black", weight=3]; 16.55/9.96 464[label="vuz3100",fontsize=16,color="green",shape="box"];462[label="primQuotInt (Pos (primPlusNat vuz5 (Succ Zero))) (gcd2 (primEqInt (Pos (primPlusNat vuz5 (Succ Zero))) (fromInt (Pos Zero))) (Pos (primPlusNat vuz5 (Succ Zero))) (Pos (Succ vuz6)))",fontsize=16,color="burlywood",shape="triangle"];3465[label="vuz5/Succ vuz50",fontsize=10,color="white",style="solid",shape="box"];462 -> 3465[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3465 -> 497[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3466[label="vuz5/Zero",fontsize=10,color="white",style="solid",shape="box"];462 -> 3466[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3466 -> 498[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 953[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];953 -> 996[label="",style="solid", color="black", weight=3]; 16.55/9.96 952[label="primQuotInt (Pos Zero) vuz47",fontsize=16,color="burlywood",shape="triangle"];3467[label="vuz47/Pos vuz470",fontsize=10,color="white",style="solid",shape="box"];952 -> 3467[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3467 -> 997[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3468[label="vuz47/Neg vuz470",fontsize=10,color="white",style="solid",shape="box"];952 -> 3468[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3468 -> 998[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 509[label="vuz3100",fontsize=16,color="green",shape="box"];510 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 510[label="primMulNat vuz3000 (Succ Zero)",fontsize=16,color="magenta"];510 -> 541[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 508[label="primQuotInt (Neg (primPlusNat vuz11 (Succ Zero))) (gcd2 (primEqInt (Neg (primPlusNat vuz11 (Succ Zero))) (fromInt (Pos Zero))) (Neg (primPlusNat vuz11 (Succ Zero))) (Pos (Succ vuz12)))",fontsize=16,color="burlywood",shape="triangle"];3469[label="vuz11/Succ vuz110",fontsize=10,color="white",style="solid",shape="box"];508 -> 3469[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3469 -> 542[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3470[label="vuz11/Zero",fontsize=10,color="white",style="solid",shape="box"];508 -> 3470[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3470 -> 543[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 259[label="primQuotInt (Neg Zero) (gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];259 -> 273[label="",style="solid", color="black", weight=3]; 16.55/9.96 495[label="primMulNat (Succ vuz30000) (Succ Zero)",fontsize=16,color="black",shape="box"];495 -> 504[label="",style="solid", color="black", weight=3]; 16.55/9.96 496[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];496 -> 505[label="",style="solid", color="black", weight=3]; 16.55/9.96 662[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos (Succ vuz160)) (Pos Zero)) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];662 -> 675[label="",style="solid", color="black", weight=3]; 16.55/9.96 663[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];663 -> 676[label="",style="solid", color="black", weight=3]; 16.55/9.96 673[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg (Succ vuz300)) (Pos Zero)) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];673 -> 685[label="",style="solid", color="black", weight=3]; 16.55/9.96 674[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];674 -> 686[label="",style="solid", color="black", weight=3]; 16.55/9.96 266[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Pos vuz300) (Neg (Succ Zero))) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (Neg (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];266 -> 280[label="",style="solid", color="black", weight=3]; 16.55/9.96 267[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (primMulInt (Neg vuz300) (Neg (Succ Zero))) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (Neg (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];267 -> 281[label="",style="solid", color="black", weight=3]; 16.55/9.96 497[label="primQuotInt (Pos (primPlusNat (Succ vuz50) (Succ Zero))) (gcd2 (primEqInt (Pos (primPlusNat (Succ vuz50) (Succ Zero))) (fromInt (Pos Zero))) (Pos (primPlusNat (Succ vuz50) (Succ Zero))) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];497 -> 506[label="",style="solid", color="black", weight=3]; 16.55/9.96 498[label="primQuotInt (Pos (primPlusNat Zero (Succ Zero))) (gcd2 (primEqInt (Pos (primPlusNat Zero (Succ Zero))) (fromInt (Pos Zero))) (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];498 -> 507[label="",style="solid", color="black", weight=3]; 16.55/9.96 996[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];996 -> 1008[label="",style="solid", color="black", weight=3]; 16.55/9.96 997[label="primQuotInt (Pos Zero) (Pos vuz470)",fontsize=16,color="burlywood",shape="box"];3471[label="vuz470/Succ vuz4700",fontsize=10,color="white",style="solid",shape="box"];997 -> 3471[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3471 -> 1009[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3472[label="vuz470/Zero",fontsize=10,color="white",style="solid",shape="box"];997 -> 3472[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3472 -> 1010[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 998[label="primQuotInt (Pos Zero) (Neg vuz470)",fontsize=16,color="burlywood",shape="box"];3473[label="vuz470/Succ vuz4700",fontsize=10,color="white",style="solid",shape="box"];998 -> 3473[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3473 -> 1011[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3474[label="vuz470/Zero",fontsize=10,color="white",style="solid",shape="box"];998 -> 3474[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3474 -> 1012[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 541[label="vuz3000",fontsize=16,color="green",shape="box"];542[label="primQuotInt (Neg (primPlusNat (Succ vuz110) (Succ Zero))) (gcd2 (primEqInt (Neg (primPlusNat (Succ vuz110) (Succ Zero))) (fromInt (Pos Zero))) (Neg (primPlusNat (Succ vuz110) (Succ Zero))) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];542 -> 546[label="",style="solid", color="black", weight=3]; 16.55/9.96 543[label="primQuotInt (Neg (primPlusNat Zero (Succ Zero))) (gcd2 (primEqInt (Neg (primPlusNat Zero (Succ Zero))) (fromInt (Pos Zero))) (Neg (primPlusNat Zero (Succ Zero))) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];543 -> 547[label="",style="solid", color="black", weight=3]; 16.55/9.96 273[label="primQuotInt (Neg Zero) (gcd2 True (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];273 -> 289[label="",style="solid", color="black", weight=3]; 16.55/9.96 504 -> 544[label="",style="dashed", color="red", weight=0]; 16.55/9.96 504[label="primPlusNat (primMulNat vuz30000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];504 -> 545[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 505[label="Zero",fontsize=16,color="green",shape="box"];675[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 False (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];675 -> 687[label="",style="solid", color="black", weight=3]; 16.55/9.96 676[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 True (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];676 -> 688[label="",style="solid", color="black", weight=3]; 16.55/9.96 685[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 False (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];685 -> 692[label="",style="solid", color="black", weight=3]; 16.55/9.96 686[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 True (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];686 -> 693[label="",style="solid", color="black", weight=3]; 16.55/9.96 280 -> 612[label="",style="dashed", color="red", weight=0]; 16.55/9.96 280[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Neg (primMulNat vuz300 (Succ Zero))) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];280 -> 623[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 280 -> 624[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 280 -> 625[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 281 -> 554[label="",style="dashed", color="red", weight=0]; 16.55/9.96 281[label="primQuotInt (Pos (Succ vuz3100)) (gcd2 (primEqInt (Pos (primMulNat vuz300 (Succ Zero))) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 (Succ Zero))) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];281 -> 565[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 281 -> 566[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 281 -> 567[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 506 -> 2317[label="",style="dashed", color="red", weight=0]; 16.55/9.96 506[label="primQuotInt (Pos (Succ (Succ (primPlusNat vuz50 Zero)))) (gcd2 (primEqInt (Pos (Succ (Succ (primPlusNat vuz50 Zero)))) (fromInt (Pos Zero))) (Pos (Succ (Succ (primPlusNat vuz50 Zero)))) (Pos (Succ vuz6)))",fontsize=16,color="magenta"];506 -> 2318[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 506 -> 2319[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 507[label="primQuotInt (Pos (Succ Zero)) (gcd2 (primEqInt (Pos (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];507 -> 549[label="",style="solid", color="black", weight=3]; 16.55/9.96 1008[label="gcd2 True (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1008 -> 1022[label="",style="solid", color="black", weight=3]; 16.55/9.96 1009[label="primQuotInt (Pos Zero) (Pos (Succ vuz4700))",fontsize=16,color="black",shape="box"];1009 -> 1023[label="",style="solid", color="black", weight=3]; 16.55/9.96 1010[label="primQuotInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1010 -> 1024[label="",style="solid", color="black", weight=3]; 16.55/9.96 1011[label="primQuotInt (Pos Zero) (Neg (Succ vuz4700))",fontsize=16,color="black",shape="box"];1011 -> 1025[label="",style="solid", color="black", weight=3]; 16.55/9.96 1012[label="primQuotInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1012 -> 1026[label="",style="solid", color="black", weight=3]; 16.55/9.96 546 -> 1410[label="",style="dashed", color="red", weight=0]; 16.55/9.96 546[label="primQuotInt (Neg (Succ (Succ (primPlusNat vuz110 Zero)))) (gcd2 (primEqInt (Neg (Succ (Succ (primPlusNat vuz110 Zero)))) (fromInt (Pos Zero))) (Neg (Succ (Succ (primPlusNat vuz110 Zero)))) (Pos (Succ vuz12)))",fontsize=16,color="magenta"];546 -> 1411[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 546 -> 1412[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 547[label="primQuotInt (Neg (Succ Zero)) (gcd2 (primEqInt (Neg (Succ Zero)) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];547 -> 605[label="",style="solid", color="black", weight=3]; 16.55/9.96 289[label="primQuotInt (Neg Zero) (gcd1 (Pos (Succ vuz3100) == fromInt (Pos Zero)) (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];289 -> 309[label="",style="solid", color="black", weight=3]; 16.55/9.96 545 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 545[label="primMulNat vuz30000 (Succ Zero)",fontsize=16,color="magenta"];545 -> 550[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 544[label="primPlusNat vuz13 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];3475[label="vuz13/Succ vuz130",fontsize=10,color="white",style="solid",shape="box"];544 -> 3475[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3475 -> 551[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3476[label="vuz13/Zero",fontsize=10,color="white",style="solid",shape="box"];544 -> 3476[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3476 -> 552[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 687[label="primQuotInt (Pos (Succ vuz3100)) (gcd0 (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="triangle"];687 -> 694[label="",style="solid", color="black", weight=3]; 16.55/9.96 688[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (Pos (Succ vuz3100) == fromInt (Pos Zero)) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];688 -> 695[label="",style="solid", color="black", weight=3]; 16.55/9.96 692[label="primQuotInt (Pos (Succ vuz3100)) (gcd0 (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="triangle"];692 -> 700[label="",style="solid", color="black", weight=3]; 16.55/9.96 693[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (Pos (Succ vuz3100) == fromInt (Pos Zero)) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];693 -> 701[label="",style="solid", color="black", weight=3]; 16.55/9.96 623 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 623[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];623 -> 664[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 624 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 624[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];624 -> 665[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 625[label="vuz3100",fontsize=16,color="green",shape="box"];565 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 565[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];565 -> 606[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 566[label="vuz3100",fontsize=16,color="green",shape="box"];567 -> 463[label="",style="dashed", color="red", weight=0]; 16.55/9.96 567[label="primMulNat vuz300 (Succ Zero)",fontsize=16,color="magenta"];567 -> 607[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 2318 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.96 2318[label="primPlusNat vuz50 Zero",fontsize=16,color="magenta"];2318 -> 2448[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 2319 -> 2449[label="",style="dashed", color="red", weight=0]; 16.55/9.96 2319[label="gcd2 (primEqInt (Pos (Succ (Succ (primPlusNat vuz50 Zero)))) (fromInt (Pos Zero))) (Pos (Succ (Succ (primPlusNat vuz50 Zero)))) (Pos (Succ vuz6))",fontsize=16,color="magenta"];2319 -> 2450[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 2319 -> 2451[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 2317[label="primQuotInt (Pos (Succ (Succ vuz68))) vuz91",fontsize=16,color="burlywood",shape="triangle"];3477[label="vuz91/Pos vuz910",fontsize=10,color="white",style="solid",shape="box"];2317 -> 3477[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3477 -> 2452[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3478[label="vuz91/Neg vuz910",fontsize=10,color="white",style="solid",shape="box"];2317 -> 3478[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3478 -> 2453[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 549[label="primQuotInt (Pos (Succ Zero)) (gcd2 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ Zero)) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];549 -> 609[label="",style="solid", color="black", weight=3]; 16.55/9.96 1022[label="gcd1 (Pos (Succ vuz3100) == fromInt (Pos Zero)) (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1022 -> 1036[label="",style="solid", color="black", weight=3]; 16.55/9.96 1023[label="Pos (primDivNatS Zero (Succ vuz4700))",fontsize=16,color="green",shape="box"];1023 -> 1037[label="",style="dashed", color="green", weight=3]; 16.55/9.96 1024[label="error []",fontsize=16,color="black",shape="triangle"];1024 -> 1038[label="",style="solid", color="black", weight=3]; 16.55/9.96 1025[label="Neg (primDivNatS Zero (Succ vuz4700))",fontsize=16,color="green",shape="box"];1025 -> 1039[label="",style="dashed", color="green", weight=3]; 16.55/9.96 1026 -> 1024[label="",style="dashed", color="red", weight=0]; 16.55/9.96 1026[label="error []",fontsize=16,color="magenta"];1411 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.96 1411[label="primPlusNat vuz110 Zero",fontsize=16,color="magenta"];1411 -> 1599[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 1412 -> 1600[label="",style="dashed", color="red", weight=0]; 16.55/9.96 1412[label="gcd2 (primEqInt (Neg (Succ (Succ (primPlusNat vuz110 Zero)))) (fromInt (Pos Zero))) (Neg (Succ (Succ (primPlusNat vuz110 Zero)))) (Pos (Succ vuz12))",fontsize=16,color="magenta"];1412 -> 1601[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 1412 -> 1602[label="",style="dashed", color="magenta", weight=3]; 16.55/9.96 1410[label="primQuotInt (Neg (Succ (Succ vuz49))) vuz50",fontsize=16,color="burlywood",shape="triangle"];3479[label="vuz50/Pos vuz500",fontsize=10,color="white",style="solid",shape="box"];1410 -> 3479[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3479 -> 1603[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 3480[label="vuz50/Neg vuz500",fontsize=10,color="white",style="solid",shape="box"];1410 -> 3480[label="",style="solid", color="burlywood", weight=9]; 16.55/9.96 3480 -> 1604[label="",style="solid", color="burlywood", weight=3]; 16.55/9.96 605[label="primQuotInt (Neg (Succ Zero)) (gcd2 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero)) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];605 -> 667[label="",style="solid", color="black", weight=3]; 16.55/9.97 309[label="primQuotInt (Neg Zero) (gcd1 (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];309 -> 327[label="",style="solid", color="black", weight=3]; 16.55/9.97 550[label="vuz30000",fontsize=16,color="green",shape="box"];551[label="primPlusNat (Succ vuz130) (Succ Zero)",fontsize=16,color="black",shape="box"];551 -> 610[label="",style="solid", color="black", weight=3]; 16.55/9.97 552[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];552 -> 611[label="",style="solid", color="black", weight=3]; 16.55/9.97 694[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd' (abs (Pos vuz14)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];694 -> 702[label="",style="solid", color="black", weight=3]; 16.55/9.97 695[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];695 -> 703[label="",style="solid", color="black", weight=3]; 16.55/9.97 700[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd' (abs (Neg vuz28)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];700 -> 716[label="",style="solid", color="black", weight=3]; 16.55/9.97 701[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];701 -> 717[label="",style="solid", color="black", weight=3]; 16.55/9.97 664[label="vuz300",fontsize=16,color="green",shape="box"];665[label="vuz300",fontsize=16,color="green",shape="box"];606[label="vuz300",fontsize=16,color="green",shape="box"];607[label="vuz300",fontsize=16,color="green",shape="box"];2448[label="vuz50",fontsize=16,color="green",shape="box"];670[label="primPlusNat vuz130 Zero",fontsize=16,color="burlywood",shape="triangle"];3481[label="vuz130/Succ vuz1300",fontsize=10,color="white",style="solid",shape="box"];670 -> 3481[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3481 -> 681[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3482[label="vuz130/Zero",fontsize=10,color="white",style="solid",shape="box"];670 -> 3482[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3482 -> 682[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 2450 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2450[label="primPlusNat vuz50 Zero",fontsize=16,color="magenta"];2450 -> 2454[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 2451 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2451[label="primPlusNat vuz50 Zero",fontsize=16,color="magenta"];2451 -> 2455[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 2449[label="gcd2 (primEqInt (Pos (Succ (Succ vuz93))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz92))) (Pos (Succ vuz6))",fontsize=16,color="black",shape="triangle"];2449 -> 2456[label="",style="solid", color="black", weight=3]; 16.55/9.97 2452[label="primQuotInt (Pos (Succ (Succ vuz68))) (Pos vuz910)",fontsize=16,color="burlywood",shape="box"];3483[label="vuz910/Succ vuz9100",fontsize=10,color="white",style="solid",shape="box"];2452 -> 3483[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3483 -> 2462[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3484[label="vuz910/Zero",fontsize=10,color="white",style="solid",shape="box"];2452 -> 3484[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3484 -> 2463[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 2453[label="primQuotInt (Pos (Succ (Succ vuz68))) (Neg vuz910)",fontsize=16,color="burlywood",shape="box"];3485[label="vuz910/Succ vuz9100",fontsize=10,color="white",style="solid",shape="box"];2453 -> 3485[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3485 -> 2464[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3486[label="vuz910/Zero",fontsize=10,color="white",style="solid",shape="box"];2453 -> 3486[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3486 -> 2465[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 609[label="primQuotInt (Pos (Succ Zero)) (gcd2 False (Pos (Succ Zero)) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];609 -> 669[label="",style="solid", color="black", weight=3]; 16.55/9.97 1036[label="gcd1 (primEqInt (Pos (Succ vuz3100)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1036 -> 1049[label="",style="solid", color="black", weight=3]; 16.55/9.97 1037[label="primDivNatS Zero (Succ vuz4700)",fontsize=16,color="black",shape="triangle"];1037 -> 1050[label="",style="solid", color="black", weight=3]; 16.55/9.97 1038[label="error []",fontsize=16,color="red",shape="box"];1039 -> 1037[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1039[label="primDivNatS Zero (Succ vuz4700)",fontsize=16,color="magenta"];1039 -> 1051[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1599[label="vuz110",fontsize=16,color="green",shape="box"];1601 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1601[label="primPlusNat vuz110 Zero",fontsize=16,color="magenta"];1601 -> 1605[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1602 -> 670[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1602[label="primPlusNat vuz110 Zero",fontsize=16,color="magenta"];1602 -> 1606[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1600[label="gcd2 (primEqInt (Neg (Succ (Succ vuz52))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz51))) (Pos (Succ vuz12))",fontsize=16,color="black",shape="triangle"];1600 -> 1607[label="",style="solid", color="black", weight=3]; 16.55/9.97 1603[label="primQuotInt (Neg (Succ (Succ vuz49))) (Pos vuz500)",fontsize=16,color="burlywood",shape="box"];3487[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1603 -> 3487[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3487 -> 1631[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3488[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1603 -> 3488[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3488 -> 1632[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 1604[label="primQuotInt (Neg (Succ (Succ vuz49))) (Neg vuz500)",fontsize=16,color="burlywood",shape="box"];3489[label="vuz500/Succ vuz5000",fontsize=10,color="white",style="solid",shape="box"];1604 -> 3489[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3489 -> 1633[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3490[label="vuz500/Zero",fontsize=10,color="white",style="solid",shape="box"];1604 -> 3490[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3490 -> 1634[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 667[label="primQuotInt (Neg (Succ Zero)) (gcd2 False (Neg (Succ Zero)) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];667 -> 678[label="",style="solid", color="black", weight=3]; 16.55/9.97 327[label="primQuotInt (Neg Zero) (gcd1 (primEqInt (Pos (Succ vuz3100)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];327 -> 347[label="",style="solid", color="black", weight=3]; 16.55/9.97 610[label="Succ (Succ (primPlusNat vuz130 Zero))",fontsize=16,color="green",shape="box"];610 -> 670[label="",style="dashed", color="green", weight=3]; 16.55/9.97 611[label="Succ Zero",fontsize=16,color="green",shape="box"];702[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'2 (abs (Pos vuz14)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];702 -> 718[label="",style="solid", color="black", weight=3]; 16.55/9.97 703[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (primEqInt (Pos (Succ vuz3100)) (Pos Zero)) (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];703 -> 719[label="",style="solid", color="black", weight=3]; 16.55/9.97 716[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'2 (abs (Neg vuz28)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];716 -> 726[label="",style="solid", color="black", weight=3]; 16.55/9.97 717[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 (primEqInt (Pos (Succ vuz3100)) (Pos Zero)) (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];717 -> 727[label="",style="solid", color="black", weight=3]; 16.55/9.97 681[label="primPlusNat (Succ vuz1300) Zero",fontsize=16,color="black",shape="box"];681 -> 709[label="",style="solid", color="black", weight=3]; 16.55/9.97 682[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];682 -> 710[label="",style="solid", color="black", weight=3]; 16.55/9.97 2454[label="vuz50",fontsize=16,color="green",shape="box"];2455[label="vuz50",fontsize=16,color="green",shape="box"];2456[label="gcd2 (primEqInt (Pos (Succ (Succ vuz93))) (Pos Zero)) (Pos (Succ (Succ vuz92))) (Pos (Succ vuz6))",fontsize=16,color="black",shape="box"];2456 -> 2466[label="",style="solid", color="black", weight=3]; 16.55/9.97 2462[label="primQuotInt (Pos (Succ (Succ vuz68))) (Pos (Succ vuz9100))",fontsize=16,color="black",shape="box"];2462 -> 2475[label="",style="solid", color="black", weight=3]; 16.55/9.97 2463[label="primQuotInt (Pos (Succ (Succ vuz68))) (Pos Zero)",fontsize=16,color="black",shape="box"];2463 -> 2476[label="",style="solid", color="black", weight=3]; 16.55/9.97 2464[label="primQuotInt (Pos (Succ (Succ vuz68))) (Neg (Succ vuz9100))",fontsize=16,color="black",shape="box"];2464 -> 2477[label="",style="solid", color="black", weight=3]; 16.55/9.97 2465[label="primQuotInt (Pos (Succ (Succ vuz68))) (Neg Zero)",fontsize=16,color="black",shape="box"];2465 -> 2478[label="",style="solid", color="black", weight=3]; 16.55/9.97 669[label="primQuotInt (Pos (Succ Zero)) (gcd0 (Pos (Succ Zero)) (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];669 -> 680[label="",style="solid", color="black", weight=3]; 16.55/9.97 1049[label="gcd1 (primEqInt (Pos (Succ vuz3100)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1049 -> 1061[label="",style="solid", color="black", weight=3]; 16.55/9.97 1050[label="Zero",fontsize=16,color="green",shape="box"];1051[label="vuz4700",fontsize=16,color="green",shape="box"];1605[label="vuz110",fontsize=16,color="green",shape="box"];1606[label="vuz110",fontsize=16,color="green",shape="box"];1607[label="gcd2 (primEqInt (Neg (Succ (Succ vuz52))) (Pos Zero)) (Neg (Succ (Succ vuz51))) (Pos (Succ vuz12))",fontsize=16,color="black",shape="box"];1607 -> 1635[label="",style="solid", color="black", weight=3]; 16.55/9.97 1631[label="primQuotInt (Neg (Succ (Succ vuz49))) (Pos (Succ vuz5000))",fontsize=16,color="black",shape="box"];1631 -> 1661[label="",style="solid", color="black", weight=3]; 16.55/9.97 1632[label="primQuotInt (Neg (Succ (Succ vuz49))) (Pos Zero)",fontsize=16,color="black",shape="box"];1632 -> 1662[label="",style="solid", color="black", weight=3]; 16.55/9.97 1633[label="primQuotInt (Neg (Succ (Succ vuz49))) (Neg (Succ vuz5000))",fontsize=16,color="black",shape="box"];1633 -> 1663[label="",style="solid", color="black", weight=3]; 16.55/9.97 1634[label="primQuotInt (Neg (Succ (Succ vuz49))) (Neg Zero)",fontsize=16,color="black",shape="box"];1634 -> 1664[label="",style="solid", color="black", weight=3]; 16.55/9.97 678[label="primQuotInt (Neg (Succ Zero)) (gcd0 (Neg (Succ Zero)) (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];678 -> 696[label="",style="solid", color="black", weight=3]; 16.55/9.97 347[label="primQuotInt (Neg Zero) (gcd1 False (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];347 -> 369[label="",style="solid", color="black", weight=3]; 16.55/9.97 718[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (abs (Pos (Succ vuz3100)) == fromInt (Pos Zero)) (abs (Pos vuz14)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];718 -> 728[label="",style="solid", color="black", weight=3]; 16.55/9.97 719[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 False (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];719 -> 729[label="",style="solid", color="black", weight=3]; 16.55/9.97 726[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (abs (Pos (Succ vuz3100)) == fromInt (Pos Zero)) (abs (Neg vuz28)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];726 -> 736[label="",style="solid", color="black", weight=3]; 16.55/9.97 727[label="primQuotInt (Pos (Succ vuz3100)) (gcd1 False (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];727 -> 737[label="",style="solid", color="black", weight=3]; 16.55/9.97 709[label="Succ vuz1300",fontsize=16,color="green",shape="box"];710[label="Zero",fontsize=16,color="green",shape="box"];2466[label="gcd2 False (Pos (Succ (Succ vuz92))) (Pos (Succ vuz6))",fontsize=16,color="black",shape="box"];2466 -> 2479[label="",style="solid", color="black", weight=3]; 16.55/9.97 2475[label="Pos (primDivNatS (Succ (Succ vuz68)) (Succ vuz9100))",fontsize=16,color="green",shape="box"];2475 -> 2490[label="",style="dashed", color="green", weight=3]; 16.55/9.97 2476 -> 1024[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2476[label="error []",fontsize=16,color="magenta"];2477[label="Neg (primDivNatS (Succ (Succ vuz68)) (Succ vuz9100))",fontsize=16,color="green",shape="box"];2477 -> 2491[label="",style="dashed", color="green", weight=3]; 16.55/9.97 2478 -> 1024[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2478[label="error []",fontsize=16,color="magenta"];680[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd' (abs (Pos (Succ Zero))) (abs (Pos (Succ vuz6))))",fontsize=16,color="black",shape="box"];680 -> 704[label="",style="solid", color="black", weight=3]; 16.55/9.97 1061[label="gcd1 False (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1061 -> 1071[label="",style="solid", color="black", weight=3]; 16.55/9.97 1635[label="gcd2 False (Neg (Succ (Succ vuz51))) (Pos (Succ vuz12))",fontsize=16,color="black",shape="box"];1635 -> 1665[label="",style="solid", color="black", weight=3]; 16.55/9.97 1661[label="Neg (primDivNatS (Succ (Succ vuz49)) (Succ vuz5000))",fontsize=16,color="green",shape="box"];1661 -> 1690[label="",style="dashed", color="green", weight=3]; 16.55/9.97 1662 -> 1024[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1662[label="error []",fontsize=16,color="magenta"];1663[label="Pos (primDivNatS (Succ (Succ vuz49)) (Succ vuz5000))",fontsize=16,color="green",shape="box"];1663 -> 1691[label="",style="dashed", color="green", weight=3]; 16.55/9.97 1664 -> 1024[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1664[label="error []",fontsize=16,color="magenta"];696[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd' (abs (Neg (Succ Zero))) (abs (Pos (Succ vuz12))))",fontsize=16,color="black",shape="box"];696 -> 708[label="",style="solid", color="black", weight=3]; 16.55/9.97 369[label="primQuotInt (Neg Zero) (gcd0 (Neg Zero) (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];369 -> 393[label="",style="solid", color="black", weight=3]; 16.55/9.97 728[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Pos vuz14)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];728 -> 738[label="",style="solid", color="black", weight=3]; 16.55/9.97 729 -> 687[label="",style="dashed", color="red", weight=0]; 16.55/9.97 729[label="primQuotInt (Pos (Succ vuz3100)) (gcd0 (Pos vuz14) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];736[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Neg vuz28)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];736 -> 745[label="",style="solid", color="black", weight=3]; 16.55/9.97 737 -> 692[label="",style="dashed", color="red", weight=0]; 16.55/9.97 737[label="primQuotInt (Pos (Succ vuz3100)) (gcd0 (Neg vuz28) (Pos (Succ vuz3100)))",fontsize=16,color="magenta"];2479[label="gcd0 (Pos (Succ (Succ vuz92))) (Pos (Succ vuz6))",fontsize=16,color="black",shape="box"];2479 -> 2492[label="",style="solid", color="black", weight=3]; 16.55/9.97 2490 -> 2674[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2490[label="primDivNatS (Succ (Succ vuz68)) (Succ vuz9100)",fontsize=16,color="magenta"];2490 -> 2675[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 2490 -> 2676[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 2491 -> 2674[label="",style="dashed", color="red", weight=0]; 16.55/9.97 2491[label="primDivNatS (Succ (Succ vuz68)) (Succ vuz9100)",fontsize=16,color="magenta"];2491 -> 2677[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 2491 -> 2678[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 704[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'2 (abs (Pos (Succ Zero))) (abs (Pos (Succ vuz6))))",fontsize=16,color="black",shape="box"];704 -> 720[label="",style="solid", color="black", weight=3]; 16.55/9.97 1071[label="gcd0 (Pos Zero) (Pos (Succ vuz3100))",fontsize=16,color="black",shape="box"];1071 -> 1081[label="",style="solid", color="black", weight=3]; 16.55/9.97 1665[label="gcd0 (Neg (Succ (Succ vuz51))) (Pos (Succ vuz12))",fontsize=16,color="black",shape="box"];1665 -> 1692[label="",style="solid", color="black", weight=3]; 16.55/9.97 1690 -> 2674[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1690[label="primDivNatS (Succ (Succ vuz49)) (Succ vuz5000)",fontsize=16,color="magenta"];1690 -> 2679[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1690 -> 2680[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1691 -> 2674[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1691[label="primDivNatS (Succ (Succ vuz49)) (Succ vuz5000)",fontsize=16,color="magenta"];1691 -> 2681[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1691 -> 2682[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 708[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'2 (abs (Neg (Succ Zero))) (abs (Pos (Succ vuz12))))",fontsize=16,color="black",shape="box"];708 -> 722[label="",style="solid", color="black", weight=3]; 16.55/9.97 393[label="primQuotInt (Neg Zero) (gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];393 -> 419[label="",style="solid", color="black", weight=3]; 16.55/9.97 738[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Pos vuz14)) (absReal (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];738 -> 746[label="",style="solid", color="black", weight=3]; 16.55/9.97 745[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Neg vuz28)) (absReal (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];745 -> 753[label="",style="solid", color="black", weight=3]; 16.55/9.97 2492[label="gcd0Gcd' (abs (Pos (Succ (Succ vuz92)))) (abs (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];2492 -> 2508[label="",style="solid", color="black", weight=3]; 16.55/9.97 2675[label="vuz9100",fontsize=16,color="green",shape="box"];2676[label="Succ vuz68",fontsize=16,color="green",shape="box"];2674[label="primDivNatS (Succ vuz99) (Succ vuz100)",fontsize=16,color="black",shape="triangle"];2674 -> 2697[label="",style="solid", color="black", weight=3]; 16.55/9.97 2677[label="vuz9100",fontsize=16,color="green",shape="box"];2678[label="Succ vuz68",fontsize=16,color="green",shape="box"];720[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (abs (Pos (Succ vuz6)) == fromInt (Pos Zero)) (abs (Pos (Succ Zero))) (abs (Pos (Succ vuz6))))",fontsize=16,color="black",shape="box"];720 -> 730[label="",style="solid", color="black", weight=3]; 16.55/9.97 1081[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];1081 -> 1093[label="",style="solid", color="black", weight=3]; 16.55/9.97 1692[label="gcd0Gcd' (abs (Neg (Succ (Succ vuz51)))) (abs (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];1692 -> 1709[label="",style="solid", color="black", weight=3]; 16.55/9.97 2679[label="vuz5000",fontsize=16,color="green",shape="box"];2680[label="Succ vuz49",fontsize=16,color="green",shape="box"];2681[label="vuz5000",fontsize=16,color="green",shape="box"];2682[label="Succ vuz49",fontsize=16,color="green",shape="box"];722[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (abs (Pos (Succ vuz12)) == fromInt (Pos Zero)) (abs (Neg (Succ Zero))) (abs (Pos (Succ vuz12))))",fontsize=16,color="black",shape="box"];722 -> 732[label="",style="solid", color="black", weight=3]; 16.55/9.97 419[label="primQuotInt (Neg Zero) (gcd0Gcd'2 (abs (Neg Zero)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];419 -> 447[label="",style="solid", color="black", weight=3]; 16.55/9.97 746[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal2 (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Pos vuz14)) (absReal2 (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];746 -> 754[label="",style="solid", color="black", weight=3]; 16.55/9.97 753[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal2 (Pos (Succ vuz3100))) (fromInt (Pos Zero))) (abs (Neg vuz28)) (absReal2 (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];753 -> 761[label="",style="solid", color="black", weight=3]; 16.55/9.97 2508[label="gcd0Gcd'2 (abs (Pos (Succ (Succ vuz92)))) (abs (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];2508 -> 2523[label="",style="solid", color="black", weight=3]; 16.55/9.97 2697[label="primDivNatS0 vuz99 vuz100 (primGEqNatS vuz99 vuz100)",fontsize=16,color="burlywood",shape="box"];3491[label="vuz99/Succ vuz990",fontsize=10,color="white",style="solid",shape="box"];2697 -> 3491[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3491 -> 2703[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3492[label="vuz99/Zero",fontsize=10,color="white",style="solid",shape="box"];2697 -> 3492[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3492 -> 2704[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 730[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuz6))) (fromInt (Pos Zero))) (abs (Pos (Succ Zero))) (abs (Pos (Succ vuz6))))",fontsize=16,color="black",shape="box"];730 -> 739[label="",style="solid", color="black", weight=3]; 16.55/9.97 1093[label="gcd0Gcd'2 (abs (Pos Zero)) (abs (Pos (Succ vuz3100)))",fontsize=16,color="black",shape="box"];1093 -> 1105[label="",style="solid", color="black", weight=3]; 16.55/9.97 1709[label="gcd0Gcd'2 (abs (Neg (Succ (Succ vuz51)))) (abs (Pos (Succ vuz12)))",fontsize=16,color="black",shape="box"];1709 -> 1736[label="",style="solid", color="black", weight=3]; 16.55/9.97 732[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuz12))) (fromInt (Pos Zero))) (abs (Neg (Succ Zero))) (abs (Pos (Succ vuz12))))",fontsize=16,color="black",shape="box"];732 -> 741[label="",style="solid", color="black", weight=3]; 16.55/9.97 447[label="primQuotInt (Neg Zero) (gcd0Gcd'1 (abs (Pos (Succ vuz3100)) == fromInt (Pos Zero)) (abs (Neg Zero)) (abs (Pos (Succ vuz3100))))",fontsize=16,color="black",shape="box"];447 -> 553[label="",style="solid", color="black", weight=3]; 16.55/9.97 754[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos vuz14)) (absReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) >= fromInt (Pos Zero))))",fontsize=16,color="black",shape="box"];754 -> 762[label="",style="solid", color="black", weight=3]; 16.55/9.97 761[label="primQuotInt (Pos (Succ vuz3100)) (gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Neg vuz28)) (absReal1 (Pos (Succ vuz3100)) (Pos (Succ vuz3100) >= fromInt (Pos Zero))))",fontsize=16,color="black",shape="box"];761 -> 769[label="",style="solid", color="black", weight=3]; 16.55/9.97 2523[label="gcd0Gcd'1 (abs (Pos (Succ vuz6)) == fromInt (Pos Zero)) (abs (Pos (Succ (Succ vuz92)))) (abs (Pos (Succ vuz6)))",fontsize=16,color="black",shape="box"];2523 -> 2539[label="",style="solid", color="black", weight=3]; 16.55/9.97 2703[label="primDivNatS0 (Succ vuz990) vuz100 (primGEqNatS (Succ vuz990) vuz100)",fontsize=16,color="burlywood",shape="box"];3493[label="vuz100/Succ vuz1000",fontsize=10,color="white",style="solid",shape="box"];2703 -> 3493[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3493 -> 2721[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3494[label="vuz100/Zero",fontsize=10,color="white",style="solid",shape="box"];2703 -> 3494[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3494 -> 2722[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 2704[label="primDivNatS0 Zero vuz100 (primGEqNatS Zero vuz100)",fontsize=16,color="burlywood",shape="box"];3495[label="vuz100/Succ vuz1000",fontsize=10,color="white",style="solid",shape="box"];2704 -> 3495[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3495 -> 2723[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3496[label="vuz100/Zero",fontsize=10,color="white",style="solid",shape="box"];2704 -> 3496[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3496 -> 2724[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 739[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuz6))) (fromInt (Pos Zero))) (abs (Pos (Succ Zero))) (absReal (Pos (Succ vuz6))))",fontsize=16,color="black",shape="box"];739 -> 747[label="",style="solid", color="black", weight=3]; 16.55/9.97 1105[label="gcd0Gcd'1 (abs (Pos (Succ vuz3100)) == fromInt (Pos Zero)) (abs (Pos Zero)) (abs (Pos (Succ 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3437[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3432 -> 1037[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3432[label="primDivNatS Zero (Succ vuz144)",fontsize=16,color="magenta"];3432 -> 3438[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3433 -> 1037[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3433[label="primDivNatS Zero (Succ vuz144)",fontsize=16,color="magenta"];3433 -> 3439[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 803[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz6)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ Zero))) (absReal1 (Pos (Succ vuz6)) (not (GT == LT))))",fontsize=16,color="black",shape="box"];803 -> 811[label="",style="solid", color="black", weight=3]; 16.55/9.97 1263[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz3100)) (not (primCmpInt (Pos (Succ vuz3100)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 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3079[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3534[label="vuz116/Zero",fontsize=10,color="white",style="solid",shape="box"];3065 -> 3534[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3534 -> 3080[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 1173[label="vuz1400",fontsize=16,color="green",shape="box"];1174[label="Zero",fontsize=16,color="green",shape="box"];2823[label="Zero",fontsize=16,color="green",shape="box"];2824[label="Succ vuz31000",fontsize=16,color="green",shape="box"];2822[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz107)) (fromInt (Pos Zero))) (Pos (Succ vuz108)) (Pos (Succ vuz107))",fontsize=16,color="black",shape="triangle"];2822 -> 2842[label="",style="solid", color="black", weight=3]; 16.55/9.97 3109[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz1080) (Succ vuz1070) (primGEqNatS (Succ vuz1080) (Succ vuz1070)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz1070))) (Pos (primModNatS0 (Succ vuz1080) (Succ 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3010[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1149[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz120) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz120))) (Pos (primModNatS0 Zero (Succ vuz120) False)))",fontsize=16,color="black",shape="box"];1149 -> 1163[label="",style="solid", color="black", weight=3]; 16.55/9.97 1150[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero True)))",fontsize=16,color="black",shape="triangle"];1150 -> 1164[label="",style="solid", color="black", weight=3]; 16.55/9.97 1080 -> 1037[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1080[label="primDivNatS Zero (Succ vuz3100)",fontsize=16,color="magenta"];1080 -> 1092[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3077[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz113) vuz114 (primGEqNatS (Succ 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16.55/9.97 3126 -> 3185[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3126 -> 3186[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3127 -> 3091[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3127[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz1080) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz1080) Zero True))",fontsize=16,color="magenta"];3127 -> 3187[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3127 -> 3188[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3128 -> 2407[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3128[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz1070) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz1070))) (Pos (primModNatS0 Zero (Succ vuz1070) False))",fontsize=16,color="magenta"];3128 -> 3189[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3129[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero 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3334[label="Zero",fontsize=16,color="green",shape="box"];3335[label="Zero",fontsize=16,color="green",shape="box"];3336[label="Zero",fontsize=16,color="green",shape="box"];3333[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS vuz138 vuz139) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS vuz138 vuz139) (Succ vuz140)))",fontsize=16,color="burlywood",shape="triangle"];3535[label="vuz138/Succ vuz1380",fontsize=10,color="white",style="solid",shape="box"];3333 -> 3535[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3535 -> 3361[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3536[label="vuz138/Zero",fontsize=10,color="white",style="solid",shape="box"];3333 -> 3536[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3536 -> 3362[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 1197[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'2 (Pos (Succ Zero)) (Pos (Succ (Succ vuz60)) `rem` 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vuz107))",fontsize=16,color="black",shape="box"];2892 -> 2911[label="",style="solid", color="black", weight=3]; 16.55/9.97 3361[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz1380) vuz139) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS (Succ vuz1380) vuz139) (Succ vuz140)))",fontsize=16,color="burlywood",shape="box"];3537[label="vuz139/Succ vuz1390",fontsize=10,color="white",style="solid",shape="box"];3361 -> 3537[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3537 -> 3367[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3538[label="vuz139/Zero",fontsize=10,color="white",style="solid",shape="box"];3361 -> 3538[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3538 -> 3368[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3362[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero vuz139) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS Zero vuz139) (Succ vuz140)))",fontsize=16,color="burlywood",shape="box"];3539[label="vuz139/Succ vuz1390",fontsize=10,color="white",style="solid",shape="box"];3362 -> 3539[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3539 -> 3369[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3540[label="vuz139/Zero",fontsize=10,color="white",style="solid",shape="box"];3362 -> 3540[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3540 -> 3370[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 1219[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (Pos (Succ (Succ vuz60)) `rem` Pos (Succ Zero) == fromInt (Pos Zero)) (Pos (Succ Zero)) (Pos (Succ (Succ vuz60)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1219 -> 1241[label="",style="solid", color="black", weight=3]; 16.55/9.97 1225[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'0 (Pos (Succ (Succ vuz120))) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1225 -> 1249[label="",style="solid", color="black", weight=3]; 16.55/9.97 1226[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ Zero)) (Pos Zero))",fontsize=16,color="black",shape="box"];1226 -> 1250[label="",style="solid", color="black", weight=3]; 16.55/9.97 2911[label="gcd0Gcd'2 (Pos (Succ vuz107)) (Pos (Succ vuz108) `rem` Pos (Succ vuz107))",fontsize=16,color="black",shape="box"];2911 -> 2950[label="",style="solid", color="black", weight=3]; 16.55/9.97 3367[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz1380) (Succ vuz1390)) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS (Succ vuz1380) (Succ vuz1390)) (Succ vuz140)))",fontsize=16,color="black",shape="box"];3367 -> 3375[label="",style="solid", color="black", weight=3]; 16.55/9.97 3368[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz1380) Zero) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS (Succ vuz1380) Zero) (Succ vuz140)))",fontsize=16,color="black",shape="box"];3368 -> 3376[label="",style="solid", color="black", weight=3]; 16.55/9.97 3369[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero (Succ vuz1390)) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS Zero (Succ vuz1390)) (Succ vuz140)))",fontsize=16,color="black",shape="box"];3369 -> 3377[label="",style="solid", color="black", weight=3]; 16.55/9.97 3370[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero Zero) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS Zero Zero) (Succ vuz140)))",fontsize=16,color="black",shape="box"];3370 -> 3378[label="",style="solid", color="black", weight=3]; 16.55/9.97 1241[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuz60)) `rem` Pos (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (Succ (Succ vuz60)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1241 -> 1269[label="",style="solid", color="black", weight=3]; 16.55/9.97 1249[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd' (Pos (Succ Zero)) (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1249 -> 1279[label="",style="solid", color="black", weight=3]; 16.55/9.97 1250[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 True (Pos (Succ Zero)) (Pos Zero))",fontsize=16,color="black",shape="box"];1250 -> 1280[label="",style="solid", color="black", weight=3]; 16.55/9.97 2950[label="gcd0Gcd'1 (Pos (Succ vuz108) `rem` Pos (Succ vuz107) == fromInt (Pos Zero)) (Pos (Succ vuz107)) (Pos (Succ vuz108) `rem` Pos (Succ vuz107))",fontsize=16,color="black",shape="box"];2950 -> 2974[label="",style="solid", color="black", weight=3]; 16.55/9.97 3375 -> 3333[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3375[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS vuz1380 vuz1390) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (primMinusNatS vuz1380 vuz1390) (Succ vuz140)))",fontsize=16,color="magenta"];3375 -> 3385[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3375 -> 3386[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3376 -> 3066[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3376[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuz1380) (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS (Succ vuz1380) (Succ vuz140)))",fontsize=16,color="magenta"];3376 -> 3387[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3376 -> 3388[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3377 -> 2202[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3377[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS Zero (Succ vuz140)))",fontsize=16,color="magenta"];3377 -> 3389[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 3378 -> 2202[label="",style="dashed", color="red", weight=0]; 16.55/9.97 3378[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuz140))) (fromInt (Pos Zero))) (Pos (Succ vuz140)) (Pos (primModNatS Zero (Succ vuz140)))",fontsize=16,color="magenta"];3378 -> 3390[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1269 -> 1064[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1269[label="primQuotInt (Pos (Succ Zero)) (gcd0Gcd'1 (primEqInt (primRemInt (Pos (Succ (Succ vuz60))) (Pos (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (primRemInt (Pos (Succ (Succ vuz60))) (Pos (Succ Zero))))",fontsize=16,color="magenta"];1269 -> 1299[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1269 -> 1300[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1279[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'2 (Pos (Succ Zero)) (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1279 -> 1310[label="",style="solid", color="black", weight=3]; 16.55/9.97 1280[label="primQuotInt (Neg (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1280 -> 1311[label="",style="solid", color="black", weight=3]; 16.55/9.97 2974[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz108) `rem` Pos (Succ vuz107)) (fromInt (Pos Zero))) (Pos (Succ vuz107)) (Pos (Succ vuz108) `rem` Pos (Succ vuz107))",fontsize=16,color="black",shape="box"];2974 -> 2994[label="",style="solid", color="black", weight=3]; 16.55/9.97 3385[label="vuz1390",fontsize=16,color="green",shape="box"];3386[label="vuz1380",fontsize=16,color="green",shape="box"];3387[label="vuz1380",fontsize=16,color="green",shape="box"];3388[label="vuz140",fontsize=16,color="green",shape="box"];3389[label="vuz140",fontsize=16,color="green",shape="box"];3390[label="vuz140",fontsize=16,color="green",shape="box"];1299[label="Succ vuz60",fontsize=16,color="green",shape="box"];1300[label="Zero",fontsize=16,color="green",shape="box"];1310[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero) == fromInt (Pos Zero)) (Pos (Succ Zero)) (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1310 -> 1341[label="",style="solid", color="black", weight=3]; 16.55/9.97 1311[label="Neg (primDivNatS (Succ Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1311 -> 1342[label="",style="dashed", color="green", weight=3]; 16.55/9.97 1341[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (Succ (Succ vuz120)) `rem` Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1341 -> 1377[label="",style="solid", color="black", weight=3]; 16.55/9.97 1342 -> 2674[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1342[label="primDivNatS (Succ Zero) (Succ Zero)",fontsize=16,color="magenta"];1342 -> 2695[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1342 -> 2696[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1377[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (primRemInt (Pos (Succ (Succ vuz120))) (Pos (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (primRemInt (Pos (Succ (Succ vuz120))) (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];1377 -> 1613[label="",style="solid", color="black", weight=3]; 16.55/9.97 2695[label="Zero",fontsize=16,color="green",shape="box"];2696[label="Zero",fontsize=16,color="green",shape="box"];1613[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ (Succ vuz120)) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS (Succ (Succ vuz120)) (Succ Zero))))",fontsize=16,color="black",shape="box"];1613 -> 1642[label="",style="solid", color="black", weight=3]; 16.55/9.97 1642[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz120) Zero (primGEqNatS (Succ vuz120) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz120) Zero (primGEqNatS (Succ vuz120) Zero))))",fontsize=16,color="black",shape="box"];1642 -> 1672[label="",style="solid", color="black", weight=3]; 16.55/9.97 1672[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz120) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz120) Zero True)))",fontsize=16,color="black",shape="triangle"];1672 -> 1713[label="",style="solid", color="black", weight=3]; 16.55/9.97 1713[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz120) Zero) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS (primMinusNatS (Succ vuz120) Zero) (Succ Zero))))",fontsize=16,color="black",shape="box"];1713 -> 1740[label="",style="solid", color="black", weight=3]; 16.55/9.97 1740[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuz120) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS (Succ vuz120) (Succ Zero))))",fontsize=16,color="black",shape="box"];1740 -> 1768[label="",style="solid", color="black", weight=3]; 16.55/9.97 1768[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 vuz120 Zero (primGEqNatS vuz120 Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 vuz120 Zero (primGEqNatS vuz120 Zero))))",fontsize=16,color="burlywood",shape="box"];3541[label="vuz120/Succ vuz1200",fontsize=10,color="white",style="solid",shape="box"];1768 -> 3541[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3541 -> 1795[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 3542[label="vuz120/Zero",fontsize=10,color="white",style="solid",shape="box"];1768 -> 3542[label="",style="solid", color="burlywood", weight=9]; 16.55/9.97 3542 -> 1796[label="",style="solid", color="burlywood", weight=3]; 16.55/9.97 1795[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz1200) Zero (primGEqNatS (Succ vuz1200) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz1200) Zero (primGEqNatS (Succ vuz1200) Zero))))",fontsize=16,color="black",shape="box"];1795 -> 1825[label="",style="solid", color="black", weight=3]; 16.55/9.97 1796[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))))",fontsize=16,color="black",shape="box"];1796 -> 1826[label="",style="solid", color="black", weight=3]; 16.55/9.97 1825 -> 1672[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1825[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz1200) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz1200) Zero True)))",fontsize=16,color="magenta"];1825 -> 1864[label="",style="dashed", color="magenta", weight=3]; 16.55/9.97 1826 -> 1150[label="",style="dashed", color="red", weight=0]; 16.55/9.97 1826[label="primQuotInt (Neg (Succ Zero)) (gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero True)))",fontsize=16,color="magenta"];1864[label="vuz1200",fontsize=16,color="green",shape="box"];} 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (12) 16.55/9.97 Complex Obligation (AND) 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (13) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Zero, Zero) -> new_primDivNatS00(vuz133, vuz134) 16.55/9.97 new_primDivNatS00(vuz133, vuz134) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 new_primDivNatS(Succ(vuz1420), Succ(vuz1430), vuz144) -> new_primDivNatS(vuz1420, vuz1430, vuz144) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Zero) -> new_primDivNatS(Succ(vuz990), Zero, Zero) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Succ(vuz1360)) -> new_primDivNatS0(vuz133, vuz134, vuz1350, vuz1360) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Zero) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Succ(vuz1000)) -> new_primDivNatS0(vuz990, vuz1000, vuz990, vuz1000) 16.55/9.97 new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 16.55/9.97 new_primDivNatS(Succ(vuz1420), Zero, vuz144) -> new_primDivNatS1(vuz1420, vuz144) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (14) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (15) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primDivNatS00(vuz133, vuz134) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 new_primDivNatS(Succ(vuz1420), Succ(vuz1430), vuz144) -> new_primDivNatS(vuz1420, vuz1430, vuz144) 16.55/9.97 new_primDivNatS(Succ(vuz1420), Zero, vuz144) -> new_primDivNatS1(vuz1420, vuz144) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Zero) -> new_primDivNatS(Succ(vuz990), Zero, Zero) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Succ(vuz1000)) -> new_primDivNatS0(vuz990, vuz1000, vuz990, vuz1000) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Zero, Zero) -> new_primDivNatS00(vuz133, vuz134) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Succ(vuz1360)) -> new_primDivNatS0(vuz133, vuz134, vuz1350, vuz1360) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Zero) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (16) QDPOrderProof (EQUIVALENT) 16.55/9.97 We use the reduction pair processor [LPAR04,JAR06]. 16.55/9.97 16.55/9.97 16.55/9.97 The following pairs can be oriented strictly and are deleted. 16.55/9.97 16.55/9.97 new_primDivNatS(Succ(vuz1420), Succ(vuz1430), vuz144) -> new_primDivNatS(vuz1420, vuz1430, vuz144) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Zero) -> new_primDivNatS(Succ(vuz990), Zero, Zero) 16.55/9.97 new_primDivNatS1(Succ(vuz990), Succ(vuz1000)) -> new_primDivNatS0(vuz990, vuz1000, vuz990, vuz1000) 16.55/9.97 The remaining pairs can at least be oriented weakly. 16.55/9.97 Used ordering: Polynomial interpretation [POLO]: 16.55/9.97 16.55/9.97 POL(Succ(x_1)) = 1 + x_1 16.55/9.97 POL(Zero) = 0 16.55/9.97 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 16.55/9.97 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 16.55/9.97 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 16.55/9.97 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 16.55/9.97 16.55/9.97 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 16.55/9.97 none 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (17) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primDivNatS00(vuz133, vuz134) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 new_primDivNatS(Succ(vuz1420), Zero, vuz144) -> new_primDivNatS1(vuz1420, vuz144) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Zero, Zero) -> new_primDivNatS00(vuz133, vuz134) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Succ(vuz1360)) -> new_primDivNatS0(vuz133, vuz134, vuz1350, vuz1360) 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Zero) -> new_primDivNatS(Succ(vuz133), Succ(vuz134), Succ(vuz134)) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (18) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (19) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Succ(vuz1360)) -> new_primDivNatS0(vuz133, vuz134, vuz1350, vuz1360) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (20) QDPSizeChangeProof (EQUIVALENT) 16.55/9.97 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 16.55/9.97 16.55/9.97 From the DPs we obtained the following set of size-change graphs: 16.55/9.97 *new_primDivNatS0(vuz133, vuz134, Succ(vuz1350), Succ(vuz1360)) -> new_primDivNatS0(vuz133, vuz134, vuz1350, vuz1360) 16.55/9.97 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (21) 16.55/9.97 YES 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (22) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primQuotInt(Succ(vuz1200)) -> new_primQuotInt(vuz1200) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (23) QDPSizeChangeProof (EQUIVALENT) 16.55/9.97 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 16.55/9.97 16.55/9.97 From the DPs we obtained the following set of size-change graphs: 16.55/9.97 *new_primQuotInt(Succ(vuz1200)) -> new_primQuotInt(vuz1200) 16.55/9.97 The graph contains the following edges 1 > 1 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (24) 16.55/9.97 YES 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (25) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primQuotInt0(Zero, Succ(vuz1400)) -> new_primQuotInt0(Zero, vuz1400) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (26) QDPSizeChangeProof (EQUIVALENT) 16.55/9.97 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 16.55/9.97 16.55/9.97 From the DPs we obtained the following set of size-change graphs: 16.55/9.97 *new_primQuotInt0(Zero, Succ(vuz1400)) -> new_primQuotInt0(Zero, vuz1400) 16.55/9.97 The graph contains the following edges 1 >= 1, 2 > 2 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (27) 16.55/9.97 YES 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (28) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'14(Zero, Succ(vuz1080)) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'15(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'14(Zero, Zero) -> new_gcd0Gcd'13(Zero, Zero, Zero) 16.55/9.97 new_gcd0Gcd'15(Zero, Zero) -> new_gcd0Gcd'13(Zero, Zero, Zero) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'1(Zero, Succ(vuz1070)) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'15(Zero, Succ(vuz1070)) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 new_gcd0Gcd'15(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'1(Zero, Zero) -> new_gcd0Gcd'13(Zero, Zero, Zero) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 new_gcd0Gcd'12(vuz31000) -> new_gcd0Gcd'14(Zero, Succ(vuz31000)) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Zero) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (29) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (30) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'1(Zero, Succ(vuz1070)) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 new_gcd0Gcd'12(vuz31000) -> new_gcd0Gcd'14(Zero, Succ(vuz31000)) 16.55/9.97 new_gcd0Gcd'14(Zero, Succ(vuz1080)) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Zero) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (31) QDPOrderProof (EQUIVALENT) 16.55/9.97 We use the reduction pair processor [LPAR04,JAR06]. 16.55/9.97 16.55/9.97 16.55/9.97 The following pairs can be oriented strictly and are deleted. 16.55/9.97 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Zero) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 The remaining pairs can at least be oriented weakly. 16.55/9.97 Used ordering: Polynomial interpretation [POLO]: 16.55/9.97 16.55/9.97 POL(Succ(x_1)) = 0 16.55/9.97 POL(Zero) = 1 16.55/9.97 POL(new_gcd0Gcd'1(x_1, x_2)) = 1 16.55/9.97 POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = 1 + x_2 16.55/9.97 POL(new_gcd0Gcd'11(x_1, x_2)) = 1 16.55/9.97 POL(new_gcd0Gcd'12(x_1)) = 1 16.55/9.97 POL(new_gcd0Gcd'13(x_1, x_2, x_3)) = 1 16.55/9.97 POL(new_gcd0Gcd'14(x_1, x_2)) = 1 + x_2 16.55/9.97 16.55/9.97 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 16.55/9.97 none 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (32) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'1(Zero, Succ(vuz1070)) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 new_gcd0Gcd'12(vuz31000) -> new_gcd0Gcd'14(Zero, Succ(vuz31000)) 16.55/9.97 new_gcd0Gcd'14(Zero, Succ(vuz1080)) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (33) QDPOrderProof (EQUIVALENT) 16.55/9.97 We use the reduction pair processor [LPAR04,JAR06]. 16.55/9.97 16.55/9.97 16.55/9.97 The following pairs can be oriented strictly and are deleted. 16.55/9.97 16.55/9.97 new_gcd0Gcd'14(Zero, Succ(vuz1080)) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 The remaining pairs can at least be oriented weakly. 16.55/9.97 Used ordering: Polynomial interpretation [POLO]: 16.55/9.97 16.55/9.97 POL(Succ(x_1)) = 1 16.55/9.97 POL(Zero) = 0 16.55/9.97 POL(new_gcd0Gcd'1(x_1, x_2)) = x_2 16.55/9.97 POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = x_2 16.55/9.97 POL(new_gcd0Gcd'11(x_1, x_2)) = x_2 16.55/9.97 POL(new_gcd0Gcd'12(x_1)) = 1 16.55/9.97 POL(new_gcd0Gcd'13(x_1, x_2, x_3)) = x_3 16.55/9.97 POL(new_gcd0Gcd'14(x_1, x_2)) = x_2 16.55/9.97 16.55/9.97 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 16.55/9.97 none 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (34) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'1(Zero, Succ(vuz1070)) -> new_gcd0Gcd'12(vuz1070) 16.55/9.97 new_gcd0Gcd'12(vuz31000) -> new_gcd0Gcd'14(Zero, Succ(vuz31000)) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (35) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (36) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (37) QDPOrderProof (EQUIVALENT) 16.55/9.97 We use the reduction pair processor [LPAR04,JAR06]. 16.55/9.97 16.55/9.97 16.55/9.97 The following pairs can be oriented strictly and are deleted. 16.55/9.97 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Zero, vuz140) -> new_gcd0Gcd'1(vuz1380, vuz140) 16.55/9.97 new_gcd0Gcd'13(Succ(vuz1380), Succ(vuz1390), vuz140) -> new_gcd0Gcd'13(vuz1380, vuz1390, vuz140) 16.55/9.97 The remaining pairs can at least be oriented weakly. 16.55/9.97 Used ordering: Polynomial interpretation [POLO]: 16.55/9.97 16.55/9.97 POL(Succ(x_1)) = 1 + x_1 16.55/9.97 POL(Zero) = 0 16.55/9.97 POL(new_gcd0Gcd'1(x_1, x_2)) = x_1 + x_2 16.55/9.97 POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 16.55/9.97 POL(new_gcd0Gcd'11(x_1, x_2)) = 1 + x_1 + x_2 16.55/9.97 POL(new_gcd0Gcd'13(x_1, x_2, x_3)) = x_1 + x_3 16.55/9.97 POL(new_gcd0Gcd'14(x_1, x_2)) = x_1 + x_2 16.55/9.97 16.55/9.97 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 16.55/9.97 none 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (38) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Zero) -> new_gcd0Gcd'11(vuz1080, Zero) 16.55/9.97 new_gcd0Gcd'11(vuz113, vuz114) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'1(Succ(vuz1080), Succ(vuz1070)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Zero) -> new_gcd0Gcd'11(vuz113, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Zero) -> new_gcd0Gcd'13(Succ(vuz113), vuz114, vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (39) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (40) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (41) InductionCalculusProof (EQUIVALENT) 16.55/9.97 Note that final constraints are written in bold face. 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x3, x4, Zero, Succ(x5)) -> new_gcd0Gcd'14(Succ(x3), x4), new_gcd0Gcd'14(Succ(x6), Succ(x7)) -> new_gcd0Gcd'10(x7, Succ(x6), x7, x6) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'14(Succ(x3), x4)=new_gcd0Gcd'14(Succ(x6), Succ(x7)) ==> new_gcd0Gcd'10(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), x4)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x3, Succ(x7), Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), Succ(x7))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'14(Succ(x11), Succ(x12)) -> new_gcd0Gcd'10(x12, Succ(x11), x12, x11), new_gcd0Gcd'10(x13, x14, Zero, Succ(x15)) -> new_gcd0Gcd'14(Succ(x13), x14) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x12, Succ(x11), x12, x11)=new_gcd0Gcd'10(x13, x14, Zero, Succ(x15)) ==> new_gcd0Gcd'14(Succ(x11), Succ(x12))_>=_new_gcd0Gcd'10(x12, Succ(x11), x12, x11)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'14(Succ(Succ(x15)), Succ(Zero))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x15)), Zero, Succ(x15))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *We consider the chain new_gcd0Gcd'14(Succ(x18), Succ(x19)) -> new_gcd0Gcd'10(x19, Succ(x18), x19, x18), new_gcd0Gcd'10(x20, x21, Succ(x22), Succ(x23)) -> new_gcd0Gcd'10(x20, x21, x22, x23) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x19, Succ(x18), x19, x18)=new_gcd0Gcd'10(x20, x21, Succ(x22), Succ(x23)) ==> new_gcd0Gcd'14(Succ(x18), Succ(x19))_>=_new_gcd0Gcd'10(x19, Succ(x18), x19, x18)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'14(Succ(Succ(x23)), Succ(Succ(x22)))_>=_new_gcd0Gcd'10(Succ(x22), Succ(Succ(x23)), Succ(x22), Succ(x23))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x24, x25, Succ(x26), Succ(x27)) -> new_gcd0Gcd'10(x24, x25, x26, x27), new_gcd0Gcd'10(x28, x29, Zero, Succ(x30)) -> new_gcd0Gcd'14(Succ(x28), x29) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x24, x25, x26, x27)=new_gcd0Gcd'10(x28, x29, Zero, Succ(x30)) ==> new_gcd0Gcd'10(x24, x25, Succ(x26), Succ(x27))_>=_new_gcd0Gcd'10(x24, x25, x26, x27)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x24, x25, Succ(Zero), Succ(Succ(x30)))_>=_new_gcd0Gcd'10(x24, x25, Zero, Succ(x30))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x35, x36, Succ(x37), Succ(x38)) -> new_gcd0Gcd'10(x35, x36, x37, x38), new_gcd0Gcd'10(x39, x40, Succ(x41), Succ(x42)) -> new_gcd0Gcd'10(x39, x40, x41, x42) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x35, x36, x37, x38)=new_gcd0Gcd'10(x39, x40, Succ(x41), Succ(x42)) ==> new_gcd0Gcd'10(x35, x36, Succ(x37), Succ(x38))_>=_new_gcd0Gcd'10(x35, x36, x37, x38)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x35, x36, Succ(Succ(x41)), Succ(Succ(x42)))_>=_new_gcd0Gcd'10(x35, x36, Succ(x41), Succ(x42))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 To summarize, we get the following constraints P__>=_ for the following pairs. 16.55/9.97 16.55/9.97 *new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x3, Succ(x7), Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), Succ(x7))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'14(Succ(Succ(x15)), Succ(Zero))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x15)), Zero, Succ(x15))) 16.55/9.97 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'14(Succ(Succ(x23)), Succ(Succ(x22)))_>=_new_gcd0Gcd'10(Succ(x22), Succ(Succ(x23)), Succ(x22), Succ(x23))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x24, x25, Succ(Zero), Succ(Succ(x30)))_>=_new_gcd0Gcd'10(x24, x25, Zero, Succ(x30))) 16.55/9.97 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x35, x36, Succ(Succ(x41)), Succ(Succ(x42)))_>=_new_gcd0Gcd'10(x35, x36, Succ(x41), Succ(x42))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (42) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (43) NonInfProof (EQUIVALENT) 16.55/9.97 The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps: 16.55/9.97 16.55/9.97 Note that final constraints are written in bold face. 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x3, x4, Zero, Succ(x5)) -> new_gcd0Gcd'14(Succ(x3), x4), new_gcd0Gcd'14(Succ(x6), Succ(x7)) -> new_gcd0Gcd'10(x7, Succ(x6), x7, x6) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'14(Succ(x3), x4)=new_gcd0Gcd'14(Succ(x6), Succ(x7)) ==> new_gcd0Gcd'10(x3, x4, Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), x4)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x3, Succ(x7), Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), Succ(x7))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'14(Succ(x11), Succ(x12)) -> new_gcd0Gcd'10(x12, Succ(x11), x12, x11), new_gcd0Gcd'10(x13, x14, Zero, Succ(x15)) -> new_gcd0Gcd'14(Succ(x13), x14) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x12, Succ(x11), x12, x11)=new_gcd0Gcd'10(x13, x14, Zero, Succ(x15)) ==> new_gcd0Gcd'14(Succ(x11), Succ(x12))_>=_new_gcd0Gcd'10(x12, Succ(x11), x12, x11)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'14(Succ(Succ(x15)), Succ(Zero))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x15)), Zero, Succ(x15))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *We consider the chain new_gcd0Gcd'14(Succ(x18), Succ(x19)) -> new_gcd0Gcd'10(x19, Succ(x18), x19, x18), new_gcd0Gcd'10(x20, x21, Succ(x22), Succ(x23)) -> new_gcd0Gcd'10(x20, x21, x22, x23) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x19, Succ(x18), x19, x18)=new_gcd0Gcd'10(x20, x21, Succ(x22), Succ(x23)) ==> new_gcd0Gcd'14(Succ(x18), Succ(x19))_>=_new_gcd0Gcd'10(x19, Succ(x18), x19, x18)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'14(Succ(Succ(x23)), Succ(Succ(x22)))_>=_new_gcd0Gcd'10(Succ(x22), Succ(Succ(x23)), Succ(x22), Succ(x23))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 For Pair new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) the following chains were created: 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x24, x25, Succ(x26), Succ(x27)) -> new_gcd0Gcd'10(x24, x25, x26, x27), new_gcd0Gcd'10(x28, x29, Zero, Succ(x30)) -> new_gcd0Gcd'14(Succ(x28), x29) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x24, x25, x26, x27)=new_gcd0Gcd'10(x28, x29, Zero, Succ(x30)) ==> new_gcd0Gcd'10(x24, x25, Succ(x26), Succ(x27))_>=_new_gcd0Gcd'10(x24, x25, x26, x27)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x24, x25, Succ(Zero), Succ(Succ(x30)))_>=_new_gcd0Gcd'10(x24, x25, Zero, Succ(x30))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *We consider the chain new_gcd0Gcd'10(x35, x36, Succ(x37), Succ(x38)) -> new_gcd0Gcd'10(x35, x36, x37, x38), new_gcd0Gcd'10(x39, x40, Succ(x41), Succ(x42)) -> new_gcd0Gcd'10(x39, x40, x41, x42) which results in the following constraint: 16.55/9.97 16.55/9.97 (1) (new_gcd0Gcd'10(x35, x36, x37, x38)=new_gcd0Gcd'10(x39, x40, Succ(x41), Succ(x42)) ==> new_gcd0Gcd'10(x35, x36, Succ(x37), Succ(x38))_>=_new_gcd0Gcd'10(x35, x36, x37, x38)) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint: 16.55/9.97 16.55/9.97 (2) (new_gcd0Gcd'10(x35, x36, Succ(Succ(x41)), Succ(Succ(x42)))_>=_new_gcd0Gcd'10(x35, x36, Succ(x41), Succ(x42))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 To summarize, we get the following constraints P__>=_ for the following pairs. 16.55/9.97 16.55/9.97 *new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x3, Succ(x7), Zero, Succ(x5))_>=_new_gcd0Gcd'14(Succ(x3), Succ(x7))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'14(Succ(Succ(x15)), Succ(Zero))_>=_new_gcd0Gcd'10(Zero, Succ(Succ(x15)), Zero, Succ(x15))) 16.55/9.97 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'14(Succ(Succ(x23)), Succ(Succ(x22)))_>=_new_gcd0Gcd'10(Succ(x22), Succ(Succ(x23)), Succ(x22), Succ(x23))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 *new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x24, x25, Succ(Zero), Succ(Succ(x30)))_>=_new_gcd0Gcd'10(x24, x25, Zero, Succ(x30))) 16.55/9.97 16.55/9.97 16.55/9.97 *(new_gcd0Gcd'10(x35, x36, Succ(Succ(x41)), Succ(Succ(x42)))_>=_new_gcd0Gcd'10(x35, x36, Succ(x41), Succ(x42))) 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 16.55/9.97 The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 16.55/9.97 16.55/9.97 Using the following integer polynomial ordering the resulting constraints can be solved 16.55/9.97 16.55/9.97 Polynomial interpretation [NONINF]: 16.55/9.97 16.55/9.97 POL(Succ(x_1)) = 1 + x_1 16.55/9.97 POL(Zero) = 0 16.55/9.97 POL(c) = -1 16.55/9.97 POL(new_gcd0Gcd'10(x_1, x_2, x_3, x_4)) = x_1 - x_3 + x_4 16.55/9.97 POL(new_gcd0Gcd'14(x_1, x_2)) = x_1 16.55/9.97 16.55/9.97 16.55/9.97 The following pairs are in P_>: 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 The following pairs are in P_bound: 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'14(Succ(vuz1070), Succ(vuz1080)) -> new_gcd0Gcd'10(vuz1080, Succ(vuz1070), vuz1080, vuz1070) 16.55/9.97 There are no usable rules 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (44) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Zero, Succ(vuz1160)) -> new_gcd0Gcd'14(Succ(vuz113), vuz114) 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (45) DependencyGraphProof (EQUIVALENT) 16.55/9.97 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (46) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (47) QDPSizeChangeProof (EQUIVALENT) 16.55/9.97 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 16.55/9.97 16.55/9.97 From the DPs we obtained the following set of size-change graphs: 16.55/9.97 *new_gcd0Gcd'10(vuz113, vuz114, Succ(vuz1150), Succ(vuz1160)) -> new_gcd0Gcd'10(vuz113, vuz114, vuz1150, vuz1160) 16.55/9.97 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (48) 16.55/9.97 YES 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (49) 16.55/9.97 Obligation: 16.55/9.97 Q DP problem: 16.55/9.97 The TRS P consists of the following rules: 16.55/9.97 16.55/9.97 new_primMulNat(Succ(vuz30000)) -> new_primMulNat(vuz30000) 16.55/9.97 16.55/9.97 R is empty. 16.55/9.97 Q is empty. 16.55/9.97 We have to consider all minimal (P,Q,R)-chains. 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (50) QDPSizeChangeProof (EQUIVALENT) 16.55/9.97 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 16.55/9.97 16.55/9.97 From the DPs we obtained the following set of size-change graphs: 16.55/9.97 *new_primMulNat(Succ(vuz30000)) -> new_primMulNat(vuz30000) 16.55/9.97 The graph contains the following edges 1 > 1 16.55/9.97 16.55/9.97 16.55/9.97 ---------------------------------------- 16.55/9.97 16.55/9.97 (51) 16.55/9.97 YES 16.67/10.05 EOF