YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 6461 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 8 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 16 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 0 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 0 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 25 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES (32) IRSwT (33) IntTRSCompressionProof [EQUIVALENT, 0 ms] (34) IRSwT (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (36) IRSwT (37) TempFilterProof [SOUND, 9 ms] (38) IntTRS (39) RankingReductionPairProof [EQUIVALENT, 0 ms] (40) YES (41) IRSwT (42) IntTRSCompressionProof [EQUIVALENT, 0 ms] (43) IRSwT (44) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (45) IRSwT (46) TempFilterProof [SOUND, 12 ms] (47) IntTRS (48) RankingReductionPairProof [EQUIVALENT, 0 ms] (49) YES (50) IRSwT (51) IntTRSCompressionProof [EQUIVALENT, 0 ms] (52) IRSwT (53) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (54) IRSwT (55) TempFilterProof [SOUND, 7 ms] (56) IntTRS (57) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (58) YES ---------------------------------------- (0) Obligation: Rules: l0(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x4 = x11 && 50 <= x4 l2(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x25 = 1 + x18 && 1 + x18 <= 50 l5(x28, x29, x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x32 = x39 l7(x42, x43, x44, x45, x46, x47, x48) -> l4(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x53 = 0 && 50 <= x43 l7(x56, x57, x58, x59, x60, x61, x62) -> l8(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x59 = x66 && x58 = x65 && x56 = x63 && x60 = x67 && x64 = 1 + x57 && 1 + x57 <= 50 l9(x70, x71, x72, x73, x74, x75, x76) -> l10(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x74 = x81 l11(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: 50 <= x84 && x98 = 0 && x92 = 0 && x88 = x95 && x84 = x91 && x86 = x93 && x87 = x94 && x89 = x96 && x90 = x97 l11(x99, x100, x101, x102, x103, x104, x105) -> l12(x106, x107, x108, x109, x110, x111, x112) :|: x105 = x112 && x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x103 = x110 && x106 = 1 + x99 && 1 + x99 <= 50 l12(x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126) :|: x119 = x126 && x118 = x125 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x117 = x124 l10(x127, x128, x129, x130, x131, x132, x133) -> l12(x134, x135, x136, x137, x138, x139, x140) :|: 50 <= x131 && x141 = 0 && x134 = 0 && x131 = x138 && x128 = x135 && x129 = x136 && x130 = x137 && x132 = x139 && x133 = x140 l10(x142, x143, x144, x145, x146, x147, x148) -> l9(x149, x150, x151, x152, x153, x154, x155) :|: x148 = x155 && x147 = x154 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x153 = 1 + x146 && 1 + x146 <= 50 l8(x156, x157, x158, x159, x160, x161, x162) -> l7(x163, x164, x165, x166, x167, x168, x169) :|: x162 = x169 && x161 = x168 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x160 = x167 l6(x170, x171, x172, x173, x174, x175, x176) -> l9(x177, x178, x179, x180, x181, x182, x183) :|: x176 = x183 && x175 = x182 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x181 = 0 && 50 <= x173 l6(x184, x185, x186, x187, x188, x189, x190) -> l5(x191, x192, x193, x194, x195, x196, x197) :|: x190 = x197 && x189 = x196 && x186 = x193 && x185 = x192 && x184 = x191 && x188 = x195 && x194 = 1 + x187 && 1 + x187 <= 50 l4(x198, x199, x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209, x210, x211) :|: x204 = x211 && x203 = x210 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x202 = x209 l1(x212, x213, x214, x215, x216, x217, x218) -> l5(x219, x220, x221, x222, x223, x224, x225) :|: 50 <= x214 && x226 = 0 && x222 = 0 && x216 = x223 && x212 = x219 && x213 = x220 && x214 = x221 && x217 = x224 && x218 = x225 l1(x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240) :|: x233 = x240 && x232 = x239 && x230 = x237 && x228 = x235 && x227 = x234 && x231 = x238 && x236 = 1 + x229 && 1 + x229 <= 50 l13(x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254) :|: x252 = 0 && x253 = x253 && x254 = x254 && x255 = 0 && x250 = 0 && x241 = x248 && x242 = x249 && x244 = x251 l14(x256, x257, x258, x259, x260, x261, x262) -> l13(x263, x264, x265, x266, x267, x268, x269) :|: x262 = x269 && x261 = x268 && x259 = x266 && x258 = x265 && x257 = x264 && x256 = x263 && x260 = x267 Start term: l14(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x4 = x11 && 50 <= x4 l2(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x25 = 1 + x18 && 1 + x18 <= 50 l5(x28, x29, x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x32 = x39 l7(x42, x43, x44, x45, x46, x47, x48) -> l4(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x53 = 0 && 50 <= x43 l7(x56, x57, x58, x59, x60, x61, x62) -> l8(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x59 = x66 && x58 = x65 && x56 = x63 && x60 = x67 && x64 = 1 + x57 && 1 + x57 <= 50 l9(x70, x71, x72, x73, x74, x75, x76) -> l10(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x74 = x81 l11(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: 50 <= x84 && x98 = 0 && x92 = 0 && x88 = x95 && x84 = x91 && x86 = x93 && x87 = x94 && x89 = x96 && x90 = x97 l11(x99, x100, x101, x102, x103, x104, x105) -> l12(x106, x107, x108, x109, x110, x111, x112) :|: x105 = x112 && x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x103 = x110 && x106 = 1 + x99 && 1 + x99 <= 50 l12(x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126) :|: x119 = x126 && x118 = x125 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x117 = x124 l10(x127, x128, x129, x130, x131, x132, x133) -> l12(x134, x135, x136, x137, x138, x139, x140) :|: 50 <= x131 && x141 = 0 && x134 = 0 && x131 = x138 && x128 = x135 && x129 = x136 && x130 = x137 && x132 = x139 && x133 = x140 l10(x142, x143, x144, x145, x146, x147, x148) -> l9(x149, x150, x151, x152, x153, x154, x155) :|: x148 = x155 && x147 = x154 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x153 = 1 + x146 && 1 + x146 <= 50 l8(x156, x157, x158, x159, x160, x161, x162) -> l7(x163, x164, x165, x166, x167, x168, x169) :|: x162 = x169 && x161 = x168 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x160 = x167 l6(x170, x171, x172, x173, x174, x175, x176) -> l9(x177, x178, x179, x180, x181, x182, x183) :|: x176 = x183 && x175 = x182 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x181 = 0 && 50 <= x173 l6(x184, x185, x186, x187, x188, x189, x190) -> l5(x191, x192, x193, x194, x195, x196, x197) :|: x190 = x197 && x189 = x196 && x186 = x193 && x185 = x192 && x184 = x191 && x188 = x195 && x194 = 1 + x187 && 1 + x187 <= 50 l4(x198, x199, x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209, x210, x211) :|: x204 = x211 && x203 = x210 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x202 = x209 l1(x212, x213, x214, x215, x216, x217, x218) -> l5(x219, x220, x221, x222, x223, x224, x225) :|: 50 <= x214 && x226 = 0 && x222 = 0 && x216 = x223 && x212 = x219 && x213 = x220 && x214 = x221 && x217 = x224 && x218 = x225 l1(x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240) :|: x233 = x240 && x232 = x239 && x230 = x237 && x228 = x235 && x227 = x234 && x231 = x238 && x236 = 1 + x229 && 1 + x229 <= 50 l13(x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254) :|: x252 = 0 && x253 = x253 && x254 = x254 && x255 = 0 && x250 = 0 && x241 = x248 && x242 = x249 && x244 = x251 l14(x256, x257, x258, x259, x260, x261, x262) -> l13(x263, x264, x265, x266, x267, x268, x269) :|: x262 = x269 && x261 = x268 && x259 = x266 && x258 = x265 && x257 = x264 && x256 = x263 && x260 = x267 Start term: l14(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost (2) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x4 = x11 && 50 <= x4 (3) l2(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x25 = 1 + x18 && 1 + x18 <= 50 (4) l5(x28, x29, x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x32 = x39 (5) l7(x42, x43, x44, x45, x46, x47, x48) -> l4(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x53 = 0 && 50 <= x43 (6) l7(x56, x57, x58, x59, x60, x61, x62) -> l8(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x59 = x66 && x58 = x65 && x56 = x63 && x60 = x67 && x64 = 1 + x57 && 1 + x57 <= 50 (7) l9(x70, x71, x72, x73, x74, x75, x76) -> l10(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x74 = x81 (8) l11(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: 50 <= x84 && x98 = 0 && x92 = 0 && x88 = x95 && x84 = x91 && x86 = x93 && x87 = x94 && x89 = x96 && x90 = x97 (9) l11(x99, x100, x101, x102, x103, x104, x105) -> l12(x106, x107, x108, x109, x110, x111, x112) :|: x105 = x112 && x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x103 = x110 && x106 = 1 + x99 && 1 + x99 <= 50 (10) l12(x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126) :|: x119 = x126 && x118 = x125 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x117 = x124 (11) l10(x127, x128, x129, x130, x131, x132, x133) -> l12(x134, x135, x136, x137, x138, x139, x140) :|: 50 <= x131 && x141 = 0 && x134 = 0 && x131 = x138 && x128 = x135 && x129 = x136 && x130 = x137 && x132 = x139 && x133 = x140 (12) l10(x142, x143, x144, x145, x146, x147, x148) -> l9(x149, x150, x151, x152, x153, x154, x155) :|: x148 = x155 && x147 = x154 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x153 = 1 + x146 && 1 + x146 <= 50 (13) l8(x156, x157, x158, x159, x160, x161, x162) -> l7(x163, x164, x165, x166, x167, x168, x169) :|: x162 = x169 && x161 = x168 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x160 = x167 (14) l6(x170, x171, x172, x173, x174, x175, x176) -> l9(x177, x178, x179, x180, x181, x182, x183) :|: x176 = x183 && x175 = x182 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x181 = 0 && 50 <= x173 (15) l6(x184, x185, x186, x187, x188, x189, x190) -> l5(x191, x192, x193, x194, x195, x196, x197) :|: x190 = x197 && x189 = x196 && x186 = x193 && x185 = x192 && x184 = x191 && x188 = x195 && x194 = 1 + x187 && 1 + x187 <= 50 (16) l4(x198, x199, x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209, x210, x211) :|: x204 = x211 && x203 = x210 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x202 = x209 (17) l1(x212, x213, x214, x215, x216, x217, x218) -> l5(x219, x220, x221, x222, x223, x224, x225) :|: 50 <= x214 && x226 = 0 && x222 = 0 && x216 = x223 && x212 = x219 && x213 = x220 && x214 = x221 && x217 = x224 && x218 = x225 (18) l1(x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240) :|: x233 = x240 && x232 = x239 && x230 = x237 && x228 = x235 && x227 = x234 && x231 = x238 && x236 = 1 + x229 && 1 + x229 <= 50 (19) l13(x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254) :|: x252 = 0 && x253 = x253 && x254 = x254 && x255 = 0 && x250 = 0 && x241 = x248 && x242 = x249 && x244 = x251 (20) l14(x256, x257, x258, x259, x260, x261, x262) -> l13(x263, x264, x265, x266, x267, x268, x269) :|: x262 = x269 && x261 = x268 && x259 = x266 && x258 = x265 && x257 = x264 && x256 = x263 && x260 = x267 Arcs: (1) -> (17), (18) (3) -> (16) (4) -> (14), (15) (5) -> (16) (6) -> (13) (7) -> (11), (12) (8) -> (13) (9) -> (10) (10) -> (8), (9) (11) -> (10) (12) -> (7) (13) -> (5), (6) (14) -> (7) (15) -> (4) (16) -> (2), (3) (17) -> (4) (18) -> (1) (19) -> (1) (20) -> (19) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost (2) l1(x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240) :|: x233 = x240 && x232 = x239 && x230 = x237 && x228 = x235 && x227 = x234 && x231 = x238 && x236 = 1 + x229 && 1 + x229 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l0(i11HAT0:0, i13HAT0:0, i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) -> l0(i11HAT0:0, i13HAT0:0, 1 + i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) :|: i7HAT0:0 < 50 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6, x7) -> l0(x3) ---------------------------------------- (9) Obligation: Rules: l0(i7HAT0:0) -> l0(1 + i7HAT0:0) :|: i7HAT0:0 < 50 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l0(x)] = 49 - x The following rules are decreasing: l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50 The following rules are bounded: l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l5(x28, x29, x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x32 = x39 (2) l6(x184, x185, x186, x187, x188, x189, x190) -> l5(x191, x192, x193, x194, x195, x196, x197) :|: x190 = x197 && x189 = x196 && x186 = x193 && x185 = x192 && x184 = x191 && x188 = x195 && x194 = 1 + x187 && 1 + x187 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l5(x191:0, x192:0, x193:0, x31:0, x195:0, x196:0, x197:0) -> l5(x191:0, x192:0, x193:0, 1 + x31:0, x195:0, x196:0, x197:0) :|: x31:0 < 50 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l5(x1, x2, x3, x4, x5, x6, x7) -> l5(x4) ---------------------------------------- (18) Obligation: Rules: l5(x31:0) -> l5(1 + x31:0) :|: x31:0 < 50 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l5(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l5(x31:0) -> l5(c) :|: c = 1 + x31:0 && x31:0 < 50 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l5 ] = -1*l5_1 The following rules are decreasing: l5(x31:0) -> l5(c) :|: c = 1 + x31:0 && x31:0 < 50 The following rules are bounded: l5(x31:0) -> l5(c) :|: c = 1 + x31:0 && x31:0 < 50 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) l9(x70, x71, x72, x73, x74, x75, x76) -> l10(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x74 = x81 (2) l10(x142, x143, x144, x145, x146, x147, x148) -> l9(x149, x150, x151, x152, x153, x154, x155) :|: x148 = x155 && x147 = x154 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x153 = 1 + x146 && 1 + x146 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: l9(x149:0, x150:0, x151:0, x152:0, x74:0, x154:0, x155:0) -> l9(x149:0, x150:0, x151:0, x152:0, 1 + x74:0, x154:0, x155:0) :|: x74:0 < 50 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l9(x1, x2, x3, x4, x5, x6, x7) -> l9(x5) ---------------------------------------- (27) Obligation: Rules: l9(x74:0) -> l9(1 + x74:0) :|: x74:0 < 50 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l9(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: l9(x74:0) -> l9(c) :|: c = 1 + x74:0 && x74:0 < 50 ---------------------------------------- (30) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l9(x)] = 49 - x The following rules are decreasing: l9(x74:0) -> l9(c) :|: c = 1 + x74:0 && x74:0 < 50 The following rules are bounded: l9(x74:0) -> l9(c) :|: c = 1 + x74:0 && x74:0 < 50 ---------------------------------------- (31) YES ---------------------------------------- (32) Obligation: Termination digraph: Nodes: (1) l12(x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126) :|: x119 = x126 && x118 = x125 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x117 = x124 (2) l11(x99, x100, x101, x102, x103, x104, x105) -> l12(x106, x107, x108, x109, x110, x111, x112) :|: x105 = x112 && x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x103 = x110 && x106 = 1 + x99 && 1 + x99 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (33) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (34) Obligation: Rules: l12(x113:0, x107:0, x108:0, x109:0, x110:0, x111:0, x112:0) -> l12(1 + x113:0, x107:0, x108:0, x109:0, x110:0, x111:0, x112:0) :|: x113:0 < 50 ---------------------------------------- (35) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l12(x1, x2, x3, x4, x5, x6, x7) -> l12(x1) ---------------------------------------- (36) Obligation: Rules: l12(x113:0) -> l12(1 + x113:0) :|: x113:0 < 50 ---------------------------------------- (37) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l12(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (38) Obligation: Rules: l12(x113:0) -> l12(c) :|: c = 1 + x113:0 && x113:0 < 50 ---------------------------------------- (39) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l12 ] = -1*l12_1 The following rules are decreasing: l12(x113:0) -> l12(c) :|: c = 1 + x113:0 && x113:0 < 50 The following rules are bounded: l12(x113:0) -> l12(c) :|: c = 1 + x113:0 && x113:0 < 50 ---------------------------------------- (40) YES ---------------------------------------- (41) Obligation: Termination digraph: Nodes: (1) l8(x156, x157, x158, x159, x160, x161, x162) -> l7(x163, x164, x165, x166, x167, x168, x169) :|: x162 = x169 && x161 = x168 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x160 = x167 (2) l7(x56, x57, x58, x59, x60, x61, x62) -> l8(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x59 = x66 && x58 = x65 && x56 = x63 && x60 = x67 && x64 = 1 + x57 && 1 + x57 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (42) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (43) Obligation: Rules: l8(x156:0, x157:0, x158:0, x159:0, x160:0, x161:0, x162:0) -> l8(x156:0, 1 + x157:0, x158:0, x159:0, x160:0, x161:0, x162:0) :|: x157:0 < 50 ---------------------------------------- (44) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l8(x1, x2, x3, x4, x5, x6, x7) -> l8(x2) ---------------------------------------- (45) Obligation: Rules: l8(x157:0) -> l8(1 + x157:0) :|: x157:0 < 50 ---------------------------------------- (46) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (47) Obligation: Rules: l8(x157:0) -> l8(c) :|: c = 1 + x157:0 && x157:0 < 50 ---------------------------------------- (48) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l8 ] = -1*l8_1 The following rules are decreasing: l8(x157:0) -> l8(c) :|: c = 1 + x157:0 && x157:0 < 50 The following rules are bounded: l8(x157:0) -> l8(c) :|: c = 1 + x157:0 && x157:0 < 50 ---------------------------------------- (49) YES ---------------------------------------- (50) Obligation: Termination digraph: Nodes: (1) l4(x198, x199, x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209, x210, x211) :|: x204 = x211 && x203 = x210 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x202 = x209 (2) l2(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x25 = 1 + x18 && 1 + x18 <= 50 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (51) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (52) Obligation: Rules: l4(x198:0, x199:0, x200:0, x201:0, x202:0, x203:0, x204:0) -> l4(x198:0, x199:0, x200:0, x201:0, 1 + x202:0, x203:0, x204:0) :|: x202:0 < 50 ---------------------------------------- (53) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l4(x1, x2, x3, x4, x5, x6, x7) -> l4(x5) ---------------------------------------- (54) Obligation: Rules: l4(x202:0) -> l4(1 + x202:0) :|: x202:0 < 50 ---------------------------------------- (55) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (56) Obligation: Rules: l4(x202:0) -> l4(c) :|: c = 1 + x202:0 && x202:0 < 50 ---------------------------------------- (57) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l4(x)] = 49 - x The following rules are decreasing: l4(x202:0) -> l4(c) :|: c = 1 + x202:0 && x202:0 < 50 The following rules are bounded: l4(x202:0) -> l4(c) :|: c = 1 + x202:0 && x202:0 < 50 ---------------------------------------- (58) YES