6.48/2.56	YES
6.48/2.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
6.48/2.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.48/2.58	
6.48/2.58	
6.48/2.58	Left Termination of the query pattern
6.48/2.58	
6.48/2.58	add(g,g,a)
6.48/2.58	
6.48/2.58	w.r.t. the given Prolog program could successfully be proven:
6.48/2.58	
6.48/2.58	(0) Prolog
6.48/2.58	(1) PrologToPiTRSProof [SOUND, 40 ms]
6.48/2.58	(2) PiTRS
6.48/2.58	(3) DependencyPairsProof [EQUIVALENT, 73 ms]
6.48/2.58	(4) PiDP
6.48/2.58	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
6.48/2.58	(6) AND
6.48/2.58	    (7) PiDP
6.48/2.58	        (8) UsableRulesProof [EQUIVALENT, 0 ms]
6.48/2.58	        (9) PiDP
6.48/2.58	        (10) PiDPToQDPProof [EQUIVALENT, 5 ms]
6.48/2.58	        (11) QDP
6.48/2.58	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.48/2.58	        (13) YES
6.48/2.58	    (14) PiDP
6.48/2.58	        (15) UsableRulesProof [EQUIVALENT, 0 ms]
6.48/2.58	        (16) PiDP
6.48/2.58	        (17) PiDPToQDPProof [SOUND, 0 ms]
6.48/2.58	        (18) QDP
6.48/2.58	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.48/2.58	        (20) YES
6.48/2.58	    (21) PiDP
6.48/2.58	        (22) UsableRulesProof [EQUIVALENT, 0 ms]
6.48/2.58	        (23) PiDP
6.48/2.58	        (24) PiDPToQDPProof [SOUND, 1 ms]
6.48/2.58	        (25) QDP
6.48/2.58	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.48/2.58	        (27) YES
6.48/2.58	
6.48/2.58	
6.48/2.58	----------------------------------------
6.48/2.58	
6.48/2.58	(0)
6.48/2.58	Obligation:
6.48/2.58	Clauses:
6.48/2.58	
6.48/2.58	add(b, b, b).
6.48/2.58	add(X, b, X) :- binaryZ(X).
6.48/2.58	add(b, Y, Y) :- binaryZ(Y).
6.48/2.58	add(X, Y, Z) :- addz(X, Y, Z).
6.48/2.58	addx(one(X), b, one(X)) :- binary(X).
6.48/2.58	addx(zero(X), b, zero(X)) :- binaryZ(X).
6.48/2.58	addx(X, Y, Z) :- addz(X, Y, Z).
6.48/2.58	addy(b, one(Y), one(Y)) :- binary(Y).
6.48/2.58	addy(b, zero(Y), zero(Y)) :- binaryZ(Y).
6.48/2.58	addy(X, Y, Z) :- addz(X, Y, Z).
6.48/2.58	addz(zero(X), zero(Y), zero(Z)) :- addz(X, Y, Z).
6.48/2.58	addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z).
6.48/2.58	addz(one(X), zero(Y), one(Z)) :- addy(X, Y, Z).
6.48/2.58	addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z).
6.48/2.58	addc(b, b, one(b)).
6.48/2.58	addc(X, b, Z) :- succZ(X, Z).
6.48/2.58	addc(b, Y, Z) :- succZ(Y, Z).
6.48/2.58	addc(X, Y, Z) :- addC(X, Y, Z).
6.48/2.58	addX(zero(X), b, one(X)) :- binaryZ(X).
6.48/2.58	addX(one(X), b, zero(Z)) :- succ(X, Z).
6.48/2.58	addX(X, Y, Z) :- addC(X, Y, Z).
6.48/2.58	addY(b, zero(Y), one(Y)) :- binaryZ(Y).
6.48/2.58	addY(b, one(Y), zero(Z)) :- succ(Y, Z).
6.48/2.58	addY(X, Y, Z) :- addC(X, Y, Z).
6.48/2.58	addC(zero(X), zero(Y), one(Z)) :- addz(X, Y, Z).
6.48/2.58	addC(zero(X), one(Y), zero(Z)) :- addX(X, Y, Z).
6.48/2.58	addC(one(X), zero(Y), zero(Z)) :- addY(X, Y, Z).
6.48/2.58	addC(one(X), one(Y), one(Z)) :- addc(X, Y, Z).
6.48/2.58	binary(b).
6.48/2.58	binary(zero(X)) :- binaryZ(X).
6.48/2.58	binary(one(X)) :- binary(X).
6.48/2.58	binaryZ(zero(X)) :- binaryZ(X).
6.48/2.58	binaryZ(one(X)) :- binary(X).
6.48/2.58	succ(b, one(b)).
6.48/2.58	succ(zero(X), one(X)) :- binaryZ(X).
6.48/2.58	succ(one(X), zero(Z)) :- succ(X, Z).
6.48/2.58	succZ(zero(X), one(X)) :- binaryZ(X).
6.48/2.58	succZ(one(X), zero(Z)) :- succ(X, Z).
6.48/2.58	times(one(b), X, X).
6.48/2.58	times(zero(R), S, zero(RS)) :- times(R, S, RS).
6.48/2.58	times(one(R), S, RSS) :- ','(times(R, S, RS), add(S, zero(RS), RSS)).
6.48/2.58	
6.48/2.58	
6.48/2.58	Query: add(g,g,a)
6.48/2.58	----------------------------------------
6.48/2.58	
6.48/2.58	(1) PrologToPiTRSProof (SOUND)
6.48/2.58	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
6.48/2.58	
6.48/2.58	add_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	binaryZ_in_1: (b)
6.48/2.58	
6.48/2.58	binary_in_1: (b)
6.48/2.58	
6.48/2.58	addz_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	addx_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	addy_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	addc_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	succZ_in_2: (b,f)
6.48/2.58	
6.48/2.58	succ_in_2: (b,f)
6.48/2.58	
6.48/2.58	addC_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	addX_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	addY_in_3: (b,b,f)
6.48/2.58	
6.48/2.58	Transforming Prolog into the following Term Rewriting System:
6.48/2.58	
6.48/2.58	Pi-finite rewrite system:
6.48/2.58	The TRS R consists of the following rules:
6.48/2.58	
6.48/2.58	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.58	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.58	   binary_in_g(b) -> binary_out_g(b)
6.48/2.58	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.58	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.58	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.58	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.58	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.58	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.58	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.58	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.58	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.58	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.58	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.58	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.58	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.58	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.58	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.58	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.58	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.58	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.58	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.58	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.58	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.58	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.58	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.58	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.58	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.58	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.58	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.58	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.58	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.58	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.58	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.58	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.58	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.58	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.58	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.58	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.58	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.58	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.58	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.58	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.58	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.58	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.58	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.58	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.58	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.58	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.58	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.58	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.58	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.58	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.58	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.58	
6.48/2.58	The argument filtering Pi contains the following mapping:
6.48/2.58	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	b  =  b
6.48/2.58	
6.48/2.58	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.58	
6.48/2.58	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.58	
6.48/2.58	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.58	
6.48/2.58	zero(x1)  =  zero(x1)
6.48/2.58	
6.48/2.58	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.58	
6.48/2.58	one(x1)  =  one(x1)
6.48/2.58	
6.48/2.58	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.58	
6.48/2.58	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.58	
6.48/2.58	binary_out_g(x1)  =  binary_out_g
6.48/2.58	
6.48/2.58	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.58	
6.48/2.58	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.58	
6.48/2.58	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.58	
6.48/2.58	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.58	
6.48/2.58	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.58	
6.48/2.58	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.58	
6.48/2.58	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.58	
6.48/2.58	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.58	
6.48/2.58	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.58	
6.48/2.58	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.58	
6.48/2.58	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.58	
6.48/2.58	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.58	
6.48/2.58	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.58	
6.48/2.58	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.58	
6.48/2.58	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.58	
6.48/2.58	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.58	
6.48/2.58	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.58	
6.48/2.58	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.58	
6.48/2.58	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.58	
6.48/2.58	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.58	
6.48/2.58	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.58	
6.48/2.58	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.58	
6.48/2.58	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.58	
6.48/2.58	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.58	
6.48/2.58	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.58	
6.48/2.58	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.58	
6.48/2.58	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.58	
6.48/2.58	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.58	
6.48/2.58	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.58	
6.48/2.58	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.58	
6.48/2.58	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.58	
6.48/2.58	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.58	
6.48/2.58	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.58	
6.48/2.58	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.58	
6.48/2.58	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.58	
6.48/2.58	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.58	
6.48/2.58	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.58	
6.48/2.58	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.58	
6.48/2.58	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.58	
6.48/2.58	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.58	
6.48/2.58	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.58	
6.48/2.58	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.58	
6.48/2.58	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.58	
6.48/2.58	
6.48/2.58	
6.48/2.58	
6.48/2.58	
6.48/2.58	Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
6.48/2.58	
6.48/2.58	
6.48/2.58	
6.48/2.58	----------------------------------------
6.48/2.58	
6.48/2.58	(2)
6.48/2.58	Obligation:
6.48/2.58	Pi-finite rewrite system:
6.48/2.58	The TRS R consists of the following rules:
6.48/2.58	
6.48/2.58	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.58	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.58	   binary_in_g(b) -> binary_out_g(b)
6.48/2.58	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.58	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.58	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.58	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.58	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.58	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.58	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.58	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.58	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.58	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.58	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.58	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.58	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.58	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.58	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.58	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.58	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.58	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.58	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.58	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.58	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.58	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.58	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.58	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.58	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.58	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.58	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.58	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.58	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.58	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.58	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.58	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.58	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.58	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.58	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.58	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.58	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.58	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.58	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.58	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.58	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.58	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.58	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.58	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.58	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.58	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.58	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.58	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.58	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.58	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.58	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.58	
6.48/2.58	The argument filtering Pi contains the following mapping:
6.48/2.58	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	b  =  b
6.48/2.58	
6.48/2.58	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.58	
6.48/2.58	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.58	
6.48/2.58	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.58	
6.48/2.58	zero(x1)  =  zero(x1)
6.48/2.58	
6.48/2.58	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.58	
6.48/2.58	one(x1)  =  one(x1)
6.48/2.58	
6.48/2.58	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.58	
6.48/2.58	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.58	
6.48/2.58	binary_out_g(x1)  =  binary_out_g
6.48/2.58	
6.48/2.58	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.58	
6.48/2.58	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.58	
6.48/2.58	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.58	
6.48/2.58	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.58	
6.48/2.58	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.58	
6.48/2.58	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.58	
6.48/2.58	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.58	
6.48/2.58	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.58	
6.48/2.58	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.58	
6.48/2.58	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.58	
6.48/2.58	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.58	
6.48/2.58	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.58	
6.48/2.58	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.58	
6.48/2.58	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.58	
6.48/2.58	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.58	
6.48/2.58	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.58	
6.48/2.58	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.58	
6.48/2.58	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.58	
6.48/2.58	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.58	
6.48/2.58	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.58	
6.48/2.58	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.58	
6.48/2.58	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.58	
6.48/2.58	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.58	
6.48/2.58	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.58	
6.48/2.58	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.58	
6.48/2.58	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.58	
6.48/2.58	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.58	
6.48/2.58	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.58	
6.48/2.58	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.58	
6.48/2.58	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.58	
6.48/2.58	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.58	
6.48/2.58	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.58	
6.48/2.58	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.58	
6.48/2.58	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.58	
6.48/2.58	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.58	
6.48/2.58	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.58	
6.48/2.58	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.58	
6.48/2.58	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.58	
6.48/2.58	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.58	
6.48/2.58	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.58	
6.48/2.58	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.58	
6.48/2.58	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.58	
6.48/2.58	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.58	
6.48/2.58	
6.48/2.58	
6.48/2.58	----------------------------------------
6.48/2.58	
6.48/2.58	(3) DependencyPairsProof (EQUIVALENT)
6.48/2.58	Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
6.48/2.58	Pi DP problem:
6.48/2.58	The TRS P consists of the following rules:
6.48/2.58	
6.48/2.58	   ADD_IN_GGA(X, b, X) -> U1_GGA(X, binaryZ_in_g(X))
6.48/2.58	   ADD_IN_GGA(X, b, X) -> BINARYZ_IN_G(X)
6.48/2.58	   BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X))
6.48/2.58	   BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X))
6.48/2.58	   BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.58	   BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X))
6.48/2.58	   BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X))
6.48/2.58	   BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.58	   ADD_IN_GGA(b, Y, Y) -> U2_GGA(Y, binaryZ_in_g(Y))
6.48/2.58	   ADD_IN_GGA(b, Y, Y) -> BINARYZ_IN_G(Y)
6.48/2.58	   ADD_IN_GGA(X, Y, Z) -> U3_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   ADD_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.58	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> U10_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.58	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> U11_GGA(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.58	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> ADDX_IN_GGA(X, Y, Z)
6.48/2.58	   ADDX_IN_GGA(one(X), b, one(X)) -> U4_GGA(X, binary_in_g(X))
6.48/2.58	   ADDX_IN_GGA(one(X), b, one(X)) -> BINARY_IN_G(X)
6.48/2.58	   ADDX_IN_GGA(zero(X), b, zero(X)) -> U5_GGA(X, binaryZ_in_g(X))
6.48/2.58	   ADDX_IN_GGA(zero(X), b, zero(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   ADDX_IN_GGA(X, Y, Z) -> U6_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   ADDX_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.58	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> U12_GGA(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.58	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> ADDY_IN_GGA(X, Y, Z)
6.48/2.58	   ADDY_IN_GGA(b, one(Y), one(Y)) -> U7_GGA(Y, binary_in_g(Y))
6.48/2.58	   ADDY_IN_GGA(b, one(Y), one(Y)) -> BINARY_IN_G(Y)
6.48/2.58	   ADDY_IN_GGA(b, zero(Y), zero(Y)) -> U8_GGA(Y, binaryZ_in_g(Y))
6.48/2.58	   ADDY_IN_GGA(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y)
6.48/2.58	   ADDY_IN_GGA(X, Y, Z) -> U9_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   ADDY_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.58	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> U13_GGA(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.58	   ADDC_IN_GGA(X, b, Z) -> U14_GGA(X, Z, succZ_in_ga(X, Z))
6.48/2.58	   ADDC_IN_GGA(X, b, Z) -> SUCCZ_IN_GA(X, Z)
6.48/2.58	   SUCCZ_IN_GA(zero(X), one(X)) -> U33_GA(X, binaryZ_in_g(X))
6.48/2.58	   SUCCZ_IN_GA(zero(X), one(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   SUCCZ_IN_GA(one(X), zero(Z)) -> U34_GA(X, Z, succ_in_ga(X, Z))
6.48/2.58	   SUCCZ_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.58	   SUCC_IN_GA(zero(X), one(X)) -> U31_GA(X, binaryZ_in_g(X))
6.48/2.58	   SUCC_IN_GA(zero(X), one(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   SUCC_IN_GA(one(X), zero(Z)) -> U32_GA(X, Z, succ_in_ga(X, Z))
6.48/2.58	   SUCC_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.58	   ADDC_IN_GGA(b, Y, Z) -> U15_GGA(Y, Z, succZ_in_ga(Y, Z))
6.48/2.58	   ADDC_IN_GGA(b, Y, Z) -> SUCCZ_IN_GA(Y, Z)
6.48/2.58	   ADDC_IN_GGA(X, Y, Z) -> U16_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   ADDC_IN_GGA(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.58	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> U23_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.58	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> U24_GGA(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.58	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_GGA^1(X, Y, Z)
6.48/2.58	   ADDX_IN_GGA^1(zero(X), b, one(X)) -> U17_GGA(X, binaryZ_in_g(X))
6.48/2.58	   ADDX_IN_GGA^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X)
6.48/2.58	   ADDX_IN_GGA^1(one(X), b, zero(Z)) -> U18_GGA(X, Z, succ_in_ga(X, Z))
6.48/2.58	   ADDX_IN_GGA^1(one(X), b, zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.58	   ADDX_IN_GGA^1(X, Y, Z) -> U19_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   ADDX_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.58	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> U25_GGA(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.58	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_GGA^1(X, Y, Z)
6.48/2.58	   ADDY_IN_GGA^1(b, zero(Y), one(Y)) -> U20_GGA(Y, binaryZ_in_g(Y))
6.48/2.58	   ADDY_IN_GGA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y)
6.48/2.58	   ADDY_IN_GGA^1(b, one(Y), zero(Z)) -> U21_GGA(Y, Z, succ_in_ga(Y, Z))
6.48/2.58	   ADDY_IN_GGA^1(b, one(Y), zero(Z)) -> SUCC_IN_GA(Y, Z)
6.48/2.58	   ADDY_IN_GGA^1(X, Y, Z) -> U22_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   ADDY_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.58	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> U26_GGA(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.58	
6.48/2.58	The TRS R consists of the following rules:
6.48/2.58	
6.48/2.58	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.58	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.58	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.58	   binary_in_g(b) -> binary_out_g(b)
6.48/2.58	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.58	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.58	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.58	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.58	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.58	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.58	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.58	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.58	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.58	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.58	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.58	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.58	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.58	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.58	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.58	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.58	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.58	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.58	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.58	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.58	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.58	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.58	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.58	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.58	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.58	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.58	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.58	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.58	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.58	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.58	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.58	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.58	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.58	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.58	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.58	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.58	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.58	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.58	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.58	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.58	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.58	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.58	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.58	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.58	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.58	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.58	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.58	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.58	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.58	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.58	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.58	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.58	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.58	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.58	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.58	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.58	
6.48/2.58	The argument filtering Pi contains the following mapping:
6.48/2.58	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	b  =  b
6.48/2.58	
6.48/2.58	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.58	
6.48/2.58	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.58	
6.48/2.58	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.58	
6.48/2.58	zero(x1)  =  zero(x1)
6.48/2.58	
6.48/2.58	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.58	
6.48/2.58	one(x1)  =  one(x1)
6.48/2.58	
6.48/2.58	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.58	
6.48/2.58	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.58	
6.48/2.58	binary_out_g(x1)  =  binary_out_g
6.48/2.58	
6.48/2.58	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.58	
6.48/2.58	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.58	
6.48/2.58	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.58	
6.48/2.58	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.58	
6.48/2.58	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.58	
6.48/2.58	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.58	
6.48/2.58	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.58	
6.48/2.58	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.58	
6.48/2.58	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.58	
6.48/2.58	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.58	
6.48/2.58	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.58	
6.48/2.58	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.58	
6.48/2.58	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.58	
6.48/2.58	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.58	
6.48/2.58	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.58	
6.48/2.58	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.58	
6.48/2.58	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.58	
6.48/2.58	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.58	
6.48/2.58	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.58	
6.48/2.58	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.58	
6.48/2.58	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.58	
6.48/2.58	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.58	
6.48/2.58	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.58	
6.48/2.58	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.58	
6.48/2.58	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.58	
6.48/2.58	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.58	
6.48/2.58	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.58	
6.48/2.58	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.58	
6.48/2.58	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.58	
6.48/2.58	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.58	
6.48/2.58	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.58	
6.48/2.58	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.58	
6.48/2.58	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.58	
6.48/2.58	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.58	
6.48/2.58	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.58	
6.48/2.58	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.58	
6.48/2.58	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.58	
6.48/2.58	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.58	
6.48/2.58	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.58	
6.48/2.58	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.58	
6.48/2.58	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.58	
6.48/2.58	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.58	
6.48/2.58	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.58	
6.48/2.58	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.58	
6.48/2.58	ADD_IN_GGA(x1, x2, x3)  =  ADD_IN_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U1_GGA(x1, x2)  =  U1_GGA(x1, x2)
6.48/2.58	
6.48/2.58	BINARYZ_IN_G(x1)  =  BINARYZ_IN_G(x1)
6.48/2.58	
6.48/2.58	U29_G(x1, x2)  =  U29_G(x2)
6.48/2.58	
6.48/2.58	U30_G(x1, x2)  =  U30_G(x2)
6.48/2.58	
6.48/2.58	BINARY_IN_G(x1)  =  BINARY_IN_G(x1)
6.48/2.58	
6.48/2.58	U27_G(x1, x2)  =  U27_G(x2)
6.48/2.58	
6.48/2.58	U28_G(x1, x2)  =  U28_G(x2)
6.48/2.58	
6.48/2.58	U2_GGA(x1, x2)  =  U2_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
6.48/2.58	
6.48/2.58	ADDZ_IN_GGA(x1, x2, x3)  =  ADDZ_IN_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U10_GGA(x1, x2, x3, x4)  =  U10_GGA(x4)
6.48/2.58	
6.48/2.58	U11_GGA(x1, x2, x3, x4)  =  U11_GGA(x4)
6.48/2.58	
6.48/2.58	ADDX_IN_GGA(x1, x2, x3)  =  ADDX_IN_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U4_GGA(x1, x2)  =  U4_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U5_GGA(x1, x2)  =  U5_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U6_GGA(x1, x2, x3, x4)  =  U6_GGA(x4)
6.48/2.58	
6.48/2.58	U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x4)
6.48/2.58	
6.48/2.58	ADDY_IN_GGA(x1, x2, x3)  =  ADDY_IN_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U7_GGA(x1, x2)  =  U7_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U8_GGA(x1, x2)  =  U8_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U9_GGA(x1, x2, x3, x4)  =  U9_GGA(x4)
6.48/2.58	
6.48/2.58	U13_GGA(x1, x2, x3, x4)  =  U13_GGA(x4)
6.48/2.58	
6.48/2.58	ADDC_IN_GGA(x1, x2, x3)  =  ADDC_IN_GGA(x1, x2)
6.48/2.58	
6.48/2.58	U14_GGA(x1, x2, x3)  =  U14_GGA(x3)
6.48/2.58	
6.48/2.58	SUCCZ_IN_GA(x1, x2)  =  SUCCZ_IN_GA(x1)
6.48/2.58	
6.48/2.58	U33_GA(x1, x2)  =  U33_GA(x1, x2)
6.48/2.58	
6.48/2.58	U34_GA(x1, x2, x3)  =  U34_GA(x3)
6.48/2.58	
6.48/2.58	SUCC_IN_GA(x1, x2)  =  SUCC_IN_GA(x1)
6.48/2.58	
6.48/2.58	U31_GA(x1, x2)  =  U31_GA(x1, x2)
6.48/2.58	
6.48/2.58	U32_GA(x1, x2, x3)  =  U32_GA(x3)
6.48/2.59	
6.48/2.59	U15_GGA(x1, x2, x3)  =  U15_GGA(x3)
6.48/2.59	
6.48/2.59	U16_GGA(x1, x2, x3, x4)  =  U16_GGA(x4)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA^1(x1, x2, x3)  =  ADDC_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U23_GGA(x1, x2, x3, x4)  =  U23_GGA(x4)
6.48/2.59	
6.48/2.59	U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x4)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA^1(x1, x2, x3)  =  ADDX_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U17_GGA(x1, x2)  =  U17_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U18_GGA(x1, x2, x3)  =  U18_GGA(x3)
6.48/2.59	
6.48/2.59	U19_GGA(x1, x2, x3, x4)  =  U19_GGA(x4)
6.48/2.59	
6.48/2.59	U25_GGA(x1, x2, x3, x4)  =  U25_GGA(x4)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA^1(x1, x2, x3)  =  ADDY_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U20_GGA(x1, x2)  =  U20_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U21_GGA(x1, x2, x3)  =  U21_GGA(x3)
6.48/2.59	
6.48/2.59	U22_GGA(x1, x2, x3, x4)  =  U22_GGA(x4)
6.48/2.59	
6.48/2.59	U26_GGA(x1, x2, x3, x4)  =  U26_GGA(x4)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(4)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   ADD_IN_GGA(X, b, X) -> U1_GGA(X, binaryZ_in_g(X))
6.48/2.59	   ADD_IN_GGA(X, b, X) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X))
6.48/2.59	   BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X))
6.48/2.59	   BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	   BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X))
6.48/2.59	   BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X))
6.48/2.59	   BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	   ADD_IN_GGA(b, Y, Y) -> U2_GGA(Y, binaryZ_in_g(Y))
6.48/2.59	   ADD_IN_GGA(b, Y, Y) -> BINARYZ_IN_G(Y)
6.48/2.59	   ADD_IN_GGA(X, Y, Z) -> U3_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   ADD_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> U10_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> U11_GGA(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.59	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> ADDX_IN_GGA(X, Y, Z)
6.48/2.59	   ADDX_IN_GGA(one(X), b, one(X)) -> U4_GGA(X, binary_in_g(X))
6.48/2.59	   ADDX_IN_GGA(one(X), b, one(X)) -> BINARY_IN_G(X)
6.48/2.59	   ADDX_IN_GGA(zero(X), b, zero(X)) -> U5_GGA(X, binaryZ_in_g(X))
6.48/2.59	   ADDX_IN_GGA(zero(X), b, zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   ADDX_IN_GGA(X, Y, Z) -> U6_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   ADDX_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> U12_GGA(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.59	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> ADDY_IN_GGA(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA(b, one(Y), one(Y)) -> U7_GGA(Y, binary_in_g(Y))
6.48/2.59	   ADDY_IN_GGA(b, one(Y), one(Y)) -> BINARY_IN_G(Y)
6.48/2.59	   ADDY_IN_GGA(b, zero(Y), zero(Y)) -> U8_GGA(Y, binaryZ_in_g(Y))
6.48/2.59	   ADDY_IN_GGA(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y)
6.48/2.59	   ADDY_IN_GGA(X, Y, Z) -> U9_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   ADDY_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> U13_GGA(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA(X, b, Z) -> U14_GGA(X, Z, succZ_in_ga(X, Z))
6.48/2.59	   ADDC_IN_GGA(X, b, Z) -> SUCCZ_IN_GA(X, Z)
6.48/2.59	   SUCCZ_IN_GA(zero(X), one(X)) -> U33_GA(X, binaryZ_in_g(X))
6.48/2.59	   SUCCZ_IN_GA(zero(X), one(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   SUCCZ_IN_GA(one(X), zero(Z)) -> U34_GA(X, Z, succ_in_ga(X, Z))
6.48/2.59	   SUCCZ_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.59	   SUCC_IN_GA(zero(X), one(X)) -> U31_GA(X, binaryZ_in_g(X))
6.48/2.59	   SUCC_IN_GA(zero(X), one(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   SUCC_IN_GA(one(X), zero(Z)) -> U32_GA(X, Z, succ_in_ga(X, Z))
6.48/2.59	   SUCC_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.59	   ADDC_IN_GGA(b, Y, Z) -> U15_GGA(Y, Z, succZ_in_ga(Y, Z))
6.48/2.59	   ADDC_IN_GGA(b, Y, Z) -> SUCCZ_IN_GA(Y, Z)
6.48/2.59	   ADDC_IN_GGA(X, Y, Z) -> U16_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   ADDC_IN_GGA(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> U23_GGA(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> U24_GGA(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.59	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDX_IN_GGA^1(zero(X), b, one(X)) -> U17_GGA(X, binaryZ_in_g(X))
6.48/2.59	   ADDX_IN_GGA^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   ADDX_IN_GGA^1(one(X), b, zero(Z)) -> U18_GGA(X, Z, succ_in_ga(X, Z))
6.48/2.59	   ADDX_IN_GGA^1(one(X), b, zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.59	   ADDX_IN_GGA^1(X, Y, Z) -> U19_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   ADDX_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> U25_GGA(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.59	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA^1(b, zero(Y), one(Y)) -> U20_GGA(Y, binaryZ_in_g(Y))
6.48/2.59	   ADDY_IN_GGA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y)
6.48/2.59	   ADDY_IN_GGA^1(b, one(Y), zero(Z)) -> U21_GGA(Y, Z, succ_in_ga(Y, Z))
6.48/2.59	   ADDY_IN_GGA^1(b, one(Y), zero(Z)) -> SUCC_IN_GA(Y, Z)
6.48/2.59	   ADDY_IN_GGA^1(X, Y, Z) -> U22_GGA(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   ADDY_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> U26_GGA(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	
6.48/2.59	The TRS R consists of the following rules:
6.48/2.59	
6.48/2.59	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.59	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.59	   binary_in_g(b) -> binary_out_g(b)
6.48/2.59	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.59	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.59	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.59	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.59	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.59	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.59	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.59	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.59	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.59	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.59	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.59	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.59	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.59	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.59	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.59	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.59	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.59	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.59	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.59	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.59	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.59	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.59	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.59	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.59	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.59	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.59	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.59	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.59	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.59	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.59	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.59	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.59	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.59	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.59	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.59	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.59	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.59	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.59	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.59	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.59	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.59	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.59	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.59	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.59	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.59	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.59	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.59	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.59	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.59	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.59	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.59	
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	b  =  b
6.48/2.59	
6.48/2.59	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.59	
6.48/2.59	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.59	
6.48/2.59	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.59	
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.59	
6.48/2.59	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.59	
6.48/2.59	binary_out_g(x1)  =  binary_out_g
6.48/2.59	
6.48/2.59	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.59	
6.48/2.59	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.59	
6.48/2.59	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.59	
6.48/2.59	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.59	
6.48/2.59	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.59	
6.48/2.59	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.59	
6.48/2.59	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.59	
6.48/2.59	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.59	
6.48/2.59	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.59	
6.48/2.59	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.59	
6.48/2.59	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.59	
6.48/2.59	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.59	
6.48/2.59	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.59	
6.48/2.59	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.59	
6.48/2.59	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.59	
6.48/2.59	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.59	
6.48/2.59	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.59	
6.48/2.59	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.59	
6.48/2.59	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.59	
6.48/2.59	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.59	
6.48/2.59	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.59	
6.48/2.59	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.59	
6.48/2.59	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.59	
6.48/2.59	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.59	
6.48/2.59	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.59	
6.48/2.59	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.59	
6.48/2.59	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.59	
6.48/2.59	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.59	
6.48/2.59	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.59	
6.48/2.59	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.59	
6.48/2.59	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.59	
6.48/2.59	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.59	
6.48/2.59	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.59	
6.48/2.59	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.59	
6.48/2.59	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.59	
6.48/2.59	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.59	
6.48/2.59	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.59	
6.48/2.59	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.59	
6.48/2.59	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.59	
6.48/2.59	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.59	
6.48/2.59	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.59	
6.48/2.59	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.59	
6.48/2.59	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.59	
6.48/2.59	ADD_IN_GGA(x1, x2, x3)  =  ADD_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U1_GGA(x1, x2)  =  U1_GGA(x1, x2)
6.48/2.59	
6.48/2.59	BINARYZ_IN_G(x1)  =  BINARYZ_IN_G(x1)
6.48/2.59	
6.48/2.59	U29_G(x1, x2)  =  U29_G(x2)
6.48/2.59	
6.48/2.59	U30_G(x1, x2)  =  U30_G(x2)
6.48/2.59	
6.48/2.59	BINARY_IN_G(x1)  =  BINARY_IN_G(x1)
6.48/2.59	
6.48/2.59	U27_G(x1, x2)  =  U27_G(x2)
6.48/2.59	
6.48/2.59	U28_G(x1, x2)  =  U28_G(x2)
6.48/2.59	
6.48/2.59	U2_GGA(x1, x2)  =  U2_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
6.48/2.59	
6.48/2.59	ADDZ_IN_GGA(x1, x2, x3)  =  ADDZ_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U10_GGA(x1, x2, x3, x4)  =  U10_GGA(x4)
6.48/2.59	
6.48/2.59	U11_GGA(x1, x2, x3, x4)  =  U11_GGA(x4)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA(x1, x2, x3)  =  ADDX_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U4_GGA(x1, x2)  =  U4_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U5_GGA(x1, x2)  =  U5_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U6_GGA(x1, x2, x3, x4)  =  U6_GGA(x4)
6.48/2.59	
6.48/2.59	U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x4)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA(x1, x2, x3)  =  ADDY_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U7_GGA(x1, x2)  =  U7_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U8_GGA(x1, x2)  =  U8_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U9_GGA(x1, x2, x3, x4)  =  U9_GGA(x4)
6.48/2.59	
6.48/2.59	U13_GGA(x1, x2, x3, x4)  =  U13_GGA(x4)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA(x1, x2, x3)  =  ADDC_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U14_GGA(x1, x2, x3)  =  U14_GGA(x3)
6.48/2.59	
6.48/2.59	SUCCZ_IN_GA(x1, x2)  =  SUCCZ_IN_GA(x1)
6.48/2.59	
6.48/2.59	U33_GA(x1, x2)  =  U33_GA(x1, x2)
6.48/2.59	
6.48/2.59	U34_GA(x1, x2, x3)  =  U34_GA(x3)
6.48/2.59	
6.48/2.59	SUCC_IN_GA(x1, x2)  =  SUCC_IN_GA(x1)
6.48/2.59	
6.48/2.59	U31_GA(x1, x2)  =  U31_GA(x1, x2)
6.48/2.59	
6.48/2.59	U32_GA(x1, x2, x3)  =  U32_GA(x3)
6.48/2.59	
6.48/2.59	U15_GGA(x1, x2, x3)  =  U15_GGA(x3)
6.48/2.59	
6.48/2.59	U16_GGA(x1, x2, x3, x4)  =  U16_GGA(x4)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA^1(x1, x2, x3)  =  ADDC_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U23_GGA(x1, x2, x3, x4)  =  U23_GGA(x4)
6.48/2.59	
6.48/2.59	U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x4)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA^1(x1, x2, x3)  =  ADDX_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U17_GGA(x1, x2)  =  U17_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U18_GGA(x1, x2, x3)  =  U18_GGA(x3)
6.48/2.59	
6.48/2.59	U19_GGA(x1, x2, x3, x4)  =  U19_GGA(x4)
6.48/2.59	
6.48/2.59	U25_GGA(x1, x2, x3, x4)  =  U25_GGA(x4)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA^1(x1, x2, x3)  =  ADDY_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	U20_GGA(x1, x2)  =  U20_GGA(x1, x2)
6.48/2.59	
6.48/2.59	U21_GGA(x1, x2, x3)  =  U21_GGA(x3)
6.48/2.59	
6.48/2.59	U22_GGA(x1, x2, x3, x4)  =  U22_GGA(x4)
6.48/2.59	
6.48/2.59	U26_GGA(x1, x2, x3, x4)  =  U26_GGA(x4)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(5) DependencyGraphProof (EQUIVALENT)
6.48/2.59	The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 50 less nodes.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(6)
6.48/2.59	Complex Obligation (AND)
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(7)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	   BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	
6.48/2.59	The TRS R consists of the following rules:
6.48/2.59	
6.48/2.59	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.59	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.59	   binary_in_g(b) -> binary_out_g(b)
6.48/2.59	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.59	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.59	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.59	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.59	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.59	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.59	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.59	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.59	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.59	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.59	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.59	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.59	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.59	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.59	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.59	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.59	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.59	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.59	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.59	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.59	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.59	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.59	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.59	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.59	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.59	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.59	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.59	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.59	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.59	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.59	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.59	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.59	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.59	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.59	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.59	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.59	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.59	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.59	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.59	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.59	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.59	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.59	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.59	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.59	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.59	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.59	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.59	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.59	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.59	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.59	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.59	
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	b  =  b
6.48/2.59	
6.48/2.59	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.59	
6.48/2.59	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.59	
6.48/2.59	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.59	
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.59	
6.48/2.59	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.59	
6.48/2.59	binary_out_g(x1)  =  binary_out_g
6.48/2.59	
6.48/2.59	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.59	
6.48/2.59	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.59	
6.48/2.59	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.59	
6.48/2.59	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.59	
6.48/2.59	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.59	
6.48/2.59	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.59	
6.48/2.59	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.59	
6.48/2.59	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.59	
6.48/2.59	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.59	
6.48/2.59	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.59	
6.48/2.59	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.59	
6.48/2.59	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.59	
6.48/2.59	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.59	
6.48/2.59	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.59	
6.48/2.59	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.59	
6.48/2.59	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.59	
6.48/2.59	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.59	
6.48/2.59	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.59	
6.48/2.59	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.59	
6.48/2.59	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.59	
6.48/2.59	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.59	
6.48/2.59	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.59	
6.48/2.59	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.59	
6.48/2.59	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.59	
6.48/2.59	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.59	
6.48/2.59	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.59	
6.48/2.59	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.59	
6.48/2.59	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.59	
6.48/2.59	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.59	
6.48/2.59	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.59	
6.48/2.59	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.59	
6.48/2.59	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.59	
6.48/2.59	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.59	
6.48/2.59	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.59	
6.48/2.59	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.59	
6.48/2.59	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.59	
6.48/2.59	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.59	
6.48/2.59	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.59	
6.48/2.59	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.59	
6.48/2.59	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.59	
6.48/2.59	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.59	
6.48/2.59	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.59	
6.48/2.59	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.59	
6.48/2.59	BINARYZ_IN_G(x1)  =  BINARYZ_IN_G(x1)
6.48/2.59	
6.48/2.59	BINARY_IN_G(x1)  =  BINARY_IN_G(x1)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(8) UsableRulesProof (EQUIVALENT)
6.48/2.59	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(9)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	   BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	Pi is empty.
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(10) PiDPToQDPProof (EQUIVALENT)
6.48/2.59	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(11)
6.48/2.59	Obligation:
6.48/2.59	Q DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	   BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	   BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	Q is empty.
6.48/2.59	We have to consider all (P,Q,R)-chains.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(12) QDPSizeChangeProof (EQUIVALENT)
6.48/2.59	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. 
6.48/2.59	
6.48/2.59	From the DPs we obtained the following set of size-change graphs:
6.48/2.59	*BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	The graph contains the following edges 1 > 1
6.48/2.59	
6.48/2.59	
6.48/2.59	*BINARY_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	The graph contains the following edges 1 > 1
6.48/2.59	
6.48/2.59	
6.48/2.59	*BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X)
6.48/2.59	The graph contains the following edges 1 > 1
6.48/2.59	
6.48/2.59	
6.48/2.59	*BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X)
6.48/2.59	The graph contains the following edges 1 > 1
6.48/2.59	
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(13)
6.48/2.59	YES
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(14)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   SUCC_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.59	
6.48/2.59	The TRS R consists of the following rules:
6.48/2.59	
6.48/2.59	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.59	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.59	   binary_in_g(b) -> binary_out_g(b)
6.48/2.59	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.59	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.59	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.59	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.59	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.59	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.59	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.59	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.59	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.59	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.59	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.59	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.59	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.59	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.59	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.59	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.59	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.59	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.59	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.59	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.59	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.59	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.59	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.59	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.59	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.59	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.59	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.59	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.59	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.59	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.59	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.59	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.59	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.59	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.59	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.59	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.59	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.59	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.59	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.59	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.59	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.59	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.59	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.59	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.59	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.59	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.59	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.59	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.59	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.59	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.59	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.59	
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	b  =  b
6.48/2.59	
6.48/2.59	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.59	
6.48/2.59	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.59	
6.48/2.59	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.59	
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.59	
6.48/2.59	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.59	
6.48/2.59	binary_out_g(x1)  =  binary_out_g
6.48/2.59	
6.48/2.59	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.59	
6.48/2.59	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.59	
6.48/2.59	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.59	
6.48/2.59	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.59	
6.48/2.59	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.59	
6.48/2.59	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.59	
6.48/2.59	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.59	
6.48/2.59	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.59	
6.48/2.59	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.59	
6.48/2.59	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.59	
6.48/2.59	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.59	
6.48/2.59	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.59	
6.48/2.59	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.59	
6.48/2.59	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.59	
6.48/2.59	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.59	
6.48/2.59	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.59	
6.48/2.59	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.59	
6.48/2.59	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.59	
6.48/2.59	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.59	
6.48/2.59	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.59	
6.48/2.59	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.59	
6.48/2.59	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.59	
6.48/2.59	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.59	
6.48/2.59	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.59	
6.48/2.59	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.59	
6.48/2.59	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.59	
6.48/2.59	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.59	
6.48/2.59	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.59	
6.48/2.59	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.59	
6.48/2.59	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.59	
6.48/2.59	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.59	
6.48/2.59	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.59	
6.48/2.59	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.59	
6.48/2.59	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.59	
6.48/2.59	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.59	
6.48/2.59	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.59	
6.48/2.59	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.59	
6.48/2.59	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.59	
6.48/2.59	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.59	
6.48/2.59	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.59	
6.48/2.59	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.59	
6.48/2.59	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.59	
6.48/2.59	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.59	
6.48/2.59	SUCC_IN_GA(x1, x2)  =  SUCC_IN_GA(x1)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(15) UsableRulesProof (EQUIVALENT)
6.48/2.59	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(16)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   SUCC_IN_GA(one(X), zero(Z)) -> SUCC_IN_GA(X, Z)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	SUCC_IN_GA(x1, x2)  =  SUCC_IN_GA(x1)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(17) PiDPToQDPProof (SOUND)
6.48/2.59	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(18)
6.48/2.59	Obligation:
6.48/2.59	Q DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   SUCC_IN_GA(one(X)) -> SUCC_IN_GA(X)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	Q is empty.
6.48/2.59	We have to consider all (P,Q,R)-chains.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(19) QDPSizeChangeProof (EQUIVALENT)
6.48/2.59	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. 
6.48/2.59	
6.48/2.59	From the DPs we obtained the following set of size-change graphs:
6.48/2.59	*SUCC_IN_GA(one(X)) -> SUCC_IN_GA(X)
6.48/2.59	The graph contains the following edges 1 > 1
6.48/2.59	
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(20)
6.48/2.59	YES
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(21)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   ADDX_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> ADDX_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> ADDY_IN_GGA(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDX_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	
6.48/2.59	The TRS R consists of the following rules:
6.48/2.59	
6.48/2.59	   add_in_gga(b, b, b) -> add_out_gga(b, b, b)
6.48/2.59	   add_in_gga(X, b, X) -> U1_gga(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X))
6.48/2.59	   binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X))
6.48/2.59	   binary_in_g(b) -> binary_out_g(b)
6.48/2.59	   binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X))
6.48/2.59	   U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X))
6.48/2.59	   binary_in_g(one(X)) -> U28_g(X, binary_in_g(X))
6.48/2.59	   U28_g(X, binary_out_g(X)) -> binary_out_g(one(X))
6.48/2.59	   U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X))
6.48/2.59	   U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X))
6.48/2.59	   U1_gga(X, binaryZ_out_g(X)) -> add_out_gga(X, b, X)
6.48/2.59	   add_in_gga(b, Y, Y) -> U2_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U2_gga(Y, binaryZ_out_g(Y)) -> add_out_gga(b, Y, Y)
6.48/2.59	   add_in_gga(X, Y, Z) -> U3_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), zero(Y), zero(Z)) -> U10_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(zero(X), one(Y), one(Z)) -> U11_gga(X, Y, Z, addx_in_gga(X, Y, Z))
6.48/2.59	   addx_in_gga(one(X), b, one(X)) -> U4_gga(X, binary_in_g(X))
6.48/2.59	   U4_gga(X, binary_out_g(X)) -> addx_out_gga(one(X), b, one(X))
6.48/2.59	   addx_in_gga(zero(X), b, zero(X)) -> U5_gga(X, binaryZ_in_g(X))
6.48/2.59	   U5_gga(X, binaryZ_out_g(X)) -> addx_out_gga(zero(X), b, zero(X))
6.48/2.59	   addx_in_gga(X, Y, Z) -> U6_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), zero(Y), one(Z)) -> U12_gga(X, Y, Z, addy_in_gga(X, Y, Z))
6.48/2.59	   addy_in_gga(b, one(Y), one(Y)) -> U7_gga(Y, binary_in_g(Y))
6.48/2.59	   U7_gga(Y, binary_out_g(Y)) -> addy_out_gga(b, one(Y), one(Y))
6.48/2.59	   addy_in_gga(b, zero(Y), zero(Y)) -> U8_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U8_gga(Y, binaryZ_out_g(Y)) -> addy_out_gga(b, zero(Y), zero(Y))
6.48/2.59	   addy_in_gga(X, Y, Z) -> U9_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   addz_in_gga(one(X), one(Y), zero(Z)) -> U13_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   addc_in_gga(b, b, one(b)) -> addc_out_gga(b, b, one(b))
6.48/2.59	   addc_in_gga(X, b, Z) -> U14_gga(X, Z, succZ_in_ga(X, Z))
6.48/2.59	   succZ_in_ga(zero(X), one(X)) -> U33_ga(X, binaryZ_in_g(X))
6.48/2.59	   U33_ga(X, binaryZ_out_g(X)) -> succZ_out_ga(zero(X), one(X))
6.48/2.59	   succZ_in_ga(one(X), zero(Z)) -> U34_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   succ_in_ga(b, one(b)) -> succ_out_ga(b, one(b))
6.48/2.59	   succ_in_ga(zero(X), one(X)) -> U31_ga(X, binaryZ_in_g(X))
6.48/2.59	   U31_ga(X, binaryZ_out_g(X)) -> succ_out_ga(zero(X), one(X))
6.48/2.59	   succ_in_ga(one(X), zero(Z)) -> U32_ga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U32_ga(X, Z, succ_out_ga(X, Z)) -> succ_out_ga(one(X), zero(Z))
6.48/2.59	   U34_ga(X, Z, succ_out_ga(X, Z)) -> succZ_out_ga(one(X), zero(Z))
6.48/2.59	   U14_gga(X, Z, succZ_out_ga(X, Z)) -> addc_out_gga(X, b, Z)
6.48/2.59	   addc_in_gga(b, Y, Z) -> U15_gga(Y, Z, succZ_in_ga(Y, Z))
6.48/2.59	   U15_gga(Y, Z, succZ_out_ga(Y, Z)) -> addc_out_gga(b, Y, Z)
6.48/2.59	   addc_in_gga(X, Y, Z) -> U16_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(zero(X), zero(Y), one(Z)) -> U23_gga(X, Y, Z, addz_in_gga(X, Y, Z))
6.48/2.59	   U23_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), zero(Y), one(Z))
6.48/2.59	   addC_in_gga(zero(X), one(Y), zero(Z)) -> U24_gga(X, Y, Z, addX_in_gga(X, Y, Z))
6.48/2.59	   addX_in_gga(zero(X), b, one(X)) -> U17_gga(X, binaryZ_in_g(X))
6.48/2.59	   U17_gga(X, binaryZ_out_g(X)) -> addX_out_gga(zero(X), b, one(X))
6.48/2.59	   addX_in_gga(one(X), b, zero(Z)) -> U18_gga(X, Z, succ_in_ga(X, Z))
6.48/2.59	   U18_gga(X, Z, succ_out_ga(X, Z)) -> addX_out_gga(one(X), b, zero(Z))
6.48/2.59	   addX_in_gga(X, Y, Z) -> U19_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), zero(Y), zero(Z)) -> U25_gga(X, Y, Z, addY_in_gga(X, Y, Z))
6.48/2.59	   addY_in_gga(b, zero(Y), one(Y)) -> U20_gga(Y, binaryZ_in_g(Y))
6.48/2.59	   U20_gga(Y, binaryZ_out_g(Y)) -> addY_out_gga(b, zero(Y), one(Y))
6.48/2.59	   addY_in_gga(b, one(Y), zero(Z)) -> U21_gga(Y, Z, succ_in_ga(Y, Z))
6.48/2.59	   U21_gga(Y, Z, succ_out_ga(Y, Z)) -> addY_out_gga(b, one(Y), zero(Z))
6.48/2.59	   addY_in_gga(X, Y, Z) -> U22_gga(X, Y, Z, addC_in_gga(X, Y, Z))
6.48/2.59	   addC_in_gga(one(X), one(Y), one(Z)) -> U26_gga(X, Y, Z, addc_in_gga(X, Y, Z))
6.48/2.59	   U26_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addC_out_gga(one(X), one(Y), one(Z))
6.48/2.59	   U22_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addY_out_gga(X, Y, Z)
6.48/2.59	   U25_gga(X, Y, Z, addY_out_gga(X, Y, Z)) -> addC_out_gga(one(X), zero(Y), zero(Z))
6.48/2.59	   U19_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addX_out_gga(X, Y, Z)
6.48/2.59	   U24_gga(X, Y, Z, addX_out_gga(X, Y, Z)) -> addC_out_gga(zero(X), one(Y), zero(Z))
6.48/2.59	   U16_gga(X, Y, Z, addC_out_gga(X, Y, Z)) -> addc_out_gga(X, Y, Z)
6.48/2.59	   U13_gga(X, Y, Z, addc_out_gga(X, Y, Z)) -> addz_out_gga(one(X), one(Y), zero(Z))
6.48/2.59	   U9_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addy_out_gga(X, Y, Z)
6.48/2.59	   U12_gga(X, Y, Z, addy_out_gga(X, Y, Z)) -> addz_out_gga(one(X), zero(Y), one(Z))
6.48/2.59	   U6_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addx_out_gga(X, Y, Z)
6.48/2.59	   U11_gga(X, Y, Z, addx_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), one(Y), one(Z))
6.48/2.59	   U10_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> addz_out_gga(zero(X), zero(Y), zero(Z))
6.48/2.59	   U3_gga(X, Y, Z, addz_out_gga(X, Y, Z)) -> add_out_gga(X, Y, Z)
6.48/2.59	
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	add_in_gga(x1, x2, x3)  =  add_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	b  =  b
6.48/2.59	
6.48/2.59	add_out_gga(x1, x2, x3)  =  add_out_gga(x3)
6.48/2.59	
6.48/2.59	U1_gga(x1, x2)  =  U1_gga(x1, x2)
6.48/2.59	
6.48/2.59	binaryZ_in_g(x1)  =  binaryZ_in_g(x1)
6.48/2.59	
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	U29_g(x1, x2)  =  U29_g(x2)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	U30_g(x1, x2)  =  U30_g(x2)
6.48/2.59	
6.48/2.59	binary_in_g(x1)  =  binary_in_g(x1)
6.48/2.59	
6.48/2.59	binary_out_g(x1)  =  binary_out_g
6.48/2.59	
6.48/2.59	U27_g(x1, x2)  =  U27_g(x2)
6.48/2.59	
6.48/2.59	binaryZ_out_g(x1)  =  binaryZ_out_g
6.48/2.59	
6.48/2.59	U28_g(x1, x2)  =  U28_g(x2)
6.48/2.59	
6.48/2.59	U2_gga(x1, x2)  =  U2_gga(x1, x2)
6.48/2.59	
6.48/2.59	U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
6.48/2.59	
6.48/2.59	addz_in_gga(x1, x2, x3)  =  addz_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U10_gga(x1, x2, x3, x4)  =  U10_gga(x4)
6.48/2.59	
6.48/2.59	U11_gga(x1, x2, x3, x4)  =  U11_gga(x4)
6.48/2.59	
6.48/2.59	addx_in_gga(x1, x2, x3)  =  addx_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U4_gga(x1, x2)  =  U4_gga(x1, x2)
6.48/2.59	
6.48/2.59	addx_out_gga(x1, x2, x3)  =  addx_out_gga(x3)
6.48/2.59	
6.48/2.59	U5_gga(x1, x2)  =  U5_gga(x1, x2)
6.48/2.59	
6.48/2.59	U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
6.48/2.59	
6.48/2.59	U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
6.48/2.59	
6.48/2.59	addy_in_gga(x1, x2, x3)  =  addy_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U7_gga(x1, x2)  =  U7_gga(x1, x2)
6.48/2.59	
6.48/2.59	addy_out_gga(x1, x2, x3)  =  addy_out_gga(x3)
6.48/2.59	
6.48/2.59	U8_gga(x1, x2)  =  U8_gga(x1, x2)
6.48/2.59	
6.48/2.59	U9_gga(x1, x2, x3, x4)  =  U9_gga(x4)
6.48/2.59	
6.48/2.59	U13_gga(x1, x2, x3, x4)  =  U13_gga(x4)
6.48/2.59	
6.48/2.59	addc_in_gga(x1, x2, x3)  =  addc_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	addc_out_gga(x1, x2, x3)  =  addc_out_gga(x3)
6.48/2.59	
6.48/2.59	U14_gga(x1, x2, x3)  =  U14_gga(x3)
6.48/2.59	
6.48/2.59	succZ_in_ga(x1, x2)  =  succZ_in_ga(x1)
6.48/2.59	
6.48/2.59	U33_ga(x1, x2)  =  U33_ga(x1, x2)
6.48/2.59	
6.48/2.59	succZ_out_ga(x1, x2)  =  succZ_out_ga(x2)
6.48/2.59	
6.48/2.59	U34_ga(x1, x2, x3)  =  U34_ga(x3)
6.48/2.59	
6.48/2.59	succ_in_ga(x1, x2)  =  succ_in_ga(x1)
6.48/2.59	
6.48/2.59	succ_out_ga(x1, x2)  =  succ_out_ga(x2)
6.48/2.59	
6.48/2.59	U31_ga(x1, x2)  =  U31_ga(x1, x2)
6.48/2.59	
6.48/2.59	U32_ga(x1, x2, x3)  =  U32_ga(x3)
6.48/2.59	
6.48/2.59	U15_gga(x1, x2, x3)  =  U15_gga(x3)
6.48/2.59	
6.48/2.59	U16_gga(x1, x2, x3, x4)  =  U16_gga(x4)
6.48/2.59	
6.48/2.59	addC_in_gga(x1, x2, x3)  =  addC_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U23_gga(x1, x2, x3, x4)  =  U23_gga(x4)
6.48/2.59	
6.48/2.59	addz_out_gga(x1, x2, x3)  =  addz_out_gga(x3)
6.48/2.59	
6.48/2.59	addC_out_gga(x1, x2, x3)  =  addC_out_gga(x3)
6.48/2.59	
6.48/2.59	U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
6.48/2.59	
6.48/2.59	addX_in_gga(x1, x2, x3)  =  addX_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U17_gga(x1, x2)  =  U17_gga(x1, x2)
6.48/2.59	
6.48/2.59	addX_out_gga(x1, x2, x3)  =  addX_out_gga(x3)
6.48/2.59	
6.48/2.59	U18_gga(x1, x2, x3)  =  U18_gga(x3)
6.48/2.59	
6.48/2.59	U19_gga(x1, x2, x3, x4)  =  U19_gga(x4)
6.48/2.59	
6.48/2.59	U25_gga(x1, x2, x3, x4)  =  U25_gga(x4)
6.48/2.59	
6.48/2.59	addY_in_gga(x1, x2, x3)  =  addY_in_gga(x1, x2)
6.48/2.59	
6.48/2.59	U20_gga(x1, x2)  =  U20_gga(x1, x2)
6.48/2.59	
6.48/2.59	addY_out_gga(x1, x2, x3)  =  addY_out_gga(x3)
6.48/2.59	
6.48/2.59	U21_gga(x1, x2, x3)  =  U21_gga(x3)
6.48/2.59	
6.48/2.59	U22_gga(x1, x2, x3, x4)  =  U22_gga(x4)
6.48/2.59	
6.48/2.59	U26_gga(x1, x2, x3, x4)  =  U26_gga(x4)
6.48/2.59	
6.48/2.59	ADDZ_IN_GGA(x1, x2, x3)  =  ADDZ_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA(x1, x2, x3)  =  ADDX_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA(x1, x2, x3)  =  ADDY_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA(x1, x2, x3)  =  ADDC_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA^1(x1, x2, x3)  =  ADDC_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA^1(x1, x2, x3)  =  ADDX_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA^1(x1, x2, x3)  =  ADDY_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(22) UsableRulesProof (EQUIVALENT)
6.48/2.59	For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(23)
6.48/2.59	Obligation:
6.48/2.59	Pi DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   ADDX_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(zero(X), one(Y), one(Z)) -> ADDX_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), zero(Y), one(Z)) -> ADDY_IN_GGA(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA(X, Y, Z) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDZ_IN_GGA(one(X), one(Y), zero(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_GGA(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDX_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDY_IN_GGA^1(X, Y, Z) -> ADDC_IN_GGA^1(X, Y, Z)
6.48/2.59	   ADDC_IN_GGA^1(one(X), one(Y), one(Z)) -> ADDC_IN_GGA(X, Y, Z)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	The argument filtering Pi contains the following mapping:
6.48/2.59	zero(x1)  =  zero(x1)
6.48/2.59	
6.48/2.59	one(x1)  =  one(x1)
6.48/2.59	
6.48/2.59	ADDZ_IN_GGA(x1, x2, x3)  =  ADDZ_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA(x1, x2, x3)  =  ADDX_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA(x1, x2, x3)  =  ADDY_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA(x1, x2, x3)  =  ADDC_IN_GGA(x1, x2)
6.48/2.59	
6.48/2.59	ADDC_IN_GGA^1(x1, x2, x3)  =  ADDC_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	ADDX_IN_GGA^1(x1, x2, x3)  =  ADDX_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	ADDY_IN_GGA^1(x1, x2, x3)  =  ADDY_IN_GGA^1(x1, x2)
6.48/2.59	
6.48/2.59	
6.48/2.59	We have to consider all (P,R,Pi)-chains
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(24) PiDPToQDPProof (SOUND)
6.48/2.59	Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(25)
6.48/2.59	Obligation:
6.48/2.59	Q DP problem:
6.48/2.59	The TRS P consists of the following rules:
6.48/2.59	
6.48/2.59	   ADDX_IN_GGA(X, Y) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	   ADDZ_IN_GGA(zero(X), zero(Y)) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	   ADDZ_IN_GGA(zero(X), one(Y)) -> ADDX_IN_GGA(X, Y)
6.48/2.59	   ADDZ_IN_GGA(one(X), zero(Y)) -> ADDY_IN_GGA(X, Y)
6.48/2.59	   ADDY_IN_GGA(X, Y) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	   ADDZ_IN_GGA(one(X), one(Y)) -> ADDC_IN_GGA(X, Y)
6.48/2.59	   ADDC_IN_GGA(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), zero(Y)) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	   ADDC_IN_GGA^1(zero(X), one(Y)) -> ADDX_IN_GGA^1(X, Y)
6.48/2.59	   ADDX_IN_GGA^1(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	   ADDC_IN_GGA^1(one(X), zero(Y)) -> ADDY_IN_GGA^1(X, Y)
6.48/2.59	   ADDY_IN_GGA^1(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	   ADDC_IN_GGA^1(one(X), one(Y)) -> ADDC_IN_GGA(X, Y)
6.48/2.59	
6.48/2.59	R is empty.
6.48/2.59	Q is empty.
6.48/2.59	We have to consider all (P,Q,R)-chains.
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(26) QDPSizeChangeProof (EQUIVALENT)
6.48/2.59	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. 
6.48/2.59	
6.48/2.59	From the DPs we obtained the following set of size-change graphs:
6.48/2.59	*ADDZ_IN_GGA(zero(X), one(Y)) -> ADDX_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDZ_IN_GGA(zero(X), zero(Y)) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDX_IN_GGA(X, Y) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 >= 1, 2 >= 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDY_IN_GGA(X, Y) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 >= 1, 2 >= 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDC_IN_GGA^1(zero(X), zero(Y)) -> ADDZ_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDZ_IN_GGA(one(X), zero(Y)) -> ADDY_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDZ_IN_GGA(one(X), one(Y)) -> ADDC_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDC_IN_GGA(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	The graph contains the following edges 1 >= 1, 2 >= 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDC_IN_GGA^1(one(X), one(Y)) -> ADDC_IN_GGA(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDX_IN_GGA^1(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	The graph contains the following edges 1 >= 1, 2 >= 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDY_IN_GGA^1(X, Y) -> ADDC_IN_GGA^1(X, Y)
6.48/2.59	The graph contains the following edges 1 >= 1, 2 >= 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDC_IN_GGA^1(zero(X), one(Y)) -> ADDX_IN_GGA^1(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	*ADDC_IN_GGA^1(one(X), zero(Y)) -> ADDY_IN_GGA^1(X, Y)
6.48/2.59	The graph contains the following edges 1 > 1, 2 > 2
6.48/2.59	
6.48/2.59	
6.48/2.59	----------------------------------------
6.48/2.59	
6.48/2.59	(27)
6.48/2.59	YES
6.48/2.64	EOF